U.S. patent application number 13/751100 was filed with the patent office on 2013-05-30 for signal processing method, signal processing apparatus, and pulse photometer using the same.
This patent application is currently assigned to NIHON KOHDEN CORPORATION. The applicant listed for this patent is NIHON KOHDEN CORPORATION. Invention is credited to Masaru Yarita.
Application Number | 20130137948 13/751100 |
Document ID | / |
Family ID | 41201686 |
Filed Date | 2013-05-30 |
United States Patent
Application |
20130137948 |
Kind Code |
A1 |
Yarita; Masaru |
May 30, 2013 |
Signal Processing Method, Signal Processing Apparatus, and Pulse
Photometer Using the Same
Abstract
A method of processing first and second signals obtained by
measuring a medium, to obtain a pulse wave signal and an artifact
signal which are separated, includes: separating vectors of the
first and second signals by using a separation matrix into a vector
of the pulse wave signal and a vector of the artifact signal, the
separation matrix including a norm ratio of a stable zone of the
pulse wave signal and a compensated norm ratio of an artifact
zone.
Inventors: |
Yarita; Masaru; (Tokyo,
JP) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
NIHON KOHDEN CORPORATION; |
Tokyo |
|
JP |
|
|
Assignee: |
NIHON KOHDEN CORPORATION
Tokyo
JP
|
Family ID: |
41201686 |
Appl. No.: |
13/751100 |
Filed: |
January 27, 2013 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
12427623 |
Apr 21, 2009 |
|
|
|
13751100 |
|
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Current U.S.
Class: |
600/324 |
Current CPC
Class: |
A61B 5/14546 20130101;
A61B 5/14551 20130101; A61B 5/7203 20130101; A61B 5/0205 20130101;
G06K 9/0051 20130101; A61B 5/7225 20130101 |
Class at
Publication: |
600/324 |
International
Class: |
A61B 5/0205 20060101
A61B005/0205; A61B 5/00 20060101 A61B005/00; A61B 5/145 20060101
A61B005/145; A61B 5/1455 20060101 A61B005/1455 |
Foreign Application Data
Date |
Code |
Application Number |
Apr 22, 2008 |
JP |
2008-111391 |
Apr 22, 2008 |
JP |
2008-111392 |
Oct 21, 2008 |
JP |
2008-270730 |
Claims
1. A method of processing first and second signals obtained by
measuring a medium, to obtain a pulse wave signal and an artifact
signal which are separated, the method comprising: separating
vectors of the first and second signals by using a separation
matrix into a vector of the pulse wave signal and a vector of the
artifact signal, the separation matrix including a norm ratio of a
stable zone of the pulse wave signal and a compensated norm ratio
of an artifact zone.
2. The method according to claim 1, wherein the compensated norm
ratio is obtained by the following expression: IR pulse 2 _ := IR
pulse 2 N pulse ##EQU00013## IR noise 2 _ := IR noise 2 N noise
##EQU00013.2## R pulse 2 _ := R pulse 2 N pulse ##EQU00013.3## R
noise 2 _ := R noise 2 N noise ##EQU00013.4## .phi. N + = ( R noise
2 _ ) 2 - ( R pulse 2 _ ) 2 ( IR noise 2 _ ) 2 - ( IR pulse 2 _ ) 2
##EQU00013.5## where ( IR noise 2 _ ) 2 .noteq. ( IR pulse 2 _ ) 2
##EQU00013.6##
3. The method according to claim 1, wherein a moving average
process with a predetermined number of points is performed on the
pulse wave signal.
4. A biological signal processing apparatus comprising: a measuring
unit measuring the first and second signals; and a processing unit
processing the first and second signals by using the method
according to claim 1.
5. A pulse photometer including the biological signal processing
apparatus according to claim 4, and calculating at least one of an
oxygen saturation of arterial blood, a dyshemoglobin concentration,
and dye concentration injected in the blood, wherein the first and
second signals are electric signals into which lights obtained by
causing two kinds of light beams, which are emitted from a light
emitter and which have different wavelengths, to be transmitted
through or reflected from living tissue corresponding to the medium
are converted, and wherein a component of the artifact signal is
removed by using the compensated norm ratio to obtain the pulse
wave signal.
Description
[0001] This application is a Divisional application and claims the
priority benefit under 35 U.S.C. .sctn.120 of co-pending U.S.
patent application Ser. No. 12/427,623 filed on Apr. 21, 2009, and
claims the priority benefit under 35 U.S.C. .sctn.119 of Japanese
Patent Application Nos. JP2008-111391; 2008-111392; and 2008-270730
filed on Apr. 22, 2008; Apr. 22, 2008 and Oct. 21, 2008
respectively, which are all hereby incorporated in their entireties
by reference.
BACKGROUND OF THE INVENTION
[0002] The present invention relates to signal processing where a
common signal component is extracted by processing two homogeneous
signals which are extracted substantially simultaneously from one
medium and, and more particularly to an improvement of signal
processing in a pulse photometer which is used in the medical
field, particularly in the diagnosis of the circulatory system.
[0003] As a method of separating signal and noise components from
two signals which are extracted substantially simultaneously from
one medium, various methods have been proposed.
[0004] The methods are performed through frequency domain
processing and time domain processing.
[0005] Also in medical practice, for example, a so-called
photoplethysmograph which measures a pulse waveform and a pulse
rate, and apparatuses for measuring the concentration of a
light-absorbing material contained in the blood, such as an
apparatus for measuring the oxygen saturation SpO2, that for
measuring the concentration of dyshemoglobin such as
carboxyhemoglobin or methemoglobin, and that for measuring the dye
concentration injected in the blood are known as a pulse
photometer.
[0006] Among such apparatuses, an apparatus for measuring the
oxygen saturation SpO2 is called a pulse oximeter.
[0007] A pulse photometer operates on the following principle.
Light beams of plural wavelengths which are different in light
absorbency to the target substance are transmitted through or
reflected from living tissue, the intensity of reflected or
transmitted light is continuously measured, and the concentration
of the target substance is obtained from a pulse wave data signal
obtained in the measurement.
[0008] When noises are mixed into the pulse wave data signal, there
is the possibility that the concentration cannot be correctly
calculated and erroneous treatment may be caused.
[0009] In order to reduce the noise level in a pulse photometer,
methods such as that where the frequency band is divided and
attention is paid on signal components, and that where a
correlation between two signals is determined have been proposed.
However, the methods have a problem that the analysis requires a
prolonged time period.
[0010] Therefore, the assignee of the present invention has
proposed an art in Japanese Patent No. 3,270,917 where light beams
having two different wavelengths impinge on living tissue, two
pulse wave signals are obtained from transmitted light beams, a
graph is formed while using the level of the two pulse wave signals
as the ordinate and abscissa, respectively to obtain a regression
line, and the oxygen saturation of arterial blood or the
concentration of a light-absorbing material is obtained on the
basis of the gradient of the regression line. According to the
related art, the measurement accuracy is improved, and the power
consumption is reduced. In order to obtain a regression line or the
gradient thereof by using many sampling data with respect to pulse
wave signals of the wavelengths, however, a large computation
processing power is required.
[0011] Furthermore, the assignee of the present invention has
proposed a method in JP-A-2003-135434 where, although a frequency
analysis is used, a pulse wave signal itself is not extracted in
the analysis unlike a related art, but fundamental frequency of the
pulse wave signal, and the pulse wave signal is filtered by using a
filter using harmonic frequencies thereof to enhance the
accuracy.
