U.S. patent application number 15/231039 was filed with the patent office on 2018-02-08 for method and system for reconstructing 3-dimensional images from spatially and temporally overlapping x-rays.
This patent application is currently assigned to ADAPTIX LTD.. The applicant listed for this patent is ADAPTIX LTD.. Invention is credited to Paul Betteridge, Raphael Hauser, Maria Klodt, Gil Travish.
Application Number | 20180038807 15/231039 |
Document ID | / |
Family ID | 59683601 |
Filed Date | 2018-02-08 |
United States Patent
Application |
20180038807 |
Kind Code |
A1 |
Hauser; Raphael ; et
al. |
February 8, 2018 |
METHOD AND SYSTEM FOR RECONSTRUCTING 3-DIMENSIONAL IMAGES FROM
SPATIALLY AND TEMPORALLY OVERLAPPING X-RAYS
Abstract
An x-ray imaging system and method for reconstructing
three-dimensional images of a region of interest from spatially and
temporally overlapping x-rays using novel reconstruction
techniques.
Inventors: |
Hauser; Raphael; (Oxford,
GB) ; Klodt; Maria; (Oxford, GB) ; Travish;
Gil; (Oxford, GB) ; Betteridge; Paul; (Witney,
GB) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
ADAPTIX LTD. |
Oxfordshire |
|
GB |
|
|
Assignee: |
ADAPTIX LTD.
Oxfordshire
GB
|
Family ID: |
59683601 |
Appl. No.: |
15/231039 |
Filed: |
August 8, 2016 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G06T 7/174 20170101;
A61B 6/469 20130101; A61B 6/589 20130101; A61B 6/4007 20130101;
G01N 2223/401 20130101; A61B 6/5241 20130101; G06T 2200/08
20130101; G01N 23/10 20130101; A61B 6/02 20130101; A61B 6/588
20130101; G06T 7/001 20130101; A61B 6/4233 20130101; A61B 6/585
20130101; A61B 6/587 20130101; H05G 1/38 20130101; A61B 6/547
20130101; A61B 6/4405 20130101; A61B 6/5205 20130101; A61B 6/4085
20130101; G01N 2223/20 20130101; G06T 2211/424 20130101; G01N 23/04
20130101; A61B 6/4452 20130101; A61B 6/582 20130101 |
International
Class: |
G01N 23/04 20060101
G01N023/04 |
Claims
1. An x-ray imaging system, comprising: a detector capable of
generating a signal in response to x-rays incident upon the
detector, wherein the signal indicates the intensity of the x-rays
incident upon a pixel of the detector, a plurality of x-ray
sources, wherein at least two of the plurality of x-ray sources are
capable of emitting x-rays such that said x-rays pass through a
region of interest (ROI) and spatially and temporally overlap at
the pixel of the detector; and a processing unit capable of
receiving the signal indicating the intensity of x-rays incident
upon the pixel of the detector and generating an estimate of the
intensity attributable to each of the two or more x-rays
overlapping at the pixel of the detector.
2. The system of claim 1, wherein the processing unit is further
capable of generating a three-dimensional representation of the ROI
using one or more estimates of the intensity attributable to each
of the two or more x-rays overlapping at the pixel of the
detector.
3. The system of claim 3, further comprising a display operably
coupled to the processing unit, wherein the display is capable of
displaying one or more two-dimensional views of the
three-dimensional representation of the ROI.
4. The system of claim 1, wherein the plurality of x-ray sources
comprises two or more emitter elements of a distributed source
array.
5. The system of claim 1, wherein the processing unit is further
capable of voxelizing the ROI into a plurality of
three-dimensional, non-overlapping voxels; estimating an
attenuation coefficient attributable to each said voxel, and
re-voxelizing the ROI into a plurality of three-dimensional,
non-overlapping voxels based on the estimated attenuation
coefficients attributable to each said voxel.
6. The system of claim 5, wherein the processing unit is further
capable of repeating said re-voxelization until a stopping
criterion is met.
7. The system of claim 6, wherein the processing unit is further
capable of estimating said attenuation coefficient attributable to
each voxel using a compressed sensing algorithm.
8. The system of claim 7, wherein the compressed sensing algorithm
comprises at least one of an optimization and linearization
algorithm, forward-backward splitting algorithm, or combination
thereof, applied to the estimated attenuation coefficients.
9. The system of claim 1, wherein the plurality of x-ray sources
and the detector each include one or more sensors capable of
determining the relative positions of the x-ray sources and the
detector.
10. The system of claim 1, further comprising a controller for
operating the x-ray imaging system, wherein the controller is
capable of activating a subset of the plurality of x-ray
sources.
11. A method of reconstructing an x-ray image comprising;
activating two or more sources to emit x-rays such that said x-rays
are delivered to a region of interest (ROI) and spatially and
temporally overlap at a pixel of the detector; detecting the
intensity of the overlapping x-rays incident upon the pixel of the
detector; and generating an estimate of the intensity attributable
to each of the two or more x-rays overlapping at the pixel of the
detector using the aggregate intensity of the overlapping x-rays
incident upon the pixel of the detector.
12. The method of claim 11, further comprising generating a
three-dimensional representation of the ROI utilizing one or more
estimates of the intensity attributable to each of the two or more
x-rays overlapping at the pixel of the detector.
13. The method of claim 12, further comprising displaying one or
more two-dimensional views of the three-dimensional representation
of the ROI.
14. The method of claim 10, further comprising voxelizing the ROI
into a plurality of three-dimensional, non-overlapping voxels;
estimating an attenuation coefficient attributable to each said
voxel; and re-voxelizing the ROI into a plurality of
three-dimensional, non-overlapping voxels based on the estimated
attenuation coefficients attributable to each said voxel.
15. The method of claim 14, further repeating said re-voxelization
until a stopping criterion is met.
16. The method of claim 15, further comprising using a compressed
sensing algorithm to estimate said attenuation coefficient
attributable to each voxel.
