U.S. patent application number 16/485772 was filed with the patent office on 20200213 for denoising of dynamic magnetic resonance spectroscopic imaging using low rank approximations in the kinetic domain.
This patent application is currently assigned to The United States of America, as represented by the Secretary, Department of Health and Human Ser... The applicant listed for this patent is The United States of America, as represented by the Secretary, Department of Health and Human Ser.., The United States of America, as represented by the Secretary, Department of Health and Human Ser... Invention is credited to Jeffrey R. Brender, Murali K. Cherukuri, Shun Kishimoto, Hellmut Merkle, James B. Mitchell, Jeeva P. Munasinghe, Kazutoshi Yamamoto.
Application Number  20200049782 16/485772 
Document ID  / 
Family ID  61283405 
Filed Date  20200213 
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United States Patent
Application 
20200049782 
Kind Code 
A1 
Brender; Jeffrey R. ; et
al. 
February 13, 2020 
DENOISING OF DYNAMIC MAGNETIC RESONANCE SPECTROSCOPIC IMAGING USING
LOW RANK APPROXIMATIONS IN THE KINETIC DOMAIN
Abstract
Kinetic monitoring of in vivo metabolism of labelled tracers is
based on singular value decomposition or Tucker Decomposition of
magnetic resonance spectral image data. Data decomposition is used
in conjunction with rank reduction to improve signaltonoise
ratio. Rank reduction can be applied in one or more of a spectral,
spatial, or temporal dimension. Rank is generally reduced based on
a number of expected analytes/metabolites or fit of measured data
to a model.
Inventors: 
Brender; Jeffrey R.;
(Washington, DC) ; Mitchell; James B.; (Damascus,
MD) ; Yamamoto; Kazutoshi; (North Bethesda, MD)
; Kishimoto; Shun; (Rockville, MD) ; Munasinghe;
Jeeva P.; (Rockville, MD) ; Merkle; Hellmut;
(Bethesda, MD) ; Cherukuri; Murali K.; (Potomac,
MD) 

Applicant: 
Name 
City 
State 
Country 
Type 
The United States of America, as represented by the Secretary,
Department of Health and Human Ser.. 
Bethesda 
MD 
US 


Assignee: 
The United States of America, as
represented by the Secretary, Department of Health and Human
Ser..
Bethesda
MD

Family ID: 
61283405 
Appl. No.: 
16/485772 
Filed: 
February 14, 2018 
PCT Filed: 
February 14, 2018 
PCT NO: 
PCT/US2018/018217 
371 Date: 
August 13, 2019 
Related U.S. Patent Documents






Application
Number 
Filing Date 
Patent Number 


62459008 
Feb 14, 2017 



Current U.S.
Class: 
1/1 
Current CPC
Class: 
G06T 5/002 20130101;
G06T 2207/10076 20130101; G06T 2207/10088 20130101; G01R 33/5608
20130101; G01R 33/485 20130101; G06T 5/10 20130101; G06T 2207/10016
20130101; G06T 5/50 20130101 
International
Class: 
G01R 33/56 20060101
G01R033/56; G01R 33/485 20060101 G01R033/485; G06T 5/00 20060101
G06T005/00 
Claims
1. A method, comprising: in a magnetic resonance imaging system:
acquiring a magnetic resonance imaging signal associated with a
plurality of chemical shifts for at least one voxel at a plurality
of times; arranging the magnetic resonance imaging signal as a data
matrix; obtaining a singular value decomposition of the data
matrix; rank reducing the singular value decomposition; and
obtaining a rankreduced data matrix based on the rankreduced
singular value decomposition.
2. The method of claim 1, further comprising rank reducing the
singular value decomposition based on a number of analytes.
3. The method of claim 2, further comprising injecting a tracer so
that the acquired magnetic resonance imaging signal is associated
with metabolism of the tracer, wherein the analytes include the
tracer or one more metabolic products associated with the
tracer.
4. The method of claim 3, wherein the number of analytes
corresponds to a number of metabolic products.
5. The method of claim 1, wherein the data matrix is an m.times.n
data matrix, m is an integer number of measurement times and n is
an integer number of measured chemical shifts and the singular
value decomposition includes matrices U, .SIGMA., V.sup.T, wherein
U is an m.times.m unitary matrix, .SIGMA. is a diagonal m.times.n
matrix with nonnegative real numbers on the diagonal, and V.sup.T
is an n.times.n orthogonal matrix.
6. The method of claim 5, wherein rank reduction includes setting r
smallest diagonal values of the matrix .SIGMA. to zero to form a
matrix .SIGMA.', wherein the rankreduced data matrix is obtained
as a matrix product U.SIGMA.'V.sup.T.
7. The method of claim 6, wherein the diagonal values of the
matrices .SIGMA. and .SIGMA.' are arranged in rows of the matrices
from largest to smallest.
8. The method of claim 1, wherein the magnetic resonance imaging
signal is associated with the plurality of chemical shifts for the
plurality of voxels at the plurality of times, and for each voxel,
the magnetic resonance imaging signal is arranged as a data matrix,
a singular value decomposition of the data matrix is obtained that
is then rank reduced, and rank reduced data matrices are produced
for each of the plurality of voxels.
9. A magnetic resonance imaging apparatus, comprising: a magnet
situated to establish an axial magnetic field in a specimen; a
plurality of coils situated to apply electromagnetic pulse
sequences to the specimen; a receiver situated to detect
electromagnetic signals from the specimen in response to the
applied electromagnetic pulse sequences; and a controller coupled
to the plurality of coils so as to selectively apply the
electromagnetic pulse sequences and to the receiver to store signal
values associated with the detected signals for a plurality of
specimen voxels, and process the detected signal by rank reducing a
singular value decomposition associated with a matrix
representation associated with at least one of the plurality of
specimen voxels.
10. The magnetic resonance imaging apparatus of claim 9, wherein
the controller processes the detected signals by rank reducing
singular value decompositions associated with matrix
representations associated with each the plurality of specimen
voxels.
11. The magnetic resonance imaging apparatus of claim 10, wherein
the rank reduction of the singular value decomposition is based on
a number of analytes.
12. The magnetic resonance imaging apparatus of claim 11, further
comprising an injector situated to inject a tracer into the
specimen, the injector coupled to the controller so that the
detected electromagnetic signals are associated with metabolism of
the injected tracer, wherein the analytes include the tracer or one
more metabolic products associated with the tracer.
13. The magnetic resonance imaging apparatus of claim 12, wherein
the number of analytes corresponds to a number of metabolic
products.
14. The magnetic resonance imaging apparatus of claim 13, wherein
the matrix representation for each voxel is an m.times.n data
matrix, wherein m is an integer number of measurement times and n
is an integer number of measured chemical shifts and the singular
value decomposition includes matrices U, .SIGMA., V.sup.T, wherein
U is an m.times.m unitary matrix, .SIGMA. is a diagonal m.times.n
matrix with nonnegative real numbers on the diagonal, and V.sup.T
is an n.times.n orthogonal matrix.
15. The magnetic resonance imaging apparatus of claim 14, wherein
rank reduction includes setting r smallest diagonal values of the
matrices .SIGMA. to zero to form matrices .SIGMA.', wherein the
rankreduced data matrices are obtained as matrix products
UE'V.sup.T.