[0012] In the use at home, particularly, it is supposed that a
pulse oximeter is used in various manners. Therefore, a wide
variety of artifacts exist, and a higher anti-artifact property is
requested in the case of SpO2 which is used in a hospital.
[0013] When an artifact is contained, the measurement system is
disturbed, and there is a case where SpO2 is erroneously
displayed.
[0014] A typical artifact is body motion. For example, such an
artifact is caused by a phenomenon where a probe which is attached
to the subject to be measured is moved by body motion, and the
optical path between the light source and a light-receiving face is
changed, or living tissue is deformed by a force applied to the
tissue.
[0015] In the case of a neonatal infant or an infant child,
particularly, an artifact is often contained, and a motion of a
hand or a foot, bitter sobbing, shiver, cough, and the like
function as an artifact source.
SUMMARY
[0016] It is therefore an object of the invention to provide a
signal processing method, signal processing apparatus, and pulse
photometer using the same in which, even in the case where a large
artifact such as motion of a hand or a foot, bitter sobbing,
shiver, or cough is contained, SpO2 can be measured more
correctly.
[0017] In order to achieve the object, according to the invention,
there is provided a method of processing first and second signals
obtained by measuring a medium, to obtain a pulse wave signal and
an artifact signal which are separated, the method comprising:
[0018] separating vectors of the first and second signals by using
a separation matrix into a vector of the pulse wave signal and a
vector of the artifact signal, the separation matrix including a
norm ratio of a stable zone of the pulse wave signal and a
compensated norm ratio of an artifact zone.
[0019] The compensated norm ratio may be obtained by the following
expression:
IR pulse 2 _ := IR pulse 2 N pulse ##EQU00001## IR noise 2 _ := IR
noise 2 N noise ##EQU00001.2## R pulse 2 _ := R pulse 2 N pulse
##EQU00001.3## R noise 2 _ := R noise 2 N noise ##EQU00001.4##
.phi. N + = ( R noise 2 _ ) 2 - ( R pulse 2 _ ) 2 ( IR noise 2 _ )
2 - ( IR pulse 2 _ ) 2 ##EQU00001.5## where ( IR noise 2 _ ) 2
.noteq. ( IR pulse 2 _ ) 2 ##EQU00001.6##
[0020] A moving average process with a predetermined number of
points may be performed on the pulse wave signal.
[0021] In order to achieve the object, according to the invention,
there is also provided a biological signal processing apparatus
comprising:
[0022] a measuring unit measuring the first and second signals;
and
[0023] a processing unit processing the first and second signals by
using the above method.
[0024] In order to achieve the object, according to the invention,
there is also provided a pulse photometer including the biological
signal processing apparatus according to claim 4, and calculating
at least one of an oxygen saturation of arterial blood, a
dyshemoglobin concentration, and dye concentration injected in the
blood,
[0025] wherein the first and second signals are electric signals
into which lights obtained by causing two kinds of light beams,
which are emitted from a light emitter and which have different
wavelengths, to be transmitted through or reflected from living
tissue corresponding to the medium are converted, and
[0026] wherein a component of the artifact signal is removed by
using the compensated norm ratio to obtain the pulse wave
signal.
[0027] In order to achieve the object, according to the invention,
there is also provided a method of processing first and second
signals obtained by measuring a medium, to obtain a pulse wave
signal and an artifact signal which are separated, the method
comprising:
[0028] separating vectors of the first and second signals by using
a separation matrix into a vector of the pulse wave signal and a
vector of the artifact signal, the separation matrix including a
norm ratio of a stable zone of the pulse wave signal and a
successively-compensated norm ratio of an artifact zone.
[0029] The successively-compensated norm ratio may be obtained by
the following expression:
IR pulse 2 _ := IR pulse 2 N pulse ##EQU00002## IR ( J ) J - k : J
+ k 2 _ := IR J - k : J + k 2 2 k + 1 ##EQU00002.2## R pulse 2 _ :=
R pulse 2 N pulse ##EQU00002.3## R ( J ) J - k : J + k 2 _ := R J -
k : J + k 2 2 k + 1 ##EQU00002.4## S .phi. N + ( J ) = ( R ( J ) J
- k : J + k 2 _ ) 2 - ( R pulse 2 _ ) 2 ( IR ( J ) J - k : J + k 2
_ ) 2 - ( IR pulse 2 _ ) 2 ##EQU00002.5## where ( IR ( J ) J - k :
J + k 2 _ ) 2 .noteq. ( IR J - k : J + k 2 _ ) 2 ##EQU00002.6##
[0030] When the successively-compensated norm ratio satisfies a
condition, the successively-compensated norm ratio may be replaced
with a prescribed value.
[0031] In order to achieve the object, according to the invention,
there is also provided a biological signal processing apparatus
comprising:
[0032] a measuring unit measuring the first and second signals;
and
[0033] a processing unit processing the first and second signals by
using the above method.
[0034] In order to achieve the object, according to the invention,
there is also provided a pulse photometer including the above
biological signal processing apparatus, and calculating at least
one of an oxygen saturation of arterial blood, a dyshemoglobin
concentration, and dye concentration injected in the blood,
[0035] wherein the first and second signals are electric signals
into which lights obtained by causing two kinds of light beams,
which are emitted from a light emitter and which have different
wavelengths, to be transmitted through or reflected from living
tissue corresponding to the medium are converted, and
[0036] wherein a component of the artifact signal is removed by
using the compensated norm ratio to obtain the pulse wave
signal.
[0037] When the successively-compensated norm ratio satisfies a
condition, the successively-compensated norm ratio may be replaced
with a value.
BRIEF DESCRIPTION OF THE DRAWINGS
[0038] FIG. 1 is a diagram showing the configuration of a pulse
oximeter which measures the oxygen saturation of arterial
blood.
[0039] FIGS. 2A and 2B are views showing a measurement example of
variations in light absorbance (light attenuation) of a
light-absorbing material in blood.
[0040] FIG. 3 shows observation signals which are measured by
attaching a two-wavelength probe to a fingertip of a healthy male
subject, and by artificially mixing an artifact.
[0041] FIG. 4 is a correlation diagram of the infrared and red
light observation signals shown in FIG. 3.
[0042] FIG. 5 is a diagram in which the example of FIG. 3 is
modeled for the signal process.
[0043] FIGS. 6A, 6B, and 6C are views showing results of three
kinds of simulations which were performed while changing
relationships between the amplitudes of a pulse wave signal (pulse)
and an artifact signal (Artifact).
[0044] FIGS. 7A and 7B are views showing a waveform which is
obtained by separating an observation signal by a separation matrix
S.
[0045] FIGS. 8A and 8B are views showing results of processes in
which pulse waves that are obtained by separating the observation
signals of FIG. 3 by the separation matrix S are further subjected
to a 17-point moving average process.
[0046] FIGS. 9A to 9D are views showing correlations after
separation.
[0047] FIG. 10 is a view showing results of evaluation of
separation of the pulse wave and the artifact by an evaluation
function H.
[0048] FIG. 11 is a view showing results of separation of the
observation signal with using "successively-compensated norm
ratio", "norm ratio", and "compensated norm ratio".
[0049] FIG. 12 is a view showing artifacts separated by separation
methods due to "successively-compensated norm ratio", "norm ratio",
and "compensated norm ratio".