17. The method of claim 16, wherein said compressed sensing
algorithm comprises at least one of an optimization and
linearization algorithm, forward-backward splitting algorithm, or
combination thereof.
18. The method of claim 11, further comprising performing a
calibration comprising the steps of activating each source to emit
x-rays one at a time; and activating sets of sources to emit x-rays
such that said x-rays overlap at the pixel of the detector.
19. The method of claim 11, further comprising selecting the two or
more sources to activate to emit x-rays so as to optimize at least
one of image acquisition speed, image quality, and ROI coverage.
Description
FIELD OF INVENTION
[0001] The present disclosure generally relates to x-ray imaging,
and more particularly to a method and system for reconstructing
three-dimensional images from spatially and temporally overlapping
x-rays.
BACKGROUND
[0002] Three-dimensional image reconstruction from x-ray
projections is an important image reconstruction problem with
applications in, among other things, medical imaging, industrial
inspection, and airport security. Traditional x-ray imaging is most
commonly based on planar radiography. This approach utilizes a
single, point-like x-ray source made up of a set of vacuum-tubes
capable of generating a single cone or fan beam of x-rays over a
wide range of energies and currents. However, the imaging
geometries possible with such point-like x-ray sources are limited,
in particular because the x-ray source must be placed a significant
distance from the object (or person) to be imaged to ensure the
x-ray covers a sufficient area.
[0003] In traditional x-ray systems, the large distance between the
source and the object--usually called the Source to Object Distance
("SOD") or stand-off distance--requires a lot of power. To provide
this power, traditional x-ray systems use large, expensive, and
heavy (in the tens of kilograms) power-supplies that often require
cooling, further adding to the bulk and weight of the system.
[0004] In addition, planar radiography as the name suggests is only
capable of generating two-dimensional images. X-ray tomography, or
imaging by sections, may be employed to generate three-dimensional
images. Typically, x-ray tomography involves taking multiple images
of a stationary object or person from a variety of directions, and
then using these multiple, two-dimensional images to reconstruct a
three-dimensional image. Usually, a mechanical gantry is needed to
move the single x-ray source (vacuum tubes) along a sequence of
locations, which adds to the size and expense of the x-ray system.
Also, because the images are taken sequentially, this setup
requires a longer overall image capture time than would otherwise
be desirable.
[0005] To minimize image capture time, multiple vacuum-tube sources
may be placed at fixed or stationary locations around an object or
person, with each source being selectively activated. This
configuration allows for a shorter overall period of image capture,
however, this system is not practical due to the cost of the
sources and its relative bulk. In addition, because of the
relatively large size of each vacuum-tube source, such a system can
accommodate only a limited number of viewing angles. In other
words, because of the size of the sources an object or person can
be imaged from only a limited number of directions, which impedes
the ability to generate high-resolution three-dimensional
images.
[0006] An alternative to these approaches is to produce multiple
x-ray sources from a single, distributed source in an emitter
array. Field Enhanced Emitter ("FEE") arrays, (sometimes referred
to as Field Emitter Arrays), such as Spindt arrays, may be used in
x-ray tubes and serve as an advanced cathode. At high voltages, an
FEE array of moderate field enhancement tips (e.g., sharp
molybdenum tips or cones) may operate as emitters for x-ray
production, where the individual tips (or sets of tips) can be
selected to emit x-rays and thus act as an x-ray source. Similarly,
cathodes produced from carbon nanotubes (CNTs) may allow for
control of electron emission at low voltages, thus allowing
individual CNTs to be selected to emit x-rays. In all cases, such
FEE arrays allow for multiple sources of x-rays to be generated
from a distributed source.
[0007] Distributed source arrays (also known as emitter arrays)
allow objects to be imaged from different viewing angles by
selectively activating the various individual emitters (e.g., the
molybdenum tips, CNTs, etc.) Thus, distributed source arrays
eliminate the need to move a heavy, vacuum tube-based source around
an object or person, or the need to employ multiple such vacuum
tube-based sources. For example, in the case of a flat-panel
emitter array, the size of the arrays can be large and allow for
significant displacement from one source (e.g., a first emitter
element) on one corner of the array to a second source (e.g., a
second emitter element) on the opposite corner. By activating the
sources, or more particularly the emitter elements, positioned
throughout the array, images may be simultaneously obtained from
different viewing angles, which minimizes image capture time as
compared to single-source systems, while also allowing an object to
be imaged from sufficient angles so as to allow reconstruction of a
three-dimensional image.
[0008] In this way, distributed source arrays allow for tomography
and tomosynthesis (high-resolution, limited-angle tomography). But
they also impose severe geometric constraints on system design.
Because each source or emitter in the array produces its own x-ray
cone, to ensure complete coverage of an object--or a region of
interest ("ROI") within an object--there must be a certain amount
of spatial overlap of the cones. However, such spatial overlap, and
in particular x-ray overlap at a detector, may cause the images
formed using such arrays to include multiple images or shadows due
to the illumination of features of the object from multiple
angles.
[0009] Conventional reconstruction methods cannot adequately
separate spatiotemporal x-ray overlap. Therefore, in conventional
systems without spatio-temporal overlap of x-rays SOD has to be
kept in a narrow range to achieve the required image resolution.
This correlation can be expressed as.
d max M 4 - M .ltoreq. .delta. .ltoreq. 4 d max 4 - M ,
##EQU00001##
where M is a design parameter that regulates the achievable image
resolution, taking values between 1 and 4 (e.g., M=2), d.sub.max is
the maximal thickness of an object that can be imaged to the
specified resolution with the given system design, and .delta. is
the SOD. The larger the value of M, the higher the achievable image
resolution, but the more constrained the SOD Since pitch distance
and collimation angle of a given source are a function of d.sub.max
and M, such restrictions severely limit source and detector
geometries. Among other things, this restriction makes it necessary
to produce different emitter array panel geometries to image
different body parts.