16. The magnetic resonance imaging apparatus of claim 15, wherein
the diagonal values of the matrices .SIGMA. and .SIGMA.' are
arranged in rows of the matrices from largest to smallest.
17. The magnetic resonance imaging apparatus of claim 16, wherein
the magnetic resonance imaging signal is associated with the
plurality of chemical shifts for the plurality of voxels at the
plurality of times, and for each voxel, the magnetic resonance
imaging signal is arranged as a data matrix, a singular value
decomposition of the data matrix is obtained that is then rank
reduced, and rank reduced data matrices are produced for each of
the plurality of voxels.
18. The magnetic resonance imaging apparatus of claim 17, further
comprising displaying an image using the rank reduced data
matrices.
19. A method, comprising: in a magnetic resonance imaging system:
acquiring a magnetic resonance imaging signal associated with a
plurality of chemical shifts for a plurality of voxels at a
plurality of times; arranging the magnetic resonance imaging signal
as a data tensor; obtaining a Tucker decomposition of the data
tensor; and spatially or temporally rank reducing the Tucker
decomposition to produce spatially or temporally denoised voxel
data for each of the plurality of voxels.
20. The method of claim 19, wherein the rank reduction is temporal
rank reduction.
21. The method of claim 20, further comprising injecting a tracer
so that the acquired magnetic resonance imaging signal is
associated with metabolism of the tracer, wherein the analytes
include the tracer or one more metabolic products associated with
the tracer.
22. The method of claim 21, wherein the rank reduction is spectral
rank reduction based on a number of metabolic products.
23. The method of claim 19, wherein the rank reduction is based on
differences between measured data and truncated model data.
24. The method of claim 19, wherein Tucker Decomposition includes a
core tensor and a plurality of orthogonal factor matrices.
25. The method of claim 1, wherein the data tensor includes data
matrices for each of the plurality of voxels, wherein the data
matrices are m.times.n data matrices, wherein m is an integer
number of measurement times and n is an integer number of measured
chemical shifts.
26. A method, comprising: in a magnetic resonance imaging system:
acquiring magnetic resonance imaging signals for a plurality of
voxels as a function of at least two parameters; arranging the
magnetic resonance imaging signals as a data tensor; obtaining a
Tucker decomposition of the data tensor; and rank reducing the
Tucker decomposition to produce processed voxel data for each of
the plurality of voxels based on at least one of the two
parameters; and
27. The method of claim 26, wherein the processed voxel data is
represented as data matrices for each of the voxels.
28. The method of claim 27, wherein the rank reducing the Tucker
decomposition to produce processed voxel data for each of the
plurality of voxels based both of the at least two parameters.
29. The method of claim 28, wherein the processed voxel data is
denoised voxel data.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit of U.S. Provisional
Application No. 62/459,008, filed Feb. 14, 2017, which is herein
incorporated by reference in its entirety.
FIELD
[0002] The disclosure pertains to methods and apparatus that can
proved improved signal to noise ratios in spectroscopic magnetic
resonance imaging.
BACKGROUND
[0003] The breakdown of exogenous metabolic tracers can be tracked
noninvasively and precisely by .sup.13C MRI, which is an advantage
over static techniques which measure the equilibrium state which
may stem from many processes. Further progress remains limited by
poor sensitivity stemming from three fundamental reasons. First,
the amount of exogenous tracer that can be injected is limited to
only small amounts due to the difficulty of preparing highly
concentrated solutions and injecting large volumes as well as the
potential toxicity of many compounds. Even in the most favorable
situations, the effective concentration of exogenous metabolic
tracers is far less than the water signal detected in conventional
MRI. As an additional complication, .sup.13C has a low gyromagnetic
ratio which translates into a relative sensitivity compared to that
of .sup.1H (the nuclei normally used in MRI) for an equivalent
number of nuclei. Finally, metabolic processes are inherently
transient. The usual approach to overcoming low sensitivity is to
simply acquire the signal for longer and average the scans. Often,
however it is the rate of turnover of a metabolite which is of
interest rather than the absolute concentration. The rate of
turnover is a direct link to the activity of metabolic enzymes that
are potential targets in cancer and other pathologies. Long signal
averaging makes recovery of the rate impossible.
[0004] To enable kinetic monitoring of in vivo metabolism, dynamic
nuclear polarization (DNP) was developed to make rapid dynamic
imaging of .sup.13C labeled tracers possible. Dynamic nuclear
polarization makes use of the fact that unpaired electrons in a
paramagnetic molecule can be aligned to a magnetic field to a much
greater extent than the atomic nuclei with spins detected by MRI.
Dynamic nuclear polarization transfers this alignment from unpaired
electrons back to the atomic nuclei for detection. Since the signal
in MRI is proportional to the degree of alignment, this
polarization transfer results in a very large increase in the MRI
signal, up to 10,000 times in favorable circumstances.
Unfortunately, the polarization transfer only occurs efficiently at
temperatures near absolute zero and decays quickly once at room
temperature. Dissolution DNP (dDNP) has been successful in
utilizing a portion of the polarization to conduct metabolic MRI by
rapidly dissolving the frozen tracer at .about.1 K to room
temperature with a significant quantity of polarization still
available for detection. DNP has been critical in many scientific
advances. Perhaps most impressively, DNP has been used to prove
drug target engagement by imaging tumor glycolysis in a mouse
model.
[0005] Despite dDNP's impressive technical achievements, it has
significant disadvantages, especially in a clinical setting:
hyperpolarization is performed at temperatures near absolute zero,
requiring an apparatus that is expensive in both capital and
operating costs. Hyperpolarization is transient, limiting analysis
of metabolic cycles to products produced immediately after the
injection of the injected metabolite. Hyperpolarization is limited
to a small set of molecules whose relaxation time is slow enough
that the polarization is not lost before the kinetics can be
determined. Many key metabolites, such as glucose, have short
relaxation times and are difficult or impossible to image with DNP
for this reason. This disclosure is directed to methods and
apparatus that can address these limitations by enabling kinetic
monitoring of in vivo metabolism of labelled tracers without
DNP.
SUMMARY
[0006] Methods comprise acquiring a magnetic resonance imaging
signal associated with a plurality of chemical shifts for at least
one voxel at a plurality of times and arranging the magnetic
resonance imaging signal as a data matrix. A singular value
decomposition of the data matrix is obtained and rank reduced, and
a rankreduced data matrix is determined based on the rankreduced
singular value decomposition. In some examples, the rank reducing
is based on a number of analytes. In further examples, a tracer is
injected so that the acquired magnetic resonance imaging signal is
associated with metabolism of the tracer, wherein the analytes
include the tracer or one more metabolic products associated with
the tracer. In one example, the number of analytes corresponds to a
number of metabolic products.
[0007] According to a representative embodiment, the data matrix is
an m.times.n data matrix, m is an integer number of measurement
times and n is an integer number of measured chemical shifts and
the singular value decomposition includes matrices U, .SIGMA.,
V.sup.T, wherein U is an m.times.m unitary matrix, .SIGMA. is a
diagonal m.times.n matrix with nonnegative real numbers on the
diagonal, and V.sup.T is an n.times.n orthogonal matrix. Typically,
rank reduction includes setting r smallest diagonal values of the
matrix .SIGMA. to zero to form a matrix .SIGMA.', wherein the
rankreduced data matrix is obtained as a matrix product
U.SIGMA.'V.sup.T. In some cases, the diagonal values of the
matrices .SIGMA. and .SIGMA.' are arranged in rows of the matrices
from largest to smallest. In still further examples, the magnetic
resonance imaging signal is associated with the plurality of
chemical shifts for the plurality of voxels at the plurality of
times, and for each voxel, the magnetic resonance imaging signal is
arranged as a data matrix, a singular value decomposition of the
data matrix is obtained that is then rank reduced, and rank reduced
data matrices are produced for each of the plurality of voxels.