[0050] FIG. 13 is a view showing results of evaluation by the
evaluation function H.
[0051] FIGS. 14A, 14B, and 14C are views showing a trend of a
successive norm ratio at a sample number k=10 which is obtained
from observation waveforms of IR and R.
[0052] FIG. 15 is a view showing relationships between a noise
magnification direction and a noise magnification coefficient.
[0053] FIGS. 16A and 16B are views showing results of a simulation
in which .PHI.S and .PHI.N of the separation matrix are set as
.PHI.S=0.55 and .PHI.N/.PHI.S=1.3.
[0054] FIG. 17 is a chart showing the flow of processes of
processing parameters related to the artifact.
[0055] FIGS. 18A to 18D are views showing results of separation in
which the pulse wave is separated from the observation waveforms in
FIGS. 14A and 14B.
[0056] FIG. 19 is a view showing results of a process in which the
pulse wave is separated with other parameters from the observation
waveforms in FIGS. 14A and 14B.
[0057] FIGS. 20A to 20D are views showing trends of the pulse wave
and "gated successively-compensated norm ratio" while the time axis
is expanded.
[0058] FIGS. 21A and 21B are views showing results of relaxation of
ill conditions by a regularization parameter in the invention.
[0059] FIGS. 22A to 22C are views showing other process examples of
a pulse wave which is buried in a tapping artifact.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
[0060] In the description of an embodiment of the invention, the
principle will be described by exemplifying a pulse oximeter which
measures the oxygen saturation of arterial blood.
[0061] The technique of the invention is not restricted to a pulse
oximeter, and can be applied also to an apparatus (pulse
photometer) which measures a light-absorbing material contained in
the blood such as dyshemoglobin (carboxyhemoglobin, methemoglobin,
and the like), and dye injected in the blood, with using the
principle of pulse photometry.
[0062] FIG. 1 which is a schematic block diagram shows the
configuration of a pulse oximeter which measures the oxygen
saturation of arterial blood.
[0063] Photo emitters 1, 2 which respectively emit light beams of
different wavelengths are driven by a driving circuit 3 so as to
alternately emit the light beams.
[0064] Preferably, the light beams emitted from the photo emitters
1, 2 are infrared light (for example, 940 [nm]) which is less
affected by the oxygen saturation of arterial blood, and red light
(for example, 660 [nm]) which is highly sensitive to a change of
the oxygen saturation of arterial blood, respectively.
[0065] The light beams emitted from the photo emitters 1, 2 are
transmitted through living tissue 4, and then received by a
photodiode 5 to be converted into electric signals.
[0066] In FIG. 1, the transmitted light beams are received.
Alternatively, reflected light beams may be received.
[0067] The converted signals are amplified by an amplifier 6, and
separately supplied by a multiplexer 7 to filters 8-1, 8-2
respectively corresponding to the light wavelengths.
[0068] The signals separately supplied to the filters are filtered
by the filters 8-1, 8-2 so that noise components are reduced, and
then digitized by an A/D converter 9.
[0069] The digitized signal trains corresponding to the infrared
light and the red light form the pulse wave signals,
respectively.
[0070] The digitized signal trains are inputted to a processor 10,
and processed by a program stored in a ROM 12. The oxygen
saturation SpO2 is measured, and the value of the saturation is
displayed on a display 11.
[0071] First, measurement of variations in light absorbance (light
attenuation) of a light-absorbing material in blood will be
described with reference to FIGS. 2A and 2B. FIGS. 2A and 2B show
pulse wave data which are obtained by transmitting the light beams
emitted from the photo emitters 1, 2 through the living tissue 4,
receiving the transmitted light beams on the photodiode 5, and
converting the light beams into electric signals. FIG. 2A shows
pulse wave data in the case of the red light, and FIG. 2B shows
those in the case of the infrared light.
[0072] In FIG. 2A, assuming that the abscissa indicates the time
and the ordinate indicates the power of received light, the power
of light received by the photodiode 5 has a waveform in which the
DC component (R') of the red light and the pulsation component
(.DELTA.R') are superimposed to each other.
[0073] In FIG. 2B, assuming that the abscissa indicates the time
and the ordinate indicates the power of received light, the power
of light received by the photodiode 5 has a waveform in which the
DC component (IR') of the infrared light and the pulsation
component (.DELTA.IR') are superimposed to each other.
[0074] Each of the measurement waveforms of FIGS. 2A and 2B
contains an artifact (noises) due to body motion. There is a
frequency band which is common to the frequency component of the
artifact and that of the signal. Therefore, it is difficult to
correctly obtain the signal component by removing the artifact
component.
[0075] In the examples of FIGS. 2A and 2B, the degree of the
artifact is small. In the following, the description will be made
based on an measurement example in which a large artifact
corresponding to a large artifact such as a motion of a hand or a
foot, bitter sobbing, shiver, cough, or the like is artificially
applied.
[0076] FIG. 3 show observation signals which are measured by
attaching a two-wavelength probe to a fingertip of a healthy male
subject.
[0077] The upper portion of the figure shows an observation signal
corresponding to the infrared light (IR), and the lower portion
shows that corresponding to the red light (R).
[0078] The wavelengths are 940 nm (infrared light) and 660 nm (red
light), respectively.
[0079] The solid line zones shown in the upper portions of the
figures of FIG. 3 indicate a tapping zone where an artifact is
artificially applied. In the tapping zone, a table surface is
tapped with a fingertip on the side where the probe is attached,
quickly (for example, about 3 Hz) and repeatedly.
[0080] In the example of FIG. 3, with respect to both the
observation signals of the infrared light and the red light, a
pulse wave is not seen in the artifact zone.
[0081] The observation signals are normalized by respective DC
transmitted light components, and then filtered by a six-pole
Butterworth filter having a bandwidth of 0.5 to 5 Hz. The sampling
interval is 16 ms.
[0082] FIG. 4 is a correlation diagram of the infrared and red
light observation signals shown in FIG. 3.
[0083] The abscissa indicates the infrared light, and the ordinate
indicates the red light.
[0084] The gradient of FIG. 4 is given as a norm ratio of the
infrared light to the red light in the artifact zone. From the
gradient, the norm ratio ".PHI.N" of the artifact is known.
[0085] Next, a signal process of separating a pulse wave signal and
noises (artifact signal) will be described with reference to FIG.
5.
[0086] FIG. 5 is a diagram in which the example of FIG. 3 is
modeled for the signal process.
[0087] A pulse wave signal p at time tn is transmitted with a
coefficient of 1 to an IR terminal, and transmitted with
coefficient .PHI.S to an R terminal.
[0088] Similarly, an artifact signal n at time tn is transmitted
with the coefficient of 1 to the IR terminal, and transmitted with
coefficient .PHI.N to the R terminal.
[0089] The coefficient .PHI.S of the pulse wave signal is
.PHI.S:=Rp, tn/IRp, tn, and the coefficient .PHI.N of the artifact
signal is .PHI.N:=Rn, tn/IRn, tn.
[0090] When the observation time is prolonged to tn: tn+k, p, n,
IR, and R are formed as vectors.
.phi..sub.S:
=.parallel.R.sub.pulse.parallel..sub.2/.parallel.IR.sub.pulse.parallel..s-
ub.2 [Exp. 1]
.phi..sub.N:=.parallel.R.sub.noise.parallel..sub.2/.parallel.IR.sub.nois-
e.parallel..sub.2 [Exp. 2]
[0091] Hereinafter, it is assumed that a bold face indicates a
vector.