[0010] Therefore, using conventional approaches for image
reconstruction, an x-ray imaging system has to be designed such
that no x-rays simultaneously overlap at a detector. This
limitation is attributable to, among other things, the fact that
measurements from overlapping x-rays are not linear, and
conventional reconstruction methods, such as linear compressed
sensing, are unable to properly handle non-linear constraints, such
as those produced by x-ray overlap. Because of these limitations
conventional approaches to x-ray image reconstruction teach away
from systems designed with spatiotemporal x-ray overlap.
[0011] Prior methods of addressing overlap have included the use of
anti-scatter grids, which serve to limit the acceptance angle of
x-rays to the detector, and thus prevent overlap. But anti-scatter
grids also limit the information available for a given exposure by
limiting the area covered by the x-rays. Alternatively, by
selectively activating emitters, it is possible to fully cover an
object without having x-ray overlap at the detector. However,
avoiding spatial overlap with a distributed source array means
either each source has to cover the entire area of interest, which
increases the power requirements, or that the image takes longer to
acquire as only certain non-overlapping emitter elements can be
activated at the same time. The latter is of particular concern,
especially in the case of children and injured patients, both of
which may have a tendency to move during scans.
[0012] Accordingly, there is a need in the art for an x-ray imaging
system and method that allow for more flexible imaging geometries,
including greater flexibility in the selection of the distance
between sources (or emitter elements) and the detector and size of
the collimation angle(s). There is also a need for a system and
method capable of generating accurate three-dimensional images,
while also minimizing the time needed for image capture as compared
to conventional systems. Moreover, there is a need for a system and
method capable of adequately handling spatiotemporally overlapping
x-rays.
SUMMARY
[0013] Embodiments of the present disclosure are directed to
systems, methods, and techniques for reconstructing
three-dimensional images from spatially and temporally overlapping
x-rays. In an aspect of the present disclosure, spatiotemporal
overlap of x-rays is intentionally created at a detector in a
controlled manner. Novel reconstruction techniques are then used to
reconstruct accurate three-dimensional images of an imaged object,
person, or ROI using, at least in part, measurements attributable
to the overlapping x-rays.
[0014] Embodiments of the present disclosure may include an x-ray
imaging system that includes a detector capable of generating
electronic signals in response to x-rays. The signals may vary
depending on the intensity of the x-rays at the detector, thus
providing a measure of the attenuation (e.g., absorption or
weakening of x-ray intensity) caused by an object or person. The
x-ray imaging system may also include multiple sources of x-ray
radiation. At least two of these sources may emit x-rays such that
the x-rays pass through an object or person, and then spatially and
temporally overlap at a pixel of the detector. In one aspect, the
x-ray sources may comprise discrete emitter elements in a
distributed source array. The x-ray imaging system may also include
a processing unit that receives the signals from the detector,
including signals attributable to overlapping x-rays, and is
capable of employing novel reconstruction techniques to estimate
the intensity attributable to each of the x-rays overlapping at the
detector and generate an accurate three-dimensional reconstruction
of a ROI of the imaged object or person. As understood by one of
skill in the art, a pixel represents a discrete element or sensor
within a detector which is capable of producing a signal that may
be distinguished from other elements of the detector.
[0015] Embodiments of the present disclosure may also include a
method for reconstructing a three-dimensional image from spatially
and temporally overlapping x-rays. In accordance with such a
method, two or more sources of x-ray radiation may be made to emit
x-rays such that the x-rays are delivered through an object or
person, or more specifically an ROI, and spatiotemporally overlap
at a detector. The intensity of the overlapping x-rays incident
upon the detector may then be detected, thus providing a measure of
the attenuation caused by the object or person. The intensity
attributable to each of the x-rays overlapping at the detector may
then be estimated, and a three-dimensional image of a ROI of the
imaged object or person generated. Novel reconstruction techniques
may be employed to estimates the intensity of each overlapping
x-ray.
[0016] Various objects, features, embodiments, and advantages of
the present invention(s) will become more apparent from the
following detailed description of embodiments of the present
disclosure, along with the accompanying drawings. The present
Summary, while providing an introduction to various embodiments, is
not intended to limit the scope of the subject matter to be
claimed. Further advantages of the present invention(s) will be
apparent to a person of skill in the art in view of the foregoing
disclosure.
BRIEF DESCRIPTION OF THE DRAWINGS
[0017] FIG. 1 is a schematic, cross-sectional representation of an
example of an x-ray imaging system in accordance with aspects of
the present disclosure.
[0018] FIG. 2 is a schematic plan-view representation of an emitter
array in accordance with aspects of the present disclosure.
[0019] FIG. 3 is a flow chart illustrating an exemplary method of
reconstructing an x-ray image in accordance with aspects of the
present disclosure.
DETAILED DESCRIPTION
[0020] FIG. 1 shows an example of an x-ray imaging system 100 in
accordance with aspects of the present disclosure. As illustrated,
x-ray imaging system 100 may include two or more sources 110 of
x-ray radiation, such as two or more emitter elements of a
distributed source array.
[0021] A collimator (not shown) may be positioned adjacent to each
source 110, and may be used to define the size and shape of each
x-ray radiation beam 130 emitted by each source 110. In typical
use, x-ray beam 130 may be conical in shape, thus forming a
conelet. Alternatively, source 110 may emit various other shapes of
x-ray beam 130.
[0022] Referring to FIG. 2, in certain embodiments of the present
disclosure, sources 110 may form part of a distributed source
array, such as an FEE. In one example, distributed source array 200
may include a plurality of separate and discrete emitter elements,
wherein each emitter element is a source 110 of x-ray radiation. As
illustrated, each source 110 may be arranged with its center at
node points of a grid of equilateral triangles, thus each source
110 may be equally spaced (vertically and horizontally) throughout
emitter array 200. Alternatively, sources 110 may be arranged in
various other configurations (e.g., spaced farther apart on the
x-axis than on the y-axis, composed of various grid patterns, such
as squares, rectangles, or hexagons, or distributed randomly or
pseudo-randomly).