[0008] Magnetic resonance imaging apparatus comprise a magnet
situated to establish an axial magnetic field in a specimen and a
plurality of coils situated to apply electromagnetic pulse
sequences to the specimen. A receiver is situated to detect
electromagnetic signals from the specimen in response to the
applied electromagnetic pulse sequences. A controller is coupled to
the plurality of coils so as to selectively apply the
electromagnetic pulse sequences and to the receiver to store signal
values associated with the detected signals for a plurality of
specimen voxels, and process the detected signals by rank reducing
a singular value decomposition associated with a matrix
representation associated with at least one of the plurality of
specimen voxels. In a representative example, the controller
processes the detected signals by rank reducing singular value
decompositions associated with matrix representations associated
with each the plurality of specimen voxels and the rank reductions
of the singular value decompositions are based on a number of
analytes. In a further example, an injector is situated to inject a
tracer into the specimen, the injector coupled to the controller so
that the detected electromagnetic signals are associated with
metabolism of the injected tracer, wherein the analytes include the
tracer or one more metabolic products associated with the tracer.
Typically, they number of analytes corresponds to a number of
metabolic products. According to typical examples, the matrix
representation for each voxel is an m.times.n data matrix, wherein
m is an integer number of measurement times and n is an integer
number of measured chemical shifts and the singular value
decomposition includes matrices U, .SIGMA., V.sup.T, wherein U is
an m.times.m unitary matrix, .SIGMA. is a diagonal m.times.n matrix
with nonnegative real numbers on the diagonal, and V.sup.T is an
n.times.n orthogonal matrix. In some embodiments, rank reduction
includes setting r smallest diagonal values of the matrices .SIGMA.
to zero to form matrices .SIGMA.', wherein the rankreduced data
matrices are obtained as matrix products U.SIGMA.'V.sup.T. In one
example, the magnetic resonance imaging signal is associated with
the plurality of chemical shifts for the plurality of voxels at the
plurality of times, and for each voxel, the magnetic resonance
imaging signal is arranged as a data matrix, a singular value
decomposition of the data matrix is obtained that is then rank
reduced, and rank reduced data matrices are produced for each of
the plurality of voxels. According to other examples, an image is
displayed using the rank reduced data matrices.
[0009] Methods comprise acquiring a magnetic resonance imaging
signal associated with a plurality of chemical shifts for a
plurality of voxels at a plurality of times and arranging the
acquired magnetic resonance imaging signals as a data tensor. A
Tucker decomposition of the data tensor and spatially or temporally
rank reduced to produce spatially or temporally denoised voxel data
for each of the plurality of voxels. According to some examples, a
tracer is injected so that the acquired magnetic resonance imaging
signal is associated with metabolism of the tracer, wherein the
analytes include the tracer or one more metabolic products
associated with the tracer. In some examples, the rank reduction is
spectral rank reduction based on a number of metabolic
products.
[0010] Other methods acquiring magnetic resonance imaging signals
for a plurality of voxels as a function of at least two parameters
and arranging the magnetic resonance imaging signals as a data
tensor. A Tucker decomposition of the data tensor is obtained and
rank reduced with respect to produce processed voxel data for each
of the plurality of voxels based on at least one of the two
parameters. In some cases, rank reduction is based on both of the
at least two parameters.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] FIG. 1 illustrates a representative magnetic resonance
imaging (MRI) system that includes singular value decomposition
(SVD) and Tucker decomposition signal processing.
[0012] FIG. 2A illustrates a representative method of acquiring MRI
spectral data and processing the acquired data using a singular
value decomposition (SVD) with rank reduction.
[0013] FIG. 2B illustrates a representative arrangement MRI
spectral data as a function of time for a single voxel.
[0014] FIGS. 3A3B show raw data from a pyruvic acid DNP
measurement with good signal to noise ratio associated with
conversion of pyruvate (chemical shift of 173 ppm) to lactate
(chemical shift of 185 ppm).
[0015] FIGS. 4A4B show the data of FIGS. 3A3B after detection and
quantification using SVD and rank reduction to 5. In the raw data
(FIGS. 3A3B), the bicarbonate peak at 162.5 ppm is not detectable
even though the overall signal to noise is high. Using the low rank
(i.e., rank reduced) approximation, a kinetic profile of
bicarbonate metabolism can be obtained as shown in FIGS. 4A4B,
allowing discrimination between drug treatment and control. No
prior information about the bicarbonate signal or kinetics was
used.
[0016] FIG. 5A shows additional noisy data, and FIG. 5B shows an
average of the data of FIG. 5A over 5 seconds.
[0017] FIG. 6A shows the signal of FIG. 5A processed with SVD and
rank reduction. Peaks corresponding to the two main metabolic
products, pyruvate and lactate, are clearly visible, as well as two
minor peaks corresponding to side products.
[0018] FIG. 6B is a graph of MRI signal amplitude as a function of
chemical shift showing a 9 fold SNR enhancement obtained with SVD
decomposition and rank reduction.
[0019] FIG. 7 shows signal to noise ratio (SNR) improvement using
SVD with rank reduction.
[0020] FIGS. 8A8D show images associated with glucose metabolism
illustrating denoising based on rank reduced SVDs.
[0021] FIGS. 9A and 9B show signals associated with an individual
voxels without and with denoising; respectively.
[0022] FIG. 9C shows denoised signals for each of 64 voxels.
[0023] FIG. 9D shows noisy data for one voxel.
[0024] FIGS. 10A10B show spectral image data from a hyperpolarized
lactate image processed without noise reduction.
[0025] FIGS. 11A11B show the image data of FIGS. 10A10B processed
with noise reduction via Tucker Decomposition with time domain rank
reduction from 40 to 4.
[0026] FIGS. 12A12B show image data of FIGS. 10A10B processed
with Tucker Decomposition, time domain rank reduction from 40 to 4,
and spatial dimension rank reduction from 32 to 16.
[0027] FIGS. 13A13B show data corresponding to the processed data
of FIGS. 12A12B, further processed in a slice dimension.
[0028] FIG. 14 is a schematic diagram of a representative data
acquisition and processing system.
[0029] FIG. 15 illustrates a representative method of image data
processing using a Tucker Decomposition with rank reduction.
[0030] FIG. 16 illustrates multianalyte data obtained with SVD
denoising.
[0031] FIG. 17 is a representative Scree plot obtained from FIG. 5A
indicating a number of eigenvalues to select in rank reduction.
[0032] FIG. 18 illustrates a signal processing method based on a
Tucker Decomposition.
[0033] FIG. 19 is a representative difference graph for use in
selecting a number of components in a Tucker Decomposition.
[0034] FIGS. 20A and 20C illustrate Tucker Decomposition.
[0035] FIG. 20B illustrates truncation (rank reduction) of a Tucker
Decomposition.