[0092] A suffix "pulse" means the stable zone of the pulse wave,
and a suffix "noise" means the artifact zone.
[0093] The stable zone of the pulse wave and the artifact zone are
different both in time and zone length from each other.
.phi..sub.S:
=.parallel.R.sub.pulse.parallel..sub.2/.parallel.IR.sub.pulse.parallel..s-
ub.2 [Exp. 1]
.phi..sub.N:=.parallel.R.sub.noise.parallel..sub.2/.parallel.IR.sub.nois-
e.parallel..sub.2 [Exp. 2]
[0094] Next, FIGS. 6A 6B, and 6C show results of three kinds of
simulations which were performed while changing the relationships
between the amplitudes of the pulse wave signal (pulse) and the
artifact signal (Artifact).
[0095] In FIGS. 6A, 6B, and 6C, the abscissa indicates the IR
signal, and the ordinate indicates the R signal.
[0096] In the simulations, the pulse wave was set to have a
saw-tooth waveform, and the artifact to have a sinusoidal
waveform.
[0097] With respect to the relationships between the amplitudes of
the pulse wave signal and the artifact signal, in FIG. 6A, the
amplitudes of the pulse wave signal (pulse) and the artifact signal
(Artifact) are (0.25:0.75).
[0098] In FIG. 6B, the amplitudes of the pulse wave signal (pulse)
and the artifact signal (Artifact) are (0.33:0.66).
[0099] In FIG. 6C, the amplitudes of the pulse wave signal (pulse)
and the artifact signal (Artifact) are (0.5:0.5).
[0100] When the norm ratio .PHI.S indicated by Exp. 1 is
.PHI.S=0.55, is the true value of the norm ratio indicated by Exp.
2 above:
.phi..sub.N.sup.true [Exp. 3]
is 1.
[0101] All of the correlation diagrams shown in FIGS. 6A to 6C have
a shape of a parallelogram. When artifact>pulse wave, the
gradient of the short side coincides with .PHI.S, and that of the
long side coincides with .PHI.N.
[0102] By contrast, when artifact<pulse wave, the gradient of
the long side coincides with .PHI.S, and that of the short side
coincides with .PHI.N.
[0103] The broken lines in the correlation diagrams of FIGS. 6A to
6C indicate the gradient of ".PHI.N" which shows "norm ratio" of
the observation signal, and the solid lines indicate the gradient
of
.phi..sub.N.sup.+ [Exp. 4]
which is "compensated norm ratio" that is proposed as a reference
example, and that will be described later.
[0104] The compensated norm ratio coincides with "true value of
norm ratio":
.phi..sub.N.sup.true [Exp. 3]
which indicates the gradient of the long side of the
parallelogram.
[0105] It is seen that, as the amplitudes of the pulse wave and the
artifact are closer to each other, the discrepancy between "norm
ratio" and "true value of norm ratio" is gradually more
increased.
[0106] Next, the separation between the pulse wave signal and the
artifact signal by the norm ratio will be described.
[0107] An observation signal [IR R].sup.T is separated by a
separation matrix S into a pulse wave signal vector p and an
artifact signal vector n.
[0108] "T" in the shoulder means transposition.
[0109] From Exp. (1) below, a mixing matrix M is determined when
".PHI.S" and ".PHI.N" are set.
[0110] The separation matrix S is an inverse matrix of M shown in
Exp. (2).
[0111] Here, ".PHI.S" is the norm ratio of the observation signal
in the stable zone of the pulse wave.
[0112] When remaining ".PHI.N" can be estimated, M in which [1
.PHI.S].sup.T and [1 .PHI.N].sup.T are base vectors is
determined.
[0113] S=M.sup.-1 in which
S-(M.sup.TM).sup.-1M.sup.T [Exp. 5]
may be used.
[0114] In the above, ".PHI.N" is the norm ratio of the observation
signal in the artifact zone.
[0115] It is assumed that ".PHI.Npulse"=1 in the stable zone of the
pulse wave.
[ Exp . 6 ] M = [ 1 1 .0. S .0. N [ S = ( M T M ) - 1 M T [ p n ] T
= S [ IR R ] T ##EQU00003##
[0116] In the above expressions, .parallel. .parallel.2 means a
two-dimensional Euclidean norm. Suffixes pulse=t.sub.1: 1+n and
noise=tj: j+k indicate the stable zone of the pulse wave, and the
artifact zone, respectively.
[0117] The time and the sample number are different in the stable
zone of the pulse wave, and the artifact zone.
[0118] The configuration where ".PHI.S" and ".PHI.N" are obtained
from the norm ratio is advantageous in that, because of the
definition of the Euclidean norm, it is firm against sporadic
noises.
[0119] The observation signal is a composite vector of a pulse wave
vector and artifact vector which are different in gradient from
each other.
[0120] Because the pulse wave is superimposed also in the artifact
zone, therefore,
.phi..sub.N:=.parallel.R.sub.noise.parallel..sub.2/.parallel.IR.sub.nois-
e.parallel..sub.2 [Exp. 2]
and
.phi..sub.N.sup.true [Exp. 3]
which is the true value of the norm ratio are discrepant from each
other.
[0121] As a reference example, therefore, there is a method in
which "compensated norm ratio"
.phi..sub.N.sup.+ [Exp. 4]
is used as means for correcting the discrepancy.
[0122] The compensation method is based on that the amplitude of
the pulse wave superimposed in the artifact zone is equal to that
in the stable zone.
[0123] The compensation is performed by following Exp. (4).
.phi..sub.N.sup.+ [Exp. 4]
is referred to as "compensated norm ratio" of the artifact zone,
and ".PHI.N" is referred to as the norm ratio of the zone.
[0124] In the artifact zone, it is often that the pulse wave signal
is buried and hardly observed.
[0125] The norm is taken in the stable zone of the pulse wave
signal, and
.parallel.IR.sub.pulse.parallel..sub.2 and
.parallel.R.sub.pulse.parallel..sub.2 [Exp. 7]
is set as the pulse wave amplitude.
[0126] The amplitude of the artifact signal is the norm of the
artifact zone:
.parallel.IR.sub.noise.parallel..sub.2 and
.parallel.R.sub.noise.parallel..sub.2 [Exp. 8]
[0127] Here, the sample number of the pulse wave zone is different
from that of the artifact zone, and hence the norms are divided by
the square root of the sample number of the respective zone.
[0128] An absolute value is used in view of that the value in the
root sign is caused to become negative by observation noises other
than the artifact.
[ Exp . 9 ] IR pulse 2 _ := IR pulse 2 N pulse IR noise 2 _ := IR
noise 2 N noise R pulse 2 _ := R pulse 2 N pulse R noise 2 _ := R
noise 2 N noise .0. N + = ( R noise 2 _ ) 2 - ( R pulse 2 _ ) 2 (
IR noise 2 _ ) 2 - ( IR pulse 2 _ ) 2 where ( IR noise 2 _ ) 2
.noteq. ( IR pulse 2 _ ) 2 ( 4 ) ##EQU00004##
[0129] A result of the separation in which the observation signal
is separated by the separation matrix S with using "compensated
norm ratio" that is the reference example will be described with
reference to FIGS. 7A and 7B.