[0023] X-ray imaging system 100 may also include one or more
detectors 140, which may include elements that produce an
electrical signal that represents the intensity of impinging x-ray
beams 130 on detector 140, and hence provide a measure of the
attenuation (e.g., absorption or weakening of x-ray intensity)
attributable to object 160. As discussed herein, because these
electrical signals provide a measure of attenuation attributable to
the scanned portions of object 160, they may be processed to
generate three-dimensional reconstructions of a ROI of object 160.
In an embodiment of the present disclosure, detector 140 may be
formed from a plurality of detector pixels (or sensing diodes),
each of which may be capable of producing an electrical signal that
represents the intensity of impinging x-ray beam 130.
[0024] As is illustrated in FIG. 1, x-ray imaging system 100 may be
configured so that, when in use, at least one exposure or scan of a
ROI involves the spatiotemporal overlap at detector 140 of x-ray
beams 130 emitted from at least two different sources 110. This
configuration may be achieved in various ways. For example,
controller 180 may be operably coupled to sources 110, and thus
used to selectively activate a subset of sources 110. In one
aspect, controller 180 may be configured to control the power
provided to each individual source 110. In this way, controller 180
may be able to provide emission point activation, making it
possible to activate a subset of sources 110 to emit x-ray beams
130, and also making it possible to select overlapping sources
110.
[0025] X-ray imaging system 100 may also include processing unit
150. Processing unit 150 may comprise one or more processors,
computers, CPUs, or similar devices, and may be configured to
process image information, such as the intensity of x-ray beams 130
incident on detector 140. For example, processing unit 150 may be
operably coupled to detector 140, so as to receive data from
detector 140, such as electronic signals corresponding to the
intensity of impinging x-ray beams 130 on detector 140.
[0026] Processing unit 150 may also be configured to implement one
or more process(es) (as described herein) to deconvolve the jointly
measured attenuation attributable to the spatiotemporal overlap of
x-ray beams 130 at detector 140. By knowing the relative locations
of sources 110 and detector 140, such as the positions of each
source 110 activated in a given exposure and the portion of the
detector 140 (e.g., the detector pixel) from which an electronic
signal representing the intensity of the x-ray beams 130 is
received, processing unit 150 may convert the electronic signals
received from detector 140 into a three-dimensional data array
representing the attenuation at various points throughout the
ROI.
[0027] In an aspect of the present disclosure, processing unit 150
may subdivide object 160, or more specifically the ROI of object
160, into three-dimensional, non-overlapping volume elements, or
voxels. Processing unit 150 may then model each voxel as being
occupied by part of object 160, and as being made up of homogenous
material whose attenuation coefficient (which characterizes how
easily x-rays pass through the material within the voxel)
represents a single data point. Processing unit 150 may then
collect all such data points in an array called a vector.
[0028] Processing unit 150 may compare the modeled vector to the
electronic signals received from detector 140 corresponding to the
intensity of the impinging x-ray beams 130 on detector 140. In this
way, processing unit 150 may compare the modeled attenuation of
each voxel to the detected attenuation attributable to each voxel.
Processing unit 150 may then utilize reconstruction algorithms
based on compressed sensing methods to iteratively refine the
modeled vector based on the actual measurements, and in turn, may
use the results of such iterations to reconstruct a
three-dimensional model of the ROI.
[0029] Referring to FIG. 1, x-ray imaging system 100 may also
include memory 170. Memory 170 may be part of processing unit 150,
or alternatively, may be operably coupled to processing unit 150.
Memory 170 may store, for later processing by processing unit 150,
data acquired during one or more x-ray scans. For example, in
typical use, an object or patient may be exposed to a short
sequence of x-ray exposures (1-50 exposures, for example, 5-10
exposures), and data from these exposures, such as the attenuation
measured during each exposure, may be stored in memory 170, and
subsequently processed or used to refine image reconstruction as
discussed herein.
[0030] As noted, in order to determine the attenuation attributable
to the portions of an ROI of object 160, the relative position
(distance and orientation) of each source 110 and detector 140, or
detector pixel, must be known. In the case of fixed installations,
the required measurements may be made at the time of installation,
and verified during routine maintenance. Alternatively, the
relative position may be determined in any number of other ways,
including via mechanical measurement.
[0031] In an aspect of the present disclosure, x-ray imaging system
100 may include one or more sensors 190 capable of determining the
relative position(s) of sources 110 to detector 140, and/or vice
versa. Sensors 190 may be any type of proximity sensor that may be
used to determine the distance between each source 110 and detector
140. This distance may be used to select a suitable subset of
sources 110 to use when imaging object 160. For example, an
operator or radiographer may utilize controller 180 to select a ROI
of object 160. In an aspect of the present disclosure, a range of
SODs may then be pre-calculated (e.g., by processing unit 150) and
provided to the operator based on the fixed pitch and collimation
angle(s) of the manufactured sources 110 and the ROI to be imaged.
The operator or radiographer may place detector 140 within the
specified range of SODs. Sensors 190 may then measure the distance
between sources 110 and detector 140 (or alternatively between
source 110 and object 160), and a subset of sources 110, including
two or more sources 110 that will spatiotemporally overlap at one
or more pixels of detector 140, may be calculated (e.g., by
processing unit 150) that optimize image acquisition speed, image
quality, and/or ROI coverage. For purposes of the present
disclosure, spatial and temporal overlap (or spatiotemporal
overlap) may include the case where two or more X-rays are incident
on a pixel of a detector within a sampling time interval.
[0032] X-ray imaging system 100 may also include a visualization
workstation and display 120. Visualization workstation and display
120 may be operably coupled to processing unit 150, and may be used
to observe reconstructed three-dimensional images of an ROI of
object 160. For example, visualization workstation 120 may perform
calculations to transform the three-dimensional data array
determined by processing unit 150 into one or more internal views
(e.g., two-dimensional slices) of the ROI that may be displayed to
an operator or radiographer.