DETAILED DESCRIPTION
[0036] As used in this application and in the claims, the singular
forms "a," "an," and "the" include the plural forms unless the
context clearly dictates otherwise. Additionally, the term
"includes" means "comprises." Further, the term "coupled" does not
exclude the presence of intermediate elements between the coupled
items.
[0037] The systems, apparatus, and methods described herein should
not be construed as limiting in any way. Instead, the present
disclosure is directed toward all novel and nonobvious features
and aspects of the various disclosed embodiments, alone and in
various combinations and subcombinations with one another. The
disclosed systems, methods, and apparatus are not limited to any
specific aspect or feature or combinations thereof, nor do the
disclosed systems, methods, and apparatus require that any one or
more specific advantages be present or problems be solved. Any
theories of operation are to facilitate explanation, but the
disclosed systems, methods, and apparatus are not limited to such
theories of operation.
[0038] Although the operations of some of the disclosed methods are
described in a particular, sequential order for convenient
presentation, it should be understood that this manner of
description encompasses rearrangement, unless a particular ordering
is required by specific language set forth below. For example,
operations described sequentially may in some cases be rearranged
or performed concurrently. Moreover, for the sake of simplicity,
the attached figures may not show the various ways in which the
disclosed systems, methods, and apparatus can be used in
conjunction with other systems, methods, and apparatus.
Additionally, the description sometimes uses terms like "produce"
and "provide" to describe the disclosed methods. These terms are
highlevel abstractions of the actual operations that are
performed. The actual operations that correspond to these terms
will vary depending on the particular implementation and are
readily discernible by one of ordinary skill in the art.
[0039] In some examples, values, procedures, or apparatus' are
referred to as "lowest", "best", "minimum," or the like. It will be
appreciated that such descriptions are intended to indicate that a
selection among many used functional alternatives can be made, and
such selections need not be better, smaller, or otherwise
preferable to other selections.
[0040] Disclosed herein are signal processing methods and magnetic
resonance imaging (MRI) apparatus that permit the recovery of
dynamic information from a noisy signal obtained by, for example, a
magnetic resonance spectroscopic imaging (MRSI) or other magnetic
resonance imaging (MRI) procedure. Typical MRI procedures include
single pulse or Chemical Shift Imaging (CSI) pulse sequences with
proton decoupling, Echo Planar Spectroscopic Imaging or Spectrally
Encoded Imaging sequences. In one representative example provided
for illustration, the disclosed approaches are used in metabolite
imaging or in single voxel measurements in response to intravenous
injection of a .sup.13C labelled tracer in the tail vein of a mouse
with leg xenograft. An infusion pump (or other pump) may be used to
scale up the procedure for human clinical applications, and
injection synchronized with metabolite measurement sequences. This
example is provided for convenient explanation, but the disclosed
methods and apparatus can use different magnetic resonance pulse
sequences and be used with other tracers, and can be generally
applied to determine time evolutions of material constituents, and
are not limited to use in estimating metabolic rates.
[0041] MR measurements of chemical shifts are generally made at a
plurality of times; while chemical shifts can be measured for a
continuous range of chemical shift values, typically chemical shift
values are processed as a series of discrete values. While it can
be convenient to select uniformly spaced chemical shifts and
measurement times, this is generally unnecessary and arbitrary
spacings can be used. Finer increments can be used for ranges of
interest or for values associated with larger rates of change. For
convenience, uniform time and chemical shift increments are used in
some examples. Data matrices and tensors are written in bold (M) or
as italics (M); elements of such matrices and tensors are written
in italics with subscripts that identify particular elements
(M.sub.ij). A transpose of a matrix M is written as M.sup.T.
Elimination of certain terms in matrix or tensor representations is
generally referred to herein as rank reduction or truncation. While
it is generally preferred to eliminate terms in rank reduction or
truncation (by, for example, setting values to 0), terms can be
assigned small values instead, generally small enough to avoid
significantly decreasing signal to noise ratios available with term
elimination.
[0042] MR measurements can be obtained using an MRI apparatus 100
as illustrated in FIG. 1. The apparatus 100 includes a
controller/interface 102 that can be configured to apply selected
magnetic fields such as constant or pulsed field gradients to a
specimen. An axial magnet controller 104 is in communication with
an axial magnet 106 that is generally configured to produce a
substantially constant magnetic field B.sub.0. A gradient
controller 108 is configured to apply a constant or timevarying
gradient magnetic field in a selected direction or in a set of
directions using magnet coils 110112 to produce respective
magnetic field gradient vector components G.sub.x, G.sub.y, G.sub.z
or combinations thereof. An RF generator 114 is configured to
deliver one or more RF pulses to a specimen using a transmitter
coil 115. An RF receiver 116 is in communication with a receiver
coil 118 and is configured to detect or measure net magnetization
of spins. Slice selection gradients can be applied with the same
hardware used to apply the diffusion gradients. The gradient
controller 108 can be configured to produce pulses or other
gradient fields along one or more axes. By selection of such
gradients and other applied pulses, various imaging and/or
measurement sequences can be applied. Sequences that produce
variations that are functions of analyte or metabolite
concentration are preferred. In typical examples, data containing
chemical shifts as functions of time is acquired.
[0043] For imaging, specimens are divided into volume elements
(voxels) and MR signals at different times are acquired. In typical
examples, amplitude as a function of chemical shift at each of a
plurality of times is obtained for some or all voxels of interest.
A computer 124 or other processing system such as a personal
computer, a workstation, a personal digital assistant, laptop
computer, smart phone, or a networked computer can be provided for
acquisition, control and/or analysis of specimen data. The computer
124 generally includes a hard disk, a removable storage medium such
as a floppy disk or CDROM, and other memory such as random access
memory (RAM). Computerexecutable instructions for data acquisition
or control can be provided on a floppy disk or other storage
medium, or delivered to the computer 124 via a local area network,
the Internet, or other network. Signal acquisition, instrument
control, and signal analysis can be performed with distributed
processing. For example, signal acquisition and signal analysis can
be performed at different locations. The computer 124 can also be
configured to improve signaltonoise using singular value
decomposition with rank reduction or Tucker decomposition using
suitable computerexecutable instructions stored in a memory 126.
Signal evaluation can be performed remotely from signal acquisition
by communicating stored data to a remote processor. Typically,
various field are applied to and detected from a subject 130 in
association with application (generally injection) of a tracer by
an injector 132.
[0044] In typical examples, MRSI sequences are used, resulting in a
data grid with a spectrum in each point (voxel) representing
metabolites present in that spatial area. In dynamic MRSI, the
image is repeatedly acquired after injection to give a time profile
of in vivo metabolism. Under normal conditions without DNP, this
signal is too noisy too use. The denoising approaches disclosed
herein are typically based on the assumption that only a few
metabolites are present, and in some cases, that the associated
signals vary smoothly as a function of time. More formally, the
number of independent peaks in the spectrum is assumed to be much
less than the number of data points (sparsity) and the second order
finite difference between time points is small. The first
assumption is essentially never violateda typical MRSI spectrum
has 256 or more points but only a dozen or so metabolites can be
detected, and then only under very favorable conditions. The second
assumption concerning smooth variation in time can be implemented
by an adjustable parameter as described below to match the expected
time scale, but while this assumption may be useful, it is
generally not necessary. While the methods and apparatus are
referred to as "denoising," noise need not be completely
removed.