[0130] FIGS. 7A and 7B are views showing a waveform which is
obtained by separating the observation signal by the separation
matrix S.
[0131] In FIGS. 7A and 7B, the sampling interval is 16 ms, and a
six-pole Butterworth filter having a bandwidth of 0.5 to 5 Hz is
used.
[0132] The horizontal lines above the waveforms in FIGS. 7A and 7B
indicate the artifact zone.
[0133] FIG. 7A shows the pulse wave which is separated by "norm
ratio" and ".PHI.S", and FIG. 78 shows the pulse wave which is
separated by above-mentioned "compensated norm ratio" and
".PHI.S".
[0134] In the former, needle-like large-amplitude artifacts are
prominent.
[0135] In the latter, the pulse wave can be clearly seen, and,
particularly at 20 seconds or later, the pulse wave is more clearly
separated.
[0136] By contrast, in the zone of 12.5 to 18.5 seconds, the
artifact is increased.
[0137] FIGS. 8A and 8B are views showing results of processes in
which pulse waves that are obtained by separating the observation
signals of FIG. 3 by the separation matrix S are further subjected
to a 17-point moving average process in the artifact zone.
[0138] FIG. 8A shows the pulse wave which is separated by "norm
ratio" and ".PHI.S", and FIG. 8B shows the pulse wave which is
separated by above-mentioned "compensated norm ratio" and
".PHI.S".
[0139] It is seen that, in the separation by "compensated norm
ratio", needle-like large-amplitude artifacts are reduced as
compared with the separation by the norm ratio ".PHI.N".
[0140] In the separation by "compensated norm ratio", in the zone
of 17 to 23 seconds, the artifact is reduced, and the pulse wave
exhibits a smooth shape. Also in the zone of 30 to 35 seconds,
because of the separation by "compensated norm ratio", the pulse
wave exhibits a smooth shape.
[0141] It is considered that the pulse wave and the artifact are
independent from each other. When the separation is adequately
performed, therefore, the correlation diagram becomes close to a
quadrangle or a rectangle.
[0142] FIGS. 9A to 9D are views showing correlations after
separation.
[0143] FIG. 9A shows correlations between a pulse wave which is
separated by "norm ratio" and ".PHI.S" and the artifact, FIG. 9B
shows correlations between a pulse wave which is separated by
"compensated norm ratio" and ".PHI.S", and the artifact, FIG. 90
shows correlations between a pulse wave which is obtained by
performing a 17-point moving average process on a pulse wave
separated by "norm ratio" and ".PHI.S", and the artifact, and FIG.
9D shows correlations between a pulse wave which is obtained by
performing a 17-point moving average process on a pulse wave
separated by "compensated norm ratio" and ".PHI.S", and the
artifact. It is seen that the case of FIG. 9B is separated more
adequately than that of FIG. 9A, and the case of FIG. 9D is
separated more adequately than that of FIG. 9C.
[0144] In observation, "true value of norm ratio" is unknown.
Therefore, the degree of approach of "compensated norm ratio" to
"true value of norm ratio" cannot be known.
[0145] Therefore, the result of separation by "compensated norm
ratio" is evaluated with an evaluation function H of Exp. (6)
below. In the expression, [.SIGMA.] means a variance-covariance
matrix of the separated pulse wave signal vector p and the artifact
signal vector n.
[0146] H is a ratio of absolute values of trace [.SIGMA.] and
on-diagonal element 2 .SIGMA..sub.12.
[0147] When compensation is adequately performed, [.SIGMA.]
approaches a diagonal matrix. As the value of H is smaller, the
independences of p and n are higher.
[ Exp . 10 ] [ ] := [ 11 12 21 22 [ = [ p n ] T [ p n ] ( 5 ) H :=
2 12 trace [ .SIGMA. ] ( 6 ) ##EQU00005##
FIG. 10 shows results of evaluation of separation of the pulse wave
and the artifact by the evaluation function H.
[0148] In FIG. 10, the upper row indicates the case where
separation is performed by "norm ratio", and the lower row
indicates the case where separation is performed by "compensated
norm ratio".
[0149] In the both cases, evaluation results in the case of a
six-pole Butterworth filter having a bandwidth of 0-5 to 5 Hz, and
the case of a 17-point moving average process after the process of
the filter are shown.
[0150] It is seen that, in the case where separation is performed
by "compensated norm ratio", smaller values H=0.0042 and H=0.0492
are attained, and the diagonality is improved.
[0151] In the observation waveforms of FIG. 3 used in the
description of "compensated norm ratio" which is the reference
example, the artifact is artificially applied, and hence
"compensated norm ratio" is a fixed value.
[0152] However, usually, an actual artifact is temporally changed.
In such a case, also
.phi..sub.N.sup.true [Exp. 3]
which is "true value of norm ratio" is changed, but "compensated
norm ratio":
.phi.N.sup.+ [Exp. 4]
is a fixed value, and cannot follow a change. Therefore, the
quality of separation is lowered.
[0153] The invention is relates to a technique of improving the
configuration where "compensated norm ratio" which is the reference
example is not sufficient for an artifact that is temporally
changed.
[0154] Therefore, the leak of an artifact into the pulse wave in
the model of FIG. 5 will be discussed.
[0155] A true mixing matrix is assumed to be
M.sup.true [Exp. 11]
and the inverse matrix thereof is assumed to be the separation
matrix S.
[ Exp . 12 ] M true = [ 1 1 .0. S true .0. N true [ M sep = [ 1 1
.0. S .0. N [ S = ( M sep T M sep ) - 1 M sep T [ p n ] T = = [ IR
R ] T SM true [ p true n true ] T = [ ( .0. N - .0. S true .0. N -
.0. S ) ( .0. N - .0. N true .0. N - .0. S ) ( .0. S true - .0. S
.0. N - .0. S ) ( .0. N true - .0. S .0. N - .0. S ) [ [ p true n
true ] T p = ( .0. N - .0. S true .0. N - .0. S ) p true + ( .0. N
- .0. N true .0. N - .0. S ) n true L = ( .0. N - .0. N true ) n
true ( .0. N - .0. S true ) p true ( 7 ) ##EQU00006##
[0156] When the true mixing matrix:
M.sup.true [Exp. 11]
is different in parameter value from the separation matrix S, the
artifact leaks into the pulse wave.
[0157] The leak ratio L can be evaluated by Exp. (7).
[0158] For example, the amplitudes of the pulse wave and the
artifact are assumed to be 1, and the pulse wave and the artifact
are mixed with each other by:
.phi..sub.S.sup.true=0.55, .phi..sub.N.sup.true=0.75 [Exp. 13]
[0159] Thereafter, separation is performed by:
.phi..sub.s0.55, .phi..sub.N=0.95.times..phi..sub.N.sup.true [Exp.
14]
When the discrepancy between "norm ratio" and "true norm ratio" is
only 5%, then, 16% of the amplitude of the artifact leaks into the
pulse wave. This leak is not small.
[0160] Usually, "true norm ratio" changes with time. By contrast,
"compensated norm ratio" is fixed in the artifact zone, and cannot
follow the temporal change of "true norm ratio". Therefore, any
countermeasure is necessary.
[0161] As described above, the phenomenon where the pulse wave is
superimposed also in the artifact zone causes "norm ratio" and
"true norm ratio" to be discrepant from each other. According to
the invention, consequently, "successively-compensated norm
ratio":
S.phi..sub.N.sup.+ [Exp. 15]
which will be described later is proposed as means for correcting
the discrepancy.