[0033] FIG. 3 is a flow chart illustrating an exemplary method of
reconstructing an x-ray image in accordance with aspects of the
present disclosure. The method may begin at step 501, wherein a
calibration procedure, such as an air calibration (or air shots),
may be performed as a means to offset air attenuation, spatial
variation of each source 110, detector 140 sensitivity variation,
and to compensate for faulty pixels of detector 140, and so forth.
Calibration data may further be used to understand, and if
necessary compensate for, non-linearity in detector 140 response;
conventional digital detectors are linear (e.g., twice the input
flux produces twice the signal output), but when the angles of
incidence are different this may no longer be true.
[0034] In an aspect of the present disclosure, a two-step
calibration may be performed whereby each source 110 may be
activated one at a time, and then subsequently sources 110 may be
activated in groups or sets wherein at least two x-ray beams 130
spatiotemporally overlap at detector 140. While such a two-step
calibration cannot account for all possible potential variations,
it does allow for the offset of primary response issues in a given
context.
[0035] This calibration may be performed as the first step of the
method illustrated in FIG. 3 (e.g., prior to step 502).
Alternatively, such calibrations need not be performed immediately
prior to the implementation of the method illustrated in FIG. 3,
and may instead be performed on a periodic basis (e.g., daily or
weekly) to capture performance variations (e.g., due to
temperature) or decay (e.g., due to aging, x-ray exposure or
physical damage). The calibration results may be used to adjust the
reconstruction algorithms described herein, and the data from such
calibrations may be stored in memory 170 and later processed by
processing unit 150.
[0036] With reference to FIG. 3, assuming the calibration results
are within acceptable limits and any configuration changes or
revised measurements have been recorded, one or more data
acquisition procedures may be performed (steps 502-505). As an
initial matter, a three-dimensional ROI of object (or person) 160
may be selected at step 502. This selection may be performed by an
operator or radiographer using controller 180, or alternatively, in
any number of ways, as would be understood by a person of skill in
the art in view of the present disclosure. Based on the selected
ROI, pitch and collimation angle(s) of sources 110, and the SOD, a
group or subset of sources 110 to be used for imaging the ROI may
be selected at step 503. Geometric calculations that take ROI
geometry, pitch and collimation angle(s), and the SOD into account
may be employed to optimize one or more of the image acquisition
speed, the image quality, and/or ROI coverage.
[0037] Although not illustrated, in one aspect of the present
disclosure a range of SODs may be calculated based on the fixed
pitch and collimation angle(s) of the manufactured sources 110, and
provided to an operator or radiographer. The operator may then
place object 160 within the calculated range of SODs, between
sources 110 and detector 140. The distance between sources 110 and
detector 140 may then be measured by, for example, sensor(s) 190,
or mechanically. Alternatively, sources 110 and detector 140 may be
kept stationary, or if mobile may be designed to move in such a way
that their relative positions are known at all times throughout the
x-ray scanning process (e.g., sources 110 and/or detector 140 may
move in known pattern).
[0038] At step 504, the group or subset of sources 110 selected at
step 503 may be activated, and the selected ROI (step 502) may be
exposed to a sequence of x-ray exposures. The local variations in
intensity of impinging x-ray beams 130 on detector 140 (after
passing through object 160) may then be measured at step 505, thus
providing a measure of the attenuation attributable to object 160.
The attenuation measured at step 505 may be stored, for example, in
memory 170 or, alternatively, at processing unit 150. These
attenuation measurements may be appended to attenuation
measurements obtained from previous scans (e.g., from previous
activation of a group or subset of sources 110) This process may be
repeated until sufficient raw data has been captured to permit
conversion of the data into a desired image of the ROI.
[0039] Next with reference to blocks 506 through 507, an iterative
reconstruction process may be implemented to reconstruct a
three-dimensional representation of the ROI of object 160. The ROI
may then be subdivided (step 506) into it three-dimensional,
non-overlapping volume elements called voxels. The process of
defining (or re-defining) such voxels may be referred to as
voxelization (or re-voxelization). Each voxel may be modeled as
having homogenous radiation absorption properties (e.g., same
attenuation coefficient) throughout. In this way, each voxel may
represent a single sample or data point (e.g., a single attenuation
coefficient). All such data points may be collected in an array
called a vector. This voxelization process may be performed by
processing unit 150, or alternatively, by any other number of
means, as would be understood by a person of skill in the art in
view of the present disclosure.
[0040] Compressed sensing methodologies, as discussed herein,
capable of determining the intensity attributable to each of two or
more spatiotemporally overlapping x-ray beams may be used to
determine a set of attenuation coefficients which best fit the
available data obtained at step 505. In this way, a suitable
voxelization may then be determined by iteratively refining the
voxelization (repeating steps 506 and 507) until a stopping
criterion is satisfied, such as achieving a predetermined
optimality condition (e.g., a desired resolution) Because the
compressed sensing methodologies used to determine the attenuation
coefficients for a particular voxelization typically involve one or
more iterations, for ease of reference, each successive refinement
of the voxelization may be referred to as an outer iteration, while
each successive iteration of the compressed sensing methodology
(within each particular voxelization) may referred to as an inner
iteration.
[0041] With reference to block 507, after voxelization (or
re-voxelization), compressed sensing methods may be used to
deconvolve intensity measurements attributable to spatiotemporally
overlapping x-rays, and thus determine the attenuation, or more
precisely attenuation coefficient, attributable to the material
occupying each voxel. Compressed sensing is a mathematical
technique that exploits the sparsity in an image to allow
reconstruction from fewer measurements than would otherwise be
required. This technique may also be referred to as a basis pursuit
problem. Conventional basis pursuit problems concern
underdetermined linear systems, which have infinitely many
solutions, with the aim of finding among these a solution with
fewest non-zero entries Mathematically, this concept may be
expressed as:
min x .di-elect cons. R n { i : x i .noteq. 0 } , ##EQU00002##
where || denotes the cardinality, or the number of elements, of a
set, A is a m.times.n matrix, and b a vector of size m, where m is
the number of measurements, n is the number of voxels, and x is the
vector of attenuation coefficients and x.sub.i is the attenuation
coefficient of the i-th voxel.