SVD with Rank Reduction
[0045] Processing starts by forming a matrix S for each voxel with
the spectrum from each time point forming a row in the matrix.
Noise reduction is achieved by reducing the rank of S. The rank of
S is the vector space spanned by the columns (spectra) of S. More
intuitively, the rank of S is the number of independent spectra
existing in the dynamic course (or alternatively, the number of
independent kinetic components, which is a mathematically
equivalent). A rank of 1 implies the signal can be completely
described as a single spectrum which decays with a single time
profile. The spectra and time profile can be any arbitrary shape,
but are uniform. In this case, no individual peak in the spectra
decays at a different rate than any other. A signal matrix with a
rank of 2 can be described as a linear combination of two spectra,
with two distinct time profiles. A rank 3 matrix is a linear
combination of three spectra with three distinct time profiles and
so on. From this definition, the rank of the matrix S is
approximately equal to the number of metabolites in the sample.
However, a rank reduction as discussed below result in a rank that
is greater than or less than a number of metabolites, and
generally, rank reduction can be selected based on a suitable
output (e.g., noise removal).
[0046] In practice, the signal is perturbed by noise. Since noise
is random and not correlated in frequency or time, the actual rank
r of the measured matrix is close to the number of spectral points
(256 or more). However, the actual signal matrix without noise is
low rank. A low rank approximation (matrix M) of matrix S is to be
determined. S is first decomposed into a product of three smaller
matrices:
S.sub.noisy=U.SIGMA.V.sup.T,
wherein [U,.SIGMA.,V] is the singular value decomposition of the
measured data matrix S.sub.noisy, and denoised low rank
approximation M.sub.low rank can be found.
S noisy .about. M low rank = [ U , .SIGMA. , V ] = arg min U ,
.SIGMA. , V { S noisy  U .SIGMA. V T 2 } . ##EQU00001##
For the original, noisy matrix, the solution for the diagonal
entries of .SIGMA. to be equal to the square roots of the
eigenvalues of S.sup.TS, the columns of V to be equal to the eigen
vectors of S.sup.TS, and the columns of U to be equal to the
eigenvectors of SS.sup.T. This is known as a singular value
decomposition. The rank r is equal the number of nonzero
eigenvalues. To get a low rank approximation, the lowest rn
diagonal entries in .SIGMA. are set to zero. The rank r can be
estimated to be slightly above the number of metabolites present
(usually known a priori) or can be estimated from a distribution of
eigenvalues using the properties of random matrices. The result is
guaranteed by the EckartYoungMirsky theorem to be the best low
rank approximation to the original signal matrix S. Smoothness can
be enforced by imposing a penalty term on the equation above:
M low rank = [ U , .SIGMA. , V ] = arg min U , .SIGMA. , V { S
noisy  U .SIGMA. V T 2 + a u B u U + a v B v V } ##EQU00002##
where B.sub.u and B.sub.v are second order finite difference
operators. This altered form of the equation penalizes rapid,
unphysiological time changes in the signal and is controlled by the
parameters a.sub.u and a.sub.v. Small values of these parameters
allow rapid changes, large values favor smoothness. The actual
value may be altered for the particular experiment. For
demonstration purposes, a.sub.u can be set to 0 to allow high
resolution in the spectral domain.
[0047] Referring to FIG. 2A, a method 200 of measuring or imaging
metabolites in vivo using SVD and rank reduction includes injecting
a tracer at 202. As used herein, a tracer is any composition that
is metabolized in vivo or stimulates metabolism of a compound. At
204, MR spectra are acquired for an image array at a plurality of
times. The image array typically includes data for a plurality of
volume elements ("voxels"), but single point (i.e., single voxel)
measurements can also be made. At 206, for each voxel of interest
(or all voxels), a matrix M of spectral data as a function of time
is formed. Such a matrix is illustrated in FIG. 2B. Each row
includes signal values S.sub.ij associated with time i, wherein
i=1, . . . , m and chemical shifts f.sub.j, wherein j=1, . . . , n.
In other examples, rows can be associated with fixed chemical
shifts and each column associated with a different time. Typically,
SVD is arranged so that column vectors span a data space, and with
such an arrangement, assigning each row to a different time
produces SVDs in which rank reduction results in temporally
denoised data. By contrast, using row vectors produces SVDs in
which rank reduction results is spatially denoised data. In FIG.
2B, only a single matrix M is shown, but such an arrangement is
generally formed for each voxel of interest, or all voxels.
[0048] At 208, SVDs of some or all m.times.n data matrices M are
obtained to find SVD arrays U, .SIGMA., V.sup.T for each M, wherein
U is an m.times.m unitary matrix, .SIGMA. is a diagonal m.times.n
matrix with nonnegative real numbers (for example, eigenvalues of
the matrix products M.sup.TM) on the diagonal, and V.sup.T is an
n.times.n unitary matrix (and typically an orthogonal matrix for
data values represented as real numbers). SVD can use other data
arrangements by interchanging rows and columns, if desired. At 210,
the diagonal matrices .SIGMA. for each (or some) voxels are rank
reduced to corresponding matrices .SIGMA.' by setting unselected
diagonal elements to zero. Typically, a number of nonzero diagonal
entries is retained that corresponds to a number of metabolites
produced in response to the tracer injection, and only the largest
diagonal values are kept. Generally rows of .SIGMA. and .SIGMA.'
are arranged so that a largest value appears in the first row, the
next largest in the second row, etc. At 212, a denoised signal
matrix M' for each voxel is then obtained as a product
M'=U.SIGMA.'V.sup.T. At 214, denoised data can be displayed as one
or more images, a sequence of images, or as numerical data, as
preferred. If desired, several different rank reductions can be
used to determine a preferred rank reduction (i.e., a preferred
matrix .SIGMA.').
[0049] Second order differences can be used as well, if desired.
Forward, central, or reverse second order differences can be used.
For example, a central second order difference of a function f(x)
defined as
f '' ( x ) = f ( x + .DELTA. )  2 f ( x ) + f ( x  .DELTA. )
.DELTA. 2 ##EQU00003##
can be used, wherein .DELTA. denotes an interval between data
values (in this case, either time or spatial intervals, depending
on whether temporal or spatial smoothing is to be applied). In this
case, denoised data is obtained from:
M low rank = [ U , .SIGMA. , V ] = arg min U , .SIGMA. , V { S
noisy  U .SIGMA. V T 2 + a u B u U + a v B v V } ##EQU00004##
as discussed above. Various values of a.sub.u and a.sub.v can be
used, and typical values are 0.01, 0.02, 0.05, 0.10, 0.20, 0.50, or
1.00 or intermediate values.
Selecting the Number of Ranks in SVD
[0050] There are several ways to select the number of ranks when
using SVD. The first is to use a priori knowledge. For example, as
noted above, if at most n metabolites are possible, the rank can be
set to a number near n. This number can be set slightly higher, to
capture low abundance metabolites that might be near the noise
level, or slightly lower, to as the kinetics of the metabolites are
linked and therefore not linearly independent. Thus, for n
metabolites, the rank can be set to n or n.+.1, 2, 3. Other values
can be used as well, values in these ranges are generally
sufficient.