[0162] The compensation method is premised on that the amplitude of
the pulse wave superimposed in the artifact zone is equal to that
of the pulse wave in the stable zone.
[0163] The compensation is successively performed at each sampling
point according to Exp. (8) below. This expression:
S .sub.N.sup.+(J) [Exp. 16]
is referred to as the successively-compensated norm ratio at sample
timing J of the artifact zone.
[0164] In the artifact zone, the pulse wave signal is buried in the
artifact and hardly observed. The norm is taken in the stable zone
of the pulse wave signal, and
.parallel.IR.sub.pulse.parallel..sub.2 and
.parallel.R.sub.pulse.parallel..sub.2 [Exp. 17]
are set as the pulse wave amplitude.
[0165] By contrast, considering J and preceding and succeeding k
points, norms of (2k+1) points in total:
.parallel.IR(J).sub.J-k:J+k.parallel..sub.2 and
.parallel.(J).sub.J-k:J+k.parallel..sub.2 [Exp. 18]
are set as the artifact amplitude at timing J.
[0166] Since the sample number of the pulse wave zone is different
from that of the artifact zone,
.parallel..parallel..sub.2 [Exp. 19]
is a value which is obtained by division with the square root of
the sample number of the respective zone, i.e.,
{square root over (N.sub.pulse)} [Exp. 20]
in the case of the pulse wave, and
{square root over (2k+1)} [Exp. 20]
in the case of the artifact. The absolute value is used in view of
that the value in the root sign is caused to become negative by
observation noises other than the artifact.
[ Exp . 21 ] IR pulse 2 _ := IR pulse 2 N pulse IR ( J ) J - k : J
+ k 2 _ := IR J - k : J + k 2 2 k + 1 R pulse 2 _ := R pulse 2 N
pulse R ( J ) J - k : J + k 2 _ := R J - k : J + k 2 2 k + 1 S .0.
N + ( J ) = ( R ( J ) J - k : J + k 2 _ ) 2 - ( R pulse 2 _ ) 2 (
IR ( J ) J - k : J + k 2 _ ) 2 - ( IR pulse 2 _ ) 2 where ( IR ( J
) J - k : J + k 2 _ ) 2 .noteq. ( IR J - k : J + k 2 _ ) 2 ( 8 )
##EQU00007##
[0167] FIG. 11 shows results of separation of the observation
signal by the separation matrix S with using
"successively-compensated norm ratio" which is given by Exp. (8)
above, together with results in the case where "norm ratio" and
"compensated norm ratio" which is the reference example are
used.
[0168] In FIG. 11, A shows the case where the artifact zone is
separated by "successively-compensated norm ratio", B shows the
case where the artifact zone is separated by "compensated norm
ratio", and C shows the case where the artifact zone is separated
by "norm ratio".
[0169] In FIG. 11, when the pulse waves in the zone of 5 to 20
seconds are compared with each other, the artifact amplitude in the
separation by "successively-compensated norm ratio" in A is smaller
than that in the cases of B and C.
[0170] In the vicinity of 20 seconds, particularly, there is a
difference in amplitude, and, in the vicinity of 8 seconds, the
pulse waves of B and C can be seen, but, in A, clear separation is
performed as a pulse wave which is well connected to the preceding
and succeeding portions.
[0171] In the base before the artifact in the vicinity of 17
seconds, the shape of the pulse wave is clearly separated as
compared with B and C.
[0172] Furthermore, also in the steep rising portion of the
artifact immediately before 20 seconds, the shape of the pulse wave
is clearly separated as compared with B and C.
[0173] FIG. 12 is a view showing artifacts separated by three kinds
(A, B, and C) of separation methods.
[0174] From FIG. 12, it is seen that the artifact amplitude is
separated in the sequence of C>B>A.
[0175] Therefore, it is seen that "successively-compensated norm
ratio" in the invention can perform correction to a more adequate
value and is superior as compared with "norm ratio" and
"compensated norm ratio" which is the reference example.
[0176] In observation, "true value of norm ratio" is unknown.
Therefore, the degree of approach of "compensated norm ratio" to
"true value of norm ratio" cannot be known.
[0177] Therefore, the result of separation by "compensated norm
ratio" is evaluated with the evaluation function H of Exp. (6)
above. In the expression, [.SIGMA.] means a variance-covariance
matrix of the separated pulse wave signal vector p and the artifact
signal vector n.
[0178] H is a ratio of absolute values of trace [.SIGMA.] and
on-diagonal element 2.SIGMA..sub.12.
[0179] When compensation is adequately performed, [.SIGMA.]
approaches a diagonal matrix. As the value of H is smaller, the
independences of p and n are higher.
[0180] FIG. 13 shows results of the evaluation.
[0181] The results of the evaluation with the evaluation function H
show that, as the value of H is smaller, the separation is
performed more satisfactorily.
[0182] Also from the results of the evaluation with the evaluation
function H, similarly with the results of FIG. 11, it is seen that
the separation is performed in the sequence of C>B>A.
[0183] Furthermore, the separation matrix S is ill-conditioned
depending on the value of "successively-compensated norm
ratio":
S.phi..sub.N.sup.+ [Exp. 15]
and oscillation or spikes are sometimes generated.
[0184] The following invention relates to an improved technique for
relaxing ill conditions of the separation matrix S.
[0185] Instability of Separation Matrix and Noise Magnification
Coefficient
[0186] (1) Unstable Zone
[0187] In an inverse problem, as a general property, the solution
is unstable when the separation matrix is ill-conditioned.
[0188] FIG. 14C shows a successive norm ratio S.PHI.N at the trend
of .PHI.N in the case where the sample number k obtained from the
observation waveforms shown in FIGS. 14A and 14B is k.about.10.
[0189] As shown in FIG. 14C, the ratio of SON is largely
changed.
[0190] The horizontal line in FIG. 14C indicates .PHI.S which is
obtained in the stable zone (1 to 3.5 seconds) of the pulse wave,
and .PHI.S=0.5357.
[0191] The vicinities of intersections of the horizontal line and
SON are regions where S.PHI.N.ident..PHI.S, the separation matrix
is ill-conditioned, and oscillation or spikes are generated.
[0192] Usually, .PHI.S of a healthy person is about 0.55.
[0193] (2) Eigenvector and Eigenvalue of Separation Matrix
[0194] When observation noises exist in the observation signal, an
abnormality such as that the amplitude is increased by separation
sometimes occurs. Such an abnormality occurs in the case where the
separation matrix is ill-conditioned, and the eigenvector and
eigenvalue of the separation matrix are related to this.
[0195] In order to study ill conditions, the separation matrix S is
assumed to be as Exp. (9):
[ Exp . 22 ] S = 1 .DELTA. [ 1 + - 1 - 1 1 + ] here .DELTA. = ( 1 +
) 2 - 1 ##EQU00008##
In the above expression, .epsilon. is a small value. Depending on
the value of .epsilon., the separation matrix is changed from
linear independent to linear dependent. When .epsilon.>0, the
column vector of S is linear independent, and, when
.epsilon..about.0, the column vector is linear dependent and an
ill-conditioned matrix.
[0196] When .epsilon..ident.0 is attained, an abnormality
occurs.
[0197] In the case of two-wavelength SpO2, the separation matrix S
is 2.times.2, and has two eigenvectors V and two eigenvalues
.lamda..