[0042] In cases where two or more x-ray beams 130 from different
sources 110 overlap at detector 140, measurements from such
overlapping x-rays will not be linear (as they are for
non-overlapping x-rays). Instead, if two x-ray beams 130 overlap at
detector 140, or more specifically at a pixel of detector 140, the
attenuation at measurement j sums up to
I D j I E j 1 + I E j 2 = I E j 1 I E j 1 + I E j 2 exp ( i = 1 n -
.xi. ij 1 x i ) + I E j 2 I E j 1 + I E j 2 exp ( i = 1 n - .xi. ij
2 x i ) . ( 1 ) ##EQU00003##
where each of the two terms on the right-hand side corresponds to
the measurements attributable to one x-ray beam 140, and where
I.sub.Ejk corresponds to radiation at the emitter (or source) k,
I.sub.Dj corresponds to radiation at the detector j, and wherein
.xi..sub.ijk denotes the distance traveled by x-ray beam 130
emanating from the k-th source 110 through the i-th voxel. For
p.sub.j x-rays overlapping at the jth pixel of detector 140 the
more general formulation is
.psi. j := I D j l = 1 p j I E j l = k = 1 p j I E jk l = 1 p j I E
jl exp ( i = 1 n - .xi. ijk x i ) . ( 2 ) ##EQU00004##
[0043] In one approach, nonlinear constraints (2) may be linearized
by neglecting the nonlinearity of the measurements by assuming that
for two sufficiently close positive a, b.epsilon.R and .lamda. in
[0,1] we have log(.lamda.a+(1-.lamda.)b).apprxeq..lamda.
log(a)+(1-.lamda.)log(b). In the context of overlapping x-ray beams
130, the constraints (2) are simplified to
.psi. j .apprxeq. exp ( - k = 1 p .lamda. jk i = 1 n .xi. ijk x i )
, ( 3 ) ##EQU00005##
where the coefficients
.lamda. jk = I E jk l = 1 p I E jl ##EQU00006##
are the weights in a convex combination, that is, they are positive
and sum to 1. Applying the logarithm to the right-hand side, the
following linear constraints are obtained:
b j := log ( .psi. j ) .apprxeq. i = 1 n ( - k = 1 p j .lamda. jk
.xi. ijk ) x i , ( j = 1 , , m ) . ( 4 ) ##EQU00007##
or Ax=b, where b is the vector of b.sub.j and where A is a matrix
consisting of a negative convex combination of distances
a.sub.ij=-.SIGMA..sub.k=1.sup.p.sup.j.lamda..sub.jk.xi..sub.ijk,
where p.sub.j denotes the number of x-ray sources that overlap at
measurement j. A can be interpreted as a compressed version of the
corresponding linear measurement matrix arising from the sequential
exposures:
A = ( - k = 1 p 1 .lamda. 1 k .xi. 1 1 k - k = 1 p 1 .lamda. 1 k
.xi. n 1 k - k = 1 p m .lamda. mk .xi. 1 mk - k = 1 p m .lamda. mk
.xi. n mk ) , A ~ = ( - .xi. 111 - .xi. n 11 .xi. 11 p 1 - .xi. m 1
p 1 - .xi. 121 - .xi. n 21 - .xi. 1 m p m - .xi. mnp m ) ( 5 )
##EQU00008##
The above provides a first linear approximation of the nonlinear
measurements. However, depending on the difference of attenuation
along the overlapping x-ray beams 130, the two terms in (4) may
differ too much to justify this simplification.
[0044] Accordingly, for each measurement j parameters .tau..sub.j
that determine the linearization may be iteratively estimated. The
corresponding model may then be optimized based on these
parameters.
[0045] For two values a.sub.k>0 (k=1, . . . , p) and convex
combination weights .lamda..sub.k>0 (k=1, . . . , p) such that
.SIGMA..sub.k=1.sup.p.lamda..sub.k=1, .tau.(a, .lamda.) is defined
as the ratio
.tau. ( a , .lamda. ) = log ( k = 1 p .lamda. k a k ) k = 1 p
.lamda. k log ( a k ) . ( 6 ) ##EQU00009##
.tau.(a, .lamda.)<1 holds when all a.sub.k<1, because of the
concavity of the logarithmic function. By applying this concept to
the measurements (3), the ratios .tau..sub.j(x) for p.sub.j
overlapping x-ray cones at measurement j are given by
.tau. j ( x ) = log ( k = 1 p j .lamda. jk exp ( i = 1 n - .xi. ijk
x i ) ) - i = 1 n k = 1 p j .lamda. jk .xi. ijk x i . ( 7 )
##EQU00010##
And thus, the following formulation is obtained for the constraints
(2), where b.sub.j=log (.psi..sub.j) as before,
.psi. j = k = 1 p j .lamda. kj exp ( i = 1 n - .xi. ijk x i ) ( 8 )
b j = log ( k = 1 p j .lamda. kj exp ( i = 1 n - .xi. ijk x i ) ) (
9 ) .revreaction. b j = .tau. j i = 1 n a ij x i , ( 10 )
##EQU00011##
where
a.sub.ij=-.SIGMA..sub.k=1.sup.p.sup.j.lamda..sub.jk.xi..sub.ijk are
the entries of matrix A. Introducing a diagonal matrix
.tau.=diag(.tau..sub.1, . . . ,.tau..sub.m) (11)
yields the constraint
.tau.Ax=b (12)
Based on the foregoing, the following reconstruction (optimization
and linearization) algorithm may be formulated, wherein the set of
measured x-rays may be represented in a sparse matrix A of
intersection lengths of x-rays and voxels, in association with
corresponding vector measurements b, where m (the number of
measurements) may be much less than n (the number of voxels): Once
the sparse matrix and vector measurements are assembled, the
following may be solved, and iteratively refined for t=1, 2, . . .