[0051] Another method is based on a Scree plot. A scree plot
displays eigenvalues associated with each component in descending
order. An ideal pattern in a scree plot is a steep curve, followed
by a bend and then a flat or horizontal line. The rank is set to
the point of the bend, as the flat line represents noise. FIG. 17
illustrates a representative Scree plot, indicating that a rank of
3 should be selected.
[0052] Scree plots are ultimately based on the statistics of the
distribution of the eigenvalues of random matrices. It has been
shown (see Gavish and Donoho, "The Optimal Hard Threshold for
Singular Values is 4/ 3," IEEE Trans. Inform. Theory 60:50405053
(2014), which is incorporated herein by reference) that the optimal
hard threshold level .tau.* for an m by n matrix is:
.tau. * = .lamda. * ( .beta. ) n .sigma. ##EQU00005## .lamda. * (
.beta. ) = def 2 ( .beta. + 1 ) + 8 .beta. ( .beta. + 1 ) + .beta.
2 + 14 .beta. + 1 . ##EQU00005.2##
.beta. is an aspect factor
.beta. = m n ##EQU00006##
and .sigma. is a standard deviation of the noise level, which can
be guessed by examining a region of the spectrum where no
metabolites are known to be present. Every singular value below
.tau.* is set to zero.
Tucker Decomposition with Rank Reduction
[0053] As discussed above, SVDbased approaches process data voxel
by voxel using data matrices for each voxel. A data matrix M having
rows and columns corresponding to selected times and chemical
shifts is defined, and denoised using SVD. For imaging,
simultaneous spatial and temporal denoising can be provided using
the Tucker Decomposition on all voxels simultaneously. The Tucker
Decomposition decomposes data into a set of matrices that
correspond to images that describe the evolution of the signal in
both space and time. Similar to SVD, a low rank approximation is
made to find a linear combination of images that suppresses noise
while retaining as much of the signal as possible. The ability to
denoise in spatial dimensions allows the method to be used on a
series of medical images of any type as long as there is some
pattern connecting the images. If desired, only selected rows or
columns or other selected data is processed, and the associated
data tensor can be of lower rank that that of a data tensor
representing a complete data set. With image and spectral data
(i.e., chemical shifts) for all points, voxel data is represented
as a fourth order tensor X which includes values for the chemical
shifts and measurement times for all voxels of an image. For
convenient explanation, only selected tensor nomenclature and
procedures are discussed herein. A summary can be found in, for
example, Kolda and Bader, "Tensor Decompositions and Applications,"
SIAM Review 51:455500 (2009), which is incorporated herein by
reference.
[0054] For images containing K by L voxels, each voxel associated
with n chemical shifts at m times, wherein K, L, M, N are all
positive integers, data tenors of rank 3 or 4 can be used. For
example, representations as fourth order data tensor X.sup.KLMN or
as a third order tensor X.sup.KLMN can be used. As with SVD, a
factorization is required. For X represented by an I by J by K
element matrix, a Tucker factorization is of the form:
X=GABC=.SIGMA..sub.p=1.sup.p.SIGMA..sub.q=1.sup.Q.SIGMA..sub.r=1.sup.Rg.
sub.pqra.sub.p.smallcircle.b.sub.q.smallcircle.c.sub.r,
wherein G can be referred to as a core tensor, A, B, C are I by P,
J by Q, and K by R factor matrices, respectively, and a.sub.p,
b.sub.q, c.sub.r refer to columns of the corresponding factor
matrices, and the symbol .smallcircle. refers to a vector outer
product. The Tucker decomposition can also be expressed element
wise as:
x.sub.ijk=.SIGMA..sub.p=1.sup.p.SIGMA..sub.q=1.sup.Q.SIGMA..sub.r=1.sup.
Rg.sub.pqra.sub.ipb.sub.jqc.sub.kr,
wherein x.sub.ijk, a.sub.ip, b.sub.jq, and c.sub.kr are elements of
G, A, B, and C. A, B, C are orthogonal matrices and the core tensor
G is an orthogonal tensor. G can be arranged so that subtensors
G.sub.i.sub.n are ordered so that
.parallel.G.sub.i.sub.n.sub.=1.parallel..gtoreq..parallel.G.sub.i.sub.n.s
ub.=2.parallel..gtoreq. . . .
.gtoreq..parallel.G.sub.i.sub.n.sub.=I.sub.n.parallel..
[0055] For images containing K by L voxels and S slices, each voxel
is associated with N free induction decay points acquired at M time
points, and wherein K, L, M, N, S are all positive integers, data
tensors of rank 4 or 5 can be used. For example, representations as
fourth order data tensor X.sup.KLMN or as a fifth order tensor
X.sup.KLMNS can be used. As with SVD, a factorization is required.
For a third order tensor X represented by an I by J by K element
matrix, a Tucker factorization is of the form:
X=GABC=.SIGMA..sub.p=1.sup.p.SIGMA..sub.q=1.sup.Q.SIGMA..sub.r=1.sup.Rg.
sub.pqra.sub.p.smallcircle.b.sub.q.smallcircle.c.sub.r,
wherein G can be referred to as a core tensor, A, B, C are I by P,
J by Q, and K by R factor matrices, respectively, and a.sub.p,
b.sub.q, c.sub.r refer to columns of the corresponding factor
matrices, and the symbol .smallcircle. refers to a vector outer
product. Tensor representations of higher order can be used, and
decomposed in the same way.
[0056] The Tucker decomposition can also be expressed element wise
as:
x ijk = p = 1 P q = 1 Q r = 1 R g pqr a ip b jq c kr
##EQU00007##
wherein g.sub.pqr, a.sub.ip, b.sub.jq, and c.sub.kr are elements of
G, A, B, and C. A, B, C are orthogonal matrices and the core tensor
G is an orthogonal tensor. G can be arranged so that subtensors
G.sub.i.sub.n are ordered so that
.parallel.G.sub.i.sub.n.sub.=1.parallel..gtoreq..parallel.G.sub.i.sub.n.s
ub.=2.parallel..gtoreq. . . .
.gtoreq..parallel.G.sub.i.sub.n.sub.=I.sub.n.parallel..
[0057] Rank reduction in Tucker Decomposition tends to be more
difficult than in SVD. In SVD, there is essentially one degree of
freedom, the number of eigenvalues to keep. The Tucker
Decomposition has additional flexibility in that compression
(truncation of the core tensor G) can be carried out in one or more
directions and not in others. For example, the rank in the spectral
dimension can be reduced, without rank reduction in image
dimensions as discussed below with reference to FIGS. 10A13B.
Generally, truncation can be selected for some or all data
dimensions, as preferred.
[0058] In one example, a procedure referred to herein as a
"DifFitcriterion" can be used, as described in Timmerman and
Kiers, "Threemode principal components analysis: Choosing the
numbers of components and sensitivity to local optima," Brit J Math
Stat Psy. 53:116 (2000), which is incorporated herein by
reference. A representative method 1800 is illustrated in FIG. 18.
At 1802, a tracer is injected and data is acquired and at 1804, a
full Tucker Decomposition is obtained. At 1806, a deviance d is
determined as a sum of squares difference between model of the
Tucker Decomposition (i.e., a truncated or rank reduced model) and
actual data, for some or all possible truncations. At 1808, within
models with a common number of components, a model with smallest
deviance is selected. A number of components in then selected at
1810 based on deviance as function of a sum of the number of
components using, for example, a graph such as shown in FIG. 19.