[0198] In Exp. (10), G indicates a signal source vector such as a
pulse wave, and O indicates an observation signal vector. The
eigenvectors and eigenvalues of the separation matrix S are as
indicated in Exp. (11) and Exp. (12). When the observation signal O
is equal to the eigenvector V, Exp. (13) holds because of the
relationship between the eigenvector and eigenvalue of a matrix.
The norm of the separated signal source vector G is expressed by
Exp, (14).
[ Exp . 23 ] G = S 0 ( 10 ) V 1 = 1 2 [ - 1 - 1 ] , V 2 = 1 2 [ - 1
1 ] ( 11 ) .lamda. 1 = 1 + 2 , .lamda. 2 = 1 ( 12 ) G = SV =
.lamda. V ( 13 ) G 1 2 = .lamda. 1 V 1 2 = 1 + 2 , G 2 2 = .lamda.
2 V 2 2 = 1 ( 14 ) ##EQU00009##
When .epsilon.<1, .lamda. has a large value.
[0199] FIG. 15 shows a noise magnification coefficient obtained
from Exp. (14).
[0200] In the figure, .PHI.N is indicated by a ratio to .PHI.S, and
.PHI.S is assumed to be 0.55. When .PHI.N/.PHI.S=1.2, the noise
magnification coefficient is about 15 times over, when
.PHI.N/.PHI.S=1.3, the noise magnification coefficient is about 10
times, and, when .PHI.N/.PHI.S=1, the noise magnification
coefficient is infinite.
[0201] (3) Noise Magnification Direction and Noise Magnification
Coefficient
[0202] The noise magnification coefficient is shown in FIG. 15.
Here, the noise magnification direction is checked. As noises of
norm 1 to be applied to the observation signal, sin of an amplitude
1 is added to the IR observation signal, and cos is added to the R
observation signal.
[0203] Independent random noise N(0, 1) is studied. FIGS. 16A and
16B show results of a simulation in which .PHI.S and .PHI.N of the
separation matrix are set as .PHI.S=0.55 and .PHI.N/.PHI.S=1.3.
[0204] The circle at the center of FIG. 16A is a unit circle formed
by sin and cos. The dashed line indicates the direction of the
eigenvector of the separation matrix in the case where
.PHI.N/.PHI.S=1.3.
[0205] The ellipse indicates the locus drawn by a separated signal
which is obtained by separating the signal forming the unit circle
with the separation matrix. The amplitude of the observation signal
is increased in the direction of the eigenvector. The amplitude is
indicated by the length between the apex of the long axis and the
origin, and, when .PHI.N/.PHI.S=1.3, is about 10 times. In FIG. 15,
when .PHI.N/.PHI.S=1.3, the magnification coefficient is about 10
times. Therefore, the results coincide with each other.
[0206] Similarly, the circular portion in FIG. 16B indicates the
applied random noise. The peak amplitude forms a substantially
circle. The dashed line indicates the eigenvector of the separation
matrix. Also in the case of random noise, the noise magnification
direction is maximum in the direction of the eigenvector of the
separation matrix. When .PHI.N/.PHI.S=1.3, the noise magnification
coefficient is about 10 times.
[0207] Relaxation of Ill Conditions by Gating
[0208] (1) Flow of Processes
[0209] As a measure for relaxing ill conditions, gating is
proposed.
[0210] FIG. 17 shows the flow of processes of processing parameters
related to the artifact.
[0211] In gating, a gate is opened under ill conditions, and
"successively-compensated norm ratio":
S.phi..sub.N.sup.+ [Exp. 15]
is replaced with
.phi..sub.N [Exp. 32]
[0212] In the above,
.phi..sub.N [Exp. 32]
is a value which is separate from .PHI.S, and which is previously
determined.
[0213] The threshold for ill conditions is set by an upper limit
.xi..sub.u and a lower limit .xi..sub.1 of .xi.. Here, .xi. is a
coefficient which multiplies .PHI.S by .xi..sub.u or .xi..sub.1
times, and determined by FIG. 15.
[0214] For example, is a coefficient in which .xi..sub.u=1.3 and
.xi..sub.1=0.7, and which is symmetric about 1.
[0215] When
.xi..sub.1.phi..sub.S>S.phi..sub.N.sup.+(J)>.xi..sub.u.phi..sub.S
[Exp. 24]
the parameter of the separation matrix is set to .PHI.S;
S.phi..sub.N.sup.+ [Exp. 15]
When
.xi..sub.1.phi..sub.S.ltoreq.S.phi..sub.N.sup.+(J).ltoreq..xi..sub.u.phi-
..sub.S [Exp. 30]
the parameter of the separation matrix is set to .PHI.S:
.phi..sub.N [Exp. 32]
Here, "gated successively-compensated norm ratio" is expressed
by:
S.phi..sub.N.sup.+g [Exp. 28]
[0216] (2) Selection of .xi..
[0217] When .xi. is selected to .xi.=.PHI.N/.PHI.S=1.3, for
example, the noise magnification coefficient is about 10. When the
signal-to-noise ratio (SNR) of the observation signal is ensured to
be 1/100 (-40 dB), the SNR after separation can be expected to be
about 1/10 (-20 dB).
[0218] Magnifying observation noises constitute a vector directed
toward the periphery of the direction of the eigenvector of the
mixing matrix. When separated from the direction of the
eigenvector, the noise magnification coefficient is reduced as
indicated by the ellipse of FIG. 16A.
[0219] (3) Parameter Values Used in Stable Zone of Pulse Wave
[0220] When the gating is
.xi..sub.1.phi..sub.S.ltoreq.S.phi..sub.N.sup.+(J).ltoreq..xi..sub.u.phi-
..sub.S [Exp. 25]
the parameter of the separation matrix is set to .PHI.S;
.phi..sub.N [Exp. 32]
[0221] In bloodless tissue, .PHI.N is about 1. Therefore,
.phi..sub.N [Exp. 32]
is set to 1.
When
[0222] .phi..sub.N [Exp. 32]
is selected as to satisfy the following relationship,
.phi..sub.N>>.phi..sub.S, [Exp. 33]
the separation matrix is approximated by Exp. (15), and the pulse
wave in the stable zone is projected as it is.
S = 1 ( .PHI. N - .0. S ) [ .PHI. N - 1 - .0. S 1 [ , S .apprxeq. [
1 - 1 .PHI. N - .0. S .PHI. N 1 .PHI. N [ .apprxeq. [ 1 0 0 0 ] (
15 ) ##EQU00010##
[0223] Evaluation Function and Evaluation of Compensation
[0224] The "true value of norm ratio"
.phi..sub.N.sup.true [Exp. 3]
is unknown.
[0225] Therefore, the degree that
S.phi..sub.N.sup.+g approaches to .phi..sub.N.sup.true [Exp.
27]
is not known. Therefore, the result of separation by "gated
successively-compensated norm ratio"
S.phi..sub.N.sup.g [Exp. 28]
is evaluated by an evaluation function H of Exp. (20). In the
expression, [.SIGMA.] means a variance-covariance matrix of the
separated pulse wave signal vector p shown in Exp. (16) and the
artifact signal vector n.
[0226] H is a ratio of absolute values of trace [.SIGMA.] and
on-diagonal element 2.SIGMA..sub.12=2.SIGMA..sub.21. When
compensation is adequately performed, [.SIGMA.] approaches a
diagonal matrix. As the value of H is smaller, the independences of
p and n are higher, and the separation is more excellent.