, until the vector x has sufficiently converged.
[0046] 1. Update x:
x .rarw. arg min x .gtoreq. 0 x .delta. + 1 2 .mu. .tau. Ax - b 2 2
, ##EQU00012##
where .mu.>0 is a regularization parameter that provides a
balance between sparsity prior and the data fidelity term, and
where the sparsity prior .parallel.x.parallel..sub.s is a
L.sub.1-norm, the Total Variation Norm, or a convex combination of
the two.
[0047] 2. Update .tau.:
.tau. .rarw. diag ( .tau. 1 ( x ) , , .tau. m ( x ) ) , where
##EQU00013## .tau. j ( x ) = log ( k = 1 p j .lamda. jk exp ( i = 1
n - .xi. ijk x i ) ) - i = 1 n k = 1 p j .lamda. jk .xi. ijk x i .
##EQU00013.2##
An initialization may be performed where the following may be
computed first:
[0048] 0. x=A.sup.Tb, .tau.=I, where I is the m.times.m identity
matrix.
[0049] The following describes an alternative way of solving the
reconstruction problem with overlap. With reference to (2),
assuming again interest in a sparse reconstruction of the vector x,
minimization with L1 prior yields
min x 1 s . t . k = 1 p j .lamda. jk exp ( - i = 1 n .xi. ijk x i )
= .psi. j ( 13 ) ##EQU00014##
with measurements
.psi..sub.j=I.sub.Dj/.SIGMA..sub.t=1.sup.p.sup.jI.sub.Ejk, (j=1, .
. . , m). The coefficients -.xi..sub.ijk may be represented with
sparse vectors r.sub.jk .epsilon.R.sup.n:
r.sub.jk=(-.xi..sub.1jk . . . -.xi..sub.njk).sup.T, (j=1, . . . ,m)
(14)
Allowing for noise in the data constraint term, the following least
squares formulation of (13) is derived:
min x .gtoreq. 0 { x 1 + 1 2 .mu. j = 1 m ( k = 1 p j .lamda. jk
exp ( r jk T x ) - .psi. j ) 2 } , ( 15 ) ##EQU00015##
with regularization parameter .mu.>0, which provides a balance
between sparsity prior and data fidelity term. The formulation (15)
corresponds to an optimization problem of the form
min x { f ( x ) + g ( x ) } ( 16 ) ##EQU00016##
with convex non-differentiable f: R.sup.n.fwdarw.R
f(x)=.parallel.x.parallel..sub.1, (17)
and partially convex, differentiable g: R.sup.n.fwdarw.R
g ( x ) = 1 2 .mu. j = 1 m ( k = 1 p j .lamda. jk exp ( r jk T x )
- .psi. j ) 2 . ( 18 ) ##EQU00017##
[0050] An optimization problem of form (16) may be solved using the
first-order, forward-backward splitting update sequence for t=0, 1,
2 . . . and x.sup.0=0:
x.sup.t+1=prox.sub..lamda.f(x.sup.t-.lamda..gradient.g(x.sup.t))
(19)
with convergence rate O(1/t) and step size .lamda.=1/L. Update
sequence (19) converges to a minimum of (16), if f is a lower
semi-continuous convex function, and g is convex, differentiable,
and has a Lipschitz continuous gradient.
[0051] To optimize (15) as a special case of (16), the
initialization for x is kept smaller than a minimizer {circumflex
over (x)}, because g is partially convex for x.ltoreq.{circumflex
over (x)}. Furthermore, step sizes .lamda. should be chosen such
that x.ltoreq.{circumflex over (x)} is assured for all iterations
t. The step sizes .lamda. may be determined using a backtracking
line search algorithm (e.g., .lamda..rarw..lamda.c). The
measurements are given with .psi..sub.j=.psi.({circumflex over
(x)}), where
.psi. j ( x ) := k = 1 p i .lamda. jk exp ( r jk T x ) ,
##EQU00018##
and hence the line search can be constrained by
.psi..sub.j(x).ltoreq..psi..sub.j, for all j=1, . . . ,m. (20)
which is a necessary, but not sufficient, condition for
x.ltoreq.{circumflex over (x)}. Based on the foregoing, the
following second reconstruction (forward-backward splitting)
algorithm may be formulated, and used to generate a
three-dimensional reconstruction of the ROI (or a portion of the
ROI): The following may be assembled based on measurements obtained
at block 505:
[0052] .psi..epsilon.R.sup.m: vector of measurements
[0053] r.sub.jk .epsilon.R.sup.n: sparse vectors of intersection
lengths or rays and voxels
[0054] c, .tau..epsilon.(0, 1): line search control parameters
L = 1 .mu. 2 mp 2 .xi. max 2 : ##EQU00019##
Lipschitz constant for g
[0055] .theta.>0: tolerance threshold for stopping criterion
Next, an initialization x.sup.0=0 may be performed, and the
following may be solved, and iteratively refined for t=1, 2,
etc.:
[0056] 1. Compute search direction:
.gradient. g ( x ) = 1 .mu. j = 1 m ( k = 1 p j .lamda. jk exp ( r
jk T x ) - .psi. j ) ( k = 1 p j .lamda. jk exp ( r jk T x ) r jk )
. ##EQU00020##
[0057] 2. Backtracking line search: [0058] .lamda.=1/L [0059] do
[0060] .lamda..rarw..lamda.c [0061] x.sup.new=x-.DELTA..gradient.g
[0062] while g (x.sup.new)-g(x)>.lamda.c|.gradient.g|.sup.2 and
.E-backward.j.epsilon.1, . . . . , m:
.psi..sub.j(x.sup.new)>.psi..sub.j
[0063] 3. Update x: [0064] x'=prox.sub..lamda.f(max {0;
x.sup.t-1-.lamda..gradient.g(x.sup.t-1)})
[0065] 4. Stopping criterion: [0066] if
.parallel.x.sup.t-x.sup.t-1.parallel..sub.2/.parallel.x.sup.t-1.parallel.-
.sub.2<.theta.: stop
[0067] Experimental results using both simulated and real-world
measurements have shown that the reconstruction algorithms
disclosed herein significantly improve reconstruction accuracies
from linear constraints. Such experiments show that the present
methods are capable of recovering nearly the same image quality as
sequential (non-overlapping) exposures up to an average overlap of
.about.2, while highly increasing robustness with respect to SOD
and emitter collimation angles, and increasing image capture times.