The reduced number of components is then used to provide denoised
data at 1812 which can be displayed at 1814 as an image or as
metabolic rates at one or more locations.
[0059] A representative example is illustrated in FIG. 19. Points
C, D, E and F are not optimal as another compression (i.e.,
truncation) with the same total number of components has a lower
deviance. B is selected as it is associated with a larger
improvement in deviance. Note the similarity to the Scree plot of
FIG. 17. Note that the points noted as C, D, and B all have the
same number of components, and provide the same noise reduction,
but the particular components associated with point B are closest
to the measured data.
[0060] Both Tucker Decomposition and multidimensional SVD (usually
referred to as higher order SVD or higher order principal component
analysis) decompose an experimental Ndimensional tensor into a
core tensor and a set of orthogonal matrices. Some characteristics
of higher order SVD are provided in Bergqvist and Larsson, "The
HigherOrder Singular Value Decomposition: Theory and an
Application," IEEE Signal Proc. Mag. 27:151154 (2010), which is
incorporated herein by reference. The difference between higher
order SVD and the Tucker Decomposition is in the nature of the core
tensor. In higher order SVD, the slices of the matrices in the core
tensor are mutually orthogonal, while in the Tucker Decomposition
they are not guaranteed to be so. Multidimensional SVD can
therefore be seen as a special case of the more general Tucker
Decomposition. Note that no analog of the EckartYoung theorem
exists for tensors, so the Tucker Decomposition to the data may be
a better approximation than multidimensional SVD.
[0061] PARAFAC (aka CANDECOMP and Canonical Polyadic decomposition)
are also special cases of the Tucker decomposition, wherein G is
assumed to be superdiagonal (all nondiagonal entries zero). This
is tantamount to making the assumption of complete separability
(see below). As used herein, Tucker Decomposition and its variants
include Multidimensional SVD, PARAFAC (aka CANDECOMP and Canonical
Polyadic decomposition).
[0062] FIG. 20A and FIG. 20C illustrate Tucker Decomposition of a
three way array. FIG. 20C illustrates how such a Tucker
Decomposition can be truncated. With the Tucker Decomposition of
FIG. 20C, truncation can be accomplished by omitted any of the
terms in the series expansion, or setting the associated values to
zero or small numbers. For example, as shown in FIG. 20B, any of
the terms in the expansion can be reduced to zero.
[0063] Both SVD and Ndimensional Tucker Decomposition rely on
sparsitythe fact that in this specific example, following the
metabolism of an injected tracer, the data can be faithfully
reconstructed using an approximation constructed from only a few
vectors. The Ndimensional Tucker Decomposition also relies on the
related concept of separability. Mathematically, strict
separability means that a matrix can be expressed as linear
combination of the vector outer products:
M=.sigma..sub.1u.sub.1v.sub.1.sup.T+.sigma..sub.2u.sub.2v.sub.2.sup.T
. . . .sigma..sub.nu.sub.nv.sub.n.sup.T
In more common language, separability means the data in each
dimension is independent of the others. The independence of the
chemical shift of the metabolites on position in the image ensures
that problem is ensures that this part of the problem is almost
completely separable. For the most part, the kinetics are partially
separable as wellthe kinetics in each voxel falls into only a few
different classes. Sparsity and separability may not hold for data
from other imaging modalities or even other MRI applications. For
instance, an fMRI signal from diffusion fMRI is likely to show a
smaller degree of separability, as the signal will vary strongly
throughout the image.
[0064] Voxelbyvoxel SVD is a fundamentally local procedure while
the Tucker Decomposition is a type of global fitting. For example,
if 5 components are selected for the spectra in both voxelbyvoxel
SVD and Tucker Decomposition, in voxelbyvoxel SVD there can be 5
different components for each voxel, while in the Tucker
Decomposition the 5 components are same throughout an image.
[0065] With reference to FIG. 15, a method 1500 include injecting a
tracer at 1502 and acquiring spectral data for an image array at a
plurality of times at 1504. The acquired data is represented as a
tensor at 1506, and processed using a Tucker Decomposition at 1508.
At 1510, the Tucker Decomposition is rank reduced to reduce noise
based on a number of metabolites or by trying several different
reductions. In the tensor representation, rank reduction can be
performed with respect to chemical shifts (i.e., spectral data),
but can also be performed with respect to temporal and spatial
dimensions, and in a slice direction as selected at 1510. As
discussed above with respect to SVD, the representative data
arrangement is associated with denoising in a spectral dimension,
but could be applied by interchanging rows and columns (or a
corresponding change in SVD computations) to denoise temporally.
With a tensor representation, denoising can be associated with one
or more of spectra, acquisition time, and/or spatial coordinates
(x, y, z). At 1512, denoised data is obtained, and at 1514, the
denoised data is used to generate a displayed image, metabolic
rates, or other features associated with the acquired data.
Example 1. Single Point Measurements
[0066] The disclosed approaches were applied to 41 mice to follow
the metabolism of .sup.13C tracer on a single pulse (not spatially
resolved) MRI experiment. 300 .mu.L of a 98 mM solution of
hyperpolarized 1.sup.13C pyruvic acid was injected into the tail
vein of nude mice bearing tumor xenografts in the left leg.
Pyruvate is metabolized to HCO.sub.3 in normal cells and lactate in
cancerous ones exhibiting the Warburg effect. The dissolution
process involved in making hyperpolarized pyruvic acid is not
always perfect, resulting in spectra of varying quality. In ideal
circumstances, the signal is strong enough after DNP that the main
pyruvate (173 ppm) to lactate (185 ppm) conversion can be detected
without additional signal processing (see FIG. 3A). In others, the
signal is barely detectable (see FIG. 5A). Since the biochemistry
is the same in each of these cases, the peak positions and
approximate kinetics in the noisy data are known a priori. FIG. 3B
shows bicarbonate intensity as a function of time with vitamin C
pre and posttreatment as obtained from raw data; FIGS. 4A4B
shows results obtained with SVD and rank reduction. A significant
improvement in signaltonoise ratio is apparent. Bicarbonate
intensity as a function of time is not apparent in FIG. 3B while
clearly shown in FIG. 4B. FIG. 5A shows raw data for a different
single pulse measurement and FIG. 5B shows data averaged over 5
scans. SVD processed, rank reduced data are shown in FIGS. 6A6B,
exhibiting significant improvement in signal to noise ratio.
[0067] FIG. 7 shows SNR improvement using rank reduction (r=3) in
41 .sup.13C pyruvate tracer single pulse dynamic nuclear
polarization experiments such as illustrated in FIGS. 4A4B and
6A6B. SNR is defined as intensity of a maximum signal divided by
the standard deviation in a 40 point region of the spectrum where
signal is known to be not present.
Example 2. Imaging
[0068] FIGS. 8A8D show images associated with glucose metabolism
illustrating denoising based on rank reduced SVDs. 50 mg of
uniformly .sup.13C labeled glucose was injected into the tail vein
of a nude mouse and an 8.times.8 image of the tumor bearing mouse
leg was acquired every 12 seconds for 90 minutes (450 images in
total). The light outlines in FIGS. 8A8D represent the tumor
boundary. FIG. 8A is an anatomical image, and FIGS. 8B8D are
contour maps of lactate, lipid, and glucose localization,
respectively, midway through the scans (i.e., at scan 225) based on
denoised data. Signals associated with an individual voxel are
shown in FIGS. 9A and 9B without and with denoising; respectively.