[ Exp . 29 ] [ .SIGMA. ] := [ .SIGMA. 11 .SIGMA. 12 .SIGMA. 21
.SIGMA. 22 ] = [ p n ] T [ p n ] ( 16 ) H := 2 .SIGMA. 12 trace [
.SIGMA. ] ( 17 ) ##EQU00011##
[0227] FIGS. 18A to 18D show results of separation in which the
pulse wave is separated from the waveforms in FIGS. 14A and
14B.
[0228] A symbol of | is drawn at the start point of an artifact
zone, and that of > is drawn at the end point.
[0229] FIG. 18A shows a result of the case where separation is
performed by "successively-compensated norm ratio"
S.phi..sub.N.sup.+ [Exp. 15]
without conducting gating. In this case, k=10. In zones where ill
conditions are caused, the amplitude is increased, and spikes are
generated.
[0230] FIG. 18B shows a result of the case where separation is
performed by "successively-compensated norm ratio"
S.phi..sub.N.sup.+ [Exp. 15]
while the gating factors are set so that .xi..sub.u=1.3,
.xi..sub.1=0.7, and k=10. In this case, spikes remain. Spikes are
generated outside the thresholds .xi..sub.u>1.3 and
.xi..sub.1<0.7. The residual spikes will be described later.
[0231] FIG. 18C shows a result of the case where separation is
performed while the gating factors are set so that .xi..sub.u=1.3,
.xi..sub.1=0.7, and k=60. In this case, spikes are not generated.
In all of first, second, and third zones of the artifact, the
artifact is greatly reduced by separation by the
successively-compensated norm ratio. Without adjustment, the value
of the evaluation function is H=0.0382.
[0232] FIG. 18D shows a result of the case where separation is
performed by the norm ratio .PHI.N of the whole observation zone.
The value of the evaluation function is H 0.2781.
[0233] FIG. 19 shows results of a process in which k=60 is set,
gating is performed by three combinations of .xi..sub.u and
.xi..sub.1, and the pulse wave is separated.
[0234] It is seen that, when the interval between .xi..sub.u and
.xi..sub.1 is narrowed, spike are frequently generated. When
.xi..sub.u=1.2 and .xi..sub.1=0.8, spikes are not generated.
[0235] When the threshold width is excessively increased, gating is
frequently performed, and zones where adequate
"successively-compensated norm ratio" is used are reduced.
Therefore, the quality of separation is lowered.
[0236] Consideration of Residual Spikes
[0237] In FIG. 18B, even after gating, spikes remain in several
places.
[0238] Therefore, the character of spikes in the vicinity of 6
seconds will be studied.
[0239] FIG. 20A to 20D show trends of the pulse wave between 5.7 to
6.2 seconds in FIG. 18B, and "gated successively-compensated norm
ratio"
S.phi..sub.N.sup.+g [Exp. 28]
In the figure, the time axis is expanded.
[0240] FIG. 20A shows the pulse wave which is separated by gating
with k=10, and in which plural residual spikes exist before 5.8
seconds and in the vicinity of 5.9 seconds.
[0241] The solid line in FIG. 20B shows a trend of "gated
successively-compensated norm ratio"
S.phi..sub.N.sup.+g [Exp. 28]
on which gating has been performed. The symbols ".largecircle."
indicate a trend of "successively-compensated norm ratio"
S.phi..sub.N.sup.+ [Exp. 15]
on which gating has not been performed.
[0242] In the ordinate of the trend, an apex for displaying the
vicinities of the thresholds is cut off.
[0243] The dashed lines indicate thresholds by which gating is
performed. The thresholds are .xi..sub.u=1.3 and
.xi..sub.1=0.7.
[0244] In the zones where the symbols ".largecircle." are within
the thresholds (for example, from the vicinity of 5.8 seconds to
before 5.9 seconds), gating is performed.
[0245] In gating, "gated successively-compensated norm ratio" is
replaced with
.phi..sub.N [Exp. 32]
which is previously determined in the zone.
[0246] The zone is shown by the straight-line portion of a value 1
which is in the vicinity of 5.8 to 5.9 seconds in FIG. 20B.
[0247] In places where the trend of "gated successively-compensated
norm ratio" is outside the thresholds, residual spikes are
generated a little before 5.8 seconds and in the vicinity of 5.9
seconds.
[0248] From the results, it is seen that gating is correctly
performed within the thresholds which are designated by
default.
[0249] FIG. 20C shows the pulse wave which is separated with k=17.
In the trend, spikes disappear.
[0250] In FIG. 20D, the whole trend of "successively-compensated
norm ratio" is above the thresholds, and hence gating is not
performed.
[0251] Residual spikes are generated outside the thresholds which
are designated by default. The spikes are generated by increase of
the amplitude which is caused because the observation noise vector
is in the same direction as the direction of the eigenvector of the
separation matrix.
[0252] Relaxation of Ill Conditions by Regularization Parameter
[0253] As shown in Exp. (18), a regularization parameter is added
as an additional term to the separation matrix, and .lamda. which
is an arbitrary small value is adjusted so that the value of the
evaluation function is minimum. In determination of .lamda.,
recurrent calculation is required, and hence there is a
disadvantage that it is difficult to adjust.
[ Exp . 31 ] S = ( M T M + .lamda. 2 [ 1 0 0 1 ] ) - 1 M T ( 18 )
##EQU00012##
[0254] FIGS. 21A and 21B show results of the relaxation of ill
conditions by the regularization parameter.
[0255] The observation waveforms of FIGS. 14A and 14B are used.
[0256] FIG. 21A shows an example in which ill conditions are
relaxed with .lamda.=0.05 and k=10. When .lamda.=0.05, the value of
the evaluation function is H=0.0042 or minimum. However, many
spikes remain.
[0257] FIG. 21B shows an example in which ill conditions are
relaxed with .lamda.=0.465 and k=10. Spikes disappear, but the
pulse wave is not well separated. The value of the evaluation
function is H=0.888 or poor.
[0258] Example of Process of Pulse Wave Buried in Tapping
Artifact
[0259] FIGS. 22A to 22C show examples in which the pulse wave that
is buried in a tapping artifact is separated with using the same
parameter as that in FIG. 18C which are the gating factors of k=60,
.lamda..sub.u=1.3, and .xi..sub.1=0.7.
[0260] FIG. 22A shows an observation waveform of IR. The pulse wave
image is buried in the artifact and hardly observed.
[0261] FIGS. 22B and 22C show a pulse wave which is separated by
the successively-compensated norm ratio due to gating. In FIG. 22B,
the pulse wave image is well separated in the tapping zone, and
spikes are not generated. In FIG. 22C, a result of a 17-point
moving average process in consideration of the cycle length of the
pulse wave is shown. The pulse wave image is clearer than that of
FIG. 22B. The value of the evaluation function is H=0.1302 and
H=0.0253.
[0262] From the above description, it is obvious that the pulse
wave can be separated by the successively-compensated norm ratio
which performs the gating in the invention, without designating an
artifact zone.
[0263] According to an aspect of the invention, it is possible to
realize a signal processing method, signal processing apparatus,
and pulse photometer using the same in which, even in the case
where a large artifact such as motion of a hand or a foot, bitter
sobbing, shiver, or cough is contained, a signal component can be
separated more correctly.
* * * * *