In other words, the present methods provide optimal results when,
on average, the spatiotemporal x-ray overlap per pixel of detector
140 is attributable to two or fewer sources 110. Because in typical
use a subset of pixels of detector 140 will detect one or fewer
x-ray beams 130, the present methods allow for a configuration
where a second subset of pixels may detect spatiotemporally
overlapping x-rays from >2 sources 110.
[0068] With reference again to step 507, at the conclusion of each
inner iteration (e.g., solving and iteratively refining the
compressed sensing algorithm), a subsequent outer iteration may be
performed (step 506). In each subsequent outer iteration, each
voxel of the previous voxelization may be modified based on the
attenuation coefficients determined at step 507. For example, to
better fit the measured attenuation, voxels may be further
subdivided into smaller voxels, or alternatively, two or more
adjacent voxels may be merged into a single voxel. An optimal
voxelization may be obtained by iteratively amending the
voxelization until a stopping criterion is met (e.g., a desired
image resolution).
[0069] At the conclusion of the iterative loop (steps 506 and 507),
the resulting x (attenuation coefficient) values derived for each
voxel may be used to produce a three-dimensional, graphical
representation of the ROI object 160. This graphical representation
may be displayed (step 508) as a three-dimensional image, or more
typically as a set of two-dimensional "slices" (e.g., along the
z-axis). In this way, the ROI may be examined by the operator or
radiographer.
[0070] Notably, the foregoing method, while presented in ordered
steps for illustrative purposes is merely exemplary. The steps
described need not be performed in the recited order. Moreover,
each of the recited steps do not need to be performed to still be
in keeping with the present disclosure.
[0071] As would be understood by a person of skill in the art in
view of the present disclosure, embodiments described herein may
overcome the design restrictions of conventional systems, because
the removal of non-overlap conditions allow for more robust system
configurations. For example, the relaxing of non-overlap conditions
may be particularly useful in the case of tomosynthesis of thick
objects. In such cases, to ensure complete x-ray coverage at the
top of the object there typically will be significant overlap at
the bottom of the object, due to the cone or fan shape of the x-ray
beams Because conventional system cannot handle such overlap, the
top of such objects are usually under-sampled (and, thus, unclear)
as compared to the bottom of the object. Because embodiments of the
present invention allow x-ray overlap, higher sampling can be
achieved at the top of such objects, thereby producing clearer
images.
[0072] In addition, in medical applications, where the total
duration of consecutive exposures is limited (typically to 0.1 sec)
due to patient movement, conventional systems have to strike a
balance between the achievable resolution in the x-y plane (the
plane of the detector) and in the z-direction (the direction
orthogonal to the x-y plane). To increase the resolution in the
z-direction, more obtuse collimation angles have to be used, which
makes it difficult to avoid overlap leading to fewer exposures
being taken over the allowable time limit (e.g., 0.1 sec.).
Embodiments of the present disclosure overcome this limitation by
making it possible to use a mixture of sources 110 (or emitters)
with sharp and obtuse collimation angles in a manner that
temporally overlap, with the sharp angles helping to increase the
resolution in the x-y plane, and the obtuse angles helping to
increase the image resolution in the z-direction.
[0073] Moreover, it may happen in medical or clinical settings that
the source(s) 110 and detector 140 are not properly aligned (e.g.,
the pitch and yaw of the source are non-coplanar with the
detector), which may lead to x-ray overlap even at otherwise
acceptable SODs. The ability of embodiments of the present
disclosure to withstand overlap eliminates this concern, and allows
more flexibility in the manner in which patients are x-rayed, e.g.,
a patient lying in bed, supine may be imaged from the foot of the
bed, eliminating the need to suspend a heavy source over the
patient.
[0074] Embodiments of the present disclosure also have significant
advantages over conventional systems with regard to handling
different ROIs. In cases where the ROI is similar in area to a
detector, x-ray overlap allows the edge of the ROI to be well
sampled without requiring additional sources 110 or emitters, which
in turn increases operation speed. In conventional systems (where
x-ray overlap cannot be tolerated), the edge sources or emitters
(e.g., the outer rows and columns of emitter on a conventional
emitter panel) typically cover a small portion of the ROI. Because
emitters, and more specifically x-rays from different emitters,
cannot overlap, this requires the operator or radiographer to
separately activate the edge emitters, and thus perform more scans
than would be necessary under embodiments of the present
disclosure.
[0075] In cases where the ROI is small compared to a detector,
embodiments of the present disclosure may effectively halve
acquisition time due to the fact that x-rays from different
emitters may overlap effectively covering the entire ROI. In this
way, an operator or radiographer can take a rapid series of images,
and thus mitigate the number of motion artifacts. This feature is
especially beneficial in the case of children or frail patients,
where movement can be a bigger concern and body thickness is
smaller.
[0076] It should be understood that, while embodiments of the
present disclosure have been described above, the present
invention(s) should not be limited by the foregoing. To the
contrary, the foregoing written description, figures, and abstract
have been presented for illustrative purposes, and are in no way
meant to limit the present invention(s). Indeed, as a person of
skill in the art in view of the present disclosure would recognize,
various changes can be made to the foregoing without departing from
the scope and spirit of the present invention(s).
* * * * *