FIG. 9C shows denoised signals for each of the 64 voxels, and FIG.
9D shows noisy data for one voxel.
Example 3. Imaging with Tucker Decomposition
[0069] Data associated with one slice from a hyperpolarized lactate
image set is illustrated in FIGS. 10A13B. Spectral image data
processed without noise reduction is shown in FIGS. 10A10B,
processed with noise reduction via Tucker Decomposition with time
domain rank reduction from 40 to 4 (FIGS. 11A11B), processed with
Tucker Decomposition, time domain rank reduction from 40 to 4, and
spatial dimension rank reduction from 32 to 16 (FIGS. 12A12B), and
further processed in a slice dimension (FIGS. 13A13B). Data was
acquired using a spectral selective pulse sequence that yields a
series of images for each metabolite, one image for each time
point.
Example 4. Detection of Multiple Products
[0070] FIG. 16 illustrates detection of multiple products using SVD
and rank reduction. Five distinct metabolic products associated
with strong and weak signals are detected and quantified
(2pyruvate (strong) 207.8 ppm, Glutumate 184 ppm, 1pyruvate
doublet (weak) 172.1 and 174 ppm, 2pyruvate hydrate (weak) 96.4
ppm, and AcylCarnitine 175 ppm). A time series of such data
permits characterization of metabolic rates.
Example 5. Data Acquisition and Control
[0071] FIG. 14 and the following discussion are intended to provide
a brief, general description of an exemplary computing/data
acquisition environment in which the disclosed technology may be
implemented. Although not required, the disclosed technology is
described in the general context of computer executable
instructions, such as program modules, being executed by a personal
computer (PC), a mobile computing device, tablet computer, or other
computational and/or control device. Generally, program modules
include routines, programs, objects, components, data structures,
etc., that perform particular tasks or implement particular
abstract data types. Moreover, the disclosed technology may be
implemented with other computer system configurations, including
hand held devices, multiprocessor systems, microprocessorbased or
programmable consumer electronics, network PCs, minicomputers,
mainframe computers, and the like. The disclosed technology may
also be practiced in distributed computing environments where tasks
are performed by remote processing devices that are linked through
a communications network. In a distributed computing environment,
program modules may be located in both local and remote memory
storage devices.
[0072] With reference to FIG. 14, an exemplary system for
implementing the disclosed technology includes a general purpose
computing device in the form of an exemplary conventional PC 1400,
including one or more processing units 1402, a system memory 1404,
and a system bus 1406 that couples various system components
including the system memory 1404 to the one or more processing
units 1402. The system bus 1406 may be any of several types of bus
structures including a memory bus or memory controller, a
peripheral bus, and a local bus using any of a variety of bus
architectures. The exemplary system memory 1404 includes read only
memory (ROM) 1408 and random access memory (RAM) 1410. A basic
input/output system (BIOS) 1412, containing the basic routines that
help with the transfer of information between elements within the
PC 1400, is stored in ROM 1408.
[0073] The exemplary PC 140 further includes one or more storage
devices 1430 such as a hard disk drive for reading from and writing
to a hard disk, a magnetic disk drive for reading from or writing
to a removable magnetic disk, an optical disk drive for reading
from or writing to a removable optical disk (such as a CDROM or
other optical media), and a solid state drive. Such storage devices
can be connected to the system bus 1406 by a hard disk drive
interface, a magnetic disk drive interface, an optical drive
interface, or a solid state drive interface, respectively. The
drives and their associated computer readable media provide
nonvolatile storage of computerreadable instructions, data
structures, program modules, and other data for the PC 1400. Other
types of computerreadable media which can store data that is
accessible by a PC, such as magnetic cassettes, flash memory cards,
digital video disks, CDs, DVDs, RAMs, ROMs, and the like, may also
be used in the exemplary operating environment.
[0074] A number of program modules may be stored in the storage
devices 1430 including an operating system, one or more application
programs, other program modules, and program data. A user may enter
commands and information into the PC 1400 through one or more input
devices 1440 such as a keyboard and a pointing device such as a
mouse. Other input devices may include a digital camera,
microphone, joystick, game pad, satellite dish, scanner, or the
like. These and other input devices are often connected to the one
or more processing units 1402 through a serial port interface that
is coupled to the system bus 1406, but may be connected by other
interfaces such as a parallel port, game port, or universal serial
bus (USB). A monitor 1446 or other type of display device is also
connected to the system bus 1406 via an interface, such as a video
adapter. Other peripheral output devices, such as speakers and
printers (not shown), may be included.
[0075] The PC 1400 may operate in a networked environment using
logical connections to one or more remote computers, such as a
remote computer 1460. In some examples, one or more network or
communication connections 1450 are included. The remote computer
1460 may be another PC, a server, a router, a network PC, or a peer
device or other common network node, and typically includes many or
all of the elements described above relative to the PC 1400,
although only a memory storage device 1462 has been illustrated in
FIG. 14. The personal computer 1400 and/or the remote computer 1460
can be connected to a logical a local area network (LAN) and a wide
area network (WAN). Such networking environments are commonplace in
offices, enterprise wide computer networks, intranets, and the
Internet.
[0076] When used in a LAN networking environment, the PC 1400 is
connected to the LAN through a network interface. When used in a
WAN networking environment, the PC 1400 typically includes a modem
or other means for establishing communications over the WAN, such
as the Internet. In a networked environment, program modules
depicted relative to the personal computer 1400, or portions
thereof, may be stored in the remote memory storage device or other
locations on the LAN or WAN. The network connections shown are
exemplary, and other means of establishing a communications link
between the computers may be used.
[0077] The memory 1404 generally includes computerexecutable
instructions for performing SVDs and Tucker Decompositions in
respective memory portions 1460, 1462, and procedures for rank
reduction and selection of suitable rank are stored in a memory
portion 1461. Computerexecutable instructions for data acquisition
and control are stored in a memory portion 1470 for use with a
tracer injector 1472 (such as a syringe pump) and a magnetic
resonance imaging system. Acquired and processed data (e.g., rank
reduced data) can be displayed using computerexecutable
instructions stored at memory portion 1471. As noted above, data
acquisition, processing, and instrument control can be provided at
an MRI system, or distribution at one or more processing devices
using a LAN or WAN.
[0078] The examples above are described with respect to a sequence
of MR images as a function of time in order to determine metabolite
rates. However, the disclosed approaches can be used with any of a
variety of data types to improve signaltonoise ratio, and provide
smoothing/noise reduction with respect to one or more data
parameters.
[0079] Having described and illustrated the technology, it will be
recognized that the illustrated embodiments can be modified in
arrangement and detail. For instance, elements of the illustrated
embodiment shown in software may be implemented in hardware and
viceversa. Also, the technologies from any example can be combined
with the technologies described in any one or more of the other
examples. It should be recognized that the illustrated embodiments
are examples and should not be taken as a limitation on the scope
of the disclosure. For instance, various components of systems and
tools described herein may be combined in function and use. We
therefore claim all subject matter that comes within the scope and
spirit of the appended claims. Alternatives specifically addressed
in these sections are merely exemplary and do not constitute all
possible alternatives to the embodiments described herein.
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