CN111820868B - Biological photoacoustic endoscopic image reconstruction method and system - Google Patents

Biological photoacoustic endoscopic image reconstruction method and system Download PDF

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CN111820868B
CN111820868B CN201910317346.7A CN201910317346A CN111820868B CN 111820868 B CN111820868 B CN 111820868B CN 201910317346 A CN201910317346 A CN 201910317346A CN 111820868 B CN111820868 B CN 111820868B
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孙正
孙立爽
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North China Electric Power University
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Abstract

The invention discloses a biological photoacoustic endoscopic image reconstruction method and a biological photoacoustic endoscopic image reconstruction system. The reconstruction method specifically comprises the following steps: acquiring a photoacoustic signal measured value of the existing sound attenuation received by the ultrasonic transducer; establishing an association equation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal; discretizing the association equation to obtain an association matrix; calculating a generalized inverse matrix of the association matrix by adopting a singular value decomposition method to obtain an association generalized inverse matrix; calculating an unattenuated photoacoustic signal of the imaging tissue according to the associated generalized inverse matrix and the photoacoustic signal measurement value to obtain an imaging unattenuated photoacoustic signal; reconstructing a light absorption energy distribution diagram on the cross section of the cavity according to the unattenuated photoacoustic signal. The resolution of biological photoacoustic endoscopic imaging is improved by establishing an equation of correlation between the measured value and the unattenuated photoacoustic signal.

Description

Biological photoacoustic endoscopic image reconstruction method and system
Technical Field
The invention relates to the technical field of medical imaging, in particular to a biological photoacoustic endoscopic image reconstruction method and system.
Background
Biological photoacoustic endoscopic imaging combines photoacoustic tomography with endoscopic detection technology, and simultaneously has high contrast of optical imaging and high resolution of ultrasonic imaging. The biological photoacoustic endoscopic imaging principle is as follows: the special catheter with the laser probe and the ultrasonic detector is inserted into the cavity, the probe emits short pulse laser to irradiate surrounding tissues, the tissues absorb laser energy to generate thermal elastic expansion, ultrasonic waves are generated and spread to the surfaces of the tissues, after the ultrasonic detector detects a photoacoustic signal, the photoacoustic signal is sent to the computer, and the computer reconstructs an initial sound pressure distribution diagram or a light absorption energy distribution diagram on the cross section of the cavity, so that the shape and the light absorption characteristic of the cross section of the cavity can be reflected.
Because of the complexity of biological tissue, current research into biological photoacoustic endoscopic image reconstruction is based on the assumption of a non-attenuating acoustic medium with uniform acoustic properties. However, in practical applications, most biological tissues have acoustic attenuation characteristics, so that the biological photoacoustic endoscopic image reconstructed on the premise of the assumption generally has problems of distortion, artifact, position offset and reduction of imaging depth, and the problem of acoustic attenuation of the tissues to be imaged cannot be solved.
Disclosure of Invention
The invention aims to provide a biological photoacoustic endoscopic image reconstruction method and system capable of reducing image distortion, artifacts and the like caused by acoustic attenuation of imaging tissues.
In order to achieve the above object, the present invention provides the following solutions:
a biological optoacoustic endoscopic image reconstruction method specifically comprises the following steps:
acquiring a photoacoustic signal measured value of the existing sound attenuation received by the ultrasonic transducer;
establishing an association equation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal;
discretizing the association equation to obtain an association matrix;
calculating a generalized inverse matrix of the association matrix by adopting a singular value decomposition method to obtain an association generalized inverse matrix;
calculating an unattenuated photoacoustic signal of the imaging tissue according to the associated generalized inverse matrix and the photoacoustic signal measurement value to obtain an imaging unattenuated photoacoustic signal;
reconstructing a light absorption energy distribution diagram on the cross section of the cavity according to the unattenuated photoacoustic signal.
Optionally, the establishing an association equation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal specifically includes:
the equation of correlation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal is:
Figure BDA0002033554600000021
wherein FT [. Cndot.]Is a fourier transform; p (r, t) is the ultrasonic transducer at position r,Sound pressure measurement values of the photoacoustic signals with sound attenuation acquired at time t; i (t) is a function of time of the incident laser pulse; i is an imaginary unit; c 0 Is the reference phase velocity of the ultrasonic wave; omega is the angular frequency of the ultrasonic wave; sgn (ω) is a sign function; p is p ideal (r, t) is the sound pressure of the silence attenuation ideal photoacoustic signal acquired by the ultrasonic transducer at the position r and at the time t; alpha (ω) is the linear attenuation coefficient of an ultrasonic wave as it propagates in a lossy medium:
α(ω)＝α 0 |ω| n (2)
wherein ,α0 ≈(10 -7 /2π)cm -1 rad -1 s is a constant coefficient of linear attenuation of ultrasonic waves when the ultrasonic waves propagate in a lossy medium; n is a power, n=1 when ultrasound propagates in biological tissue;
inverse fourier transform is performed on both ends of formula (1), resulting in:
Figure BDA0002033554600000022
wherein ,FT-1 [·]Representing an inverse fourier transform; and (3) making:
Figure BDA0002033554600000023
wherein ,
Figure BDA0002033554600000024
is the intermediate sound pressure data obtained from p (r, t). Then formula (3) is rewritten as:
Figure BDA0002033554600000025
optionally, the discretizing processes the association equation, and obtaining the association matrix specifically includes:
the two-dimensional discrete form of formula (5) is:
Figure BDA0002033554600000031
wherein ,rm Is the m-th measurement position of the ultrasonic transducer, m=1, 2, N; n is the number of measurement positions; t is t j Is the j-th moment, j=1, 2,., L; t is t k ' is the kth time, k=1, 2,. -%, L; l is the length of the photoacoustic pressure time series acquired at each measurement position;
the matrix form of formula (6) is:
Figure BDA0002033554600000032
wherein the matrix
Figure BDA0002033554600000033
Is an N x L dimensional parameter matrix of the correlation equation:
Figure BDA0002033554600000034
wherein ,
Figure BDA0002033554600000035
is->
Figure BDA0002033554600000036
The element on the mth row j of (c) is calculated from the photoacoustic signal measurement value in the presence of acoustic attenuation according to equation (4), m=1, 2, N, j=1, 2,. -%, L; matrix P ideal Is an N x L dimensional matrix of silently attenuated photoacoustic signal data:
Figure BDA0002033554600000037
/>
wherein ,pideal (r m ,t k ') is a matrix P ideal M=1, 2,..n, k=1, 2,..l; the matrix Θ is an association matrix in the l×l dimension:
Figure BDA0002033554600000038
optionally, the calculating the unattenuated photoacoustic signal of the imaged tissue according to the associated generalized inverse matrix and the photoacoustic signal measurement value specifically includes:
obtaining a matrix of silence-attenuated ideal photoacoustic signal data according to equation (7):
Figure BDA0002033554600000041
wherein ,Θ-1 Is a generalized inverse matrix of Θ, and the specific calculation method is as follows:
singular value decomposition of matrix Θ:
Θ＝USV T (12)
wherein U is an L×L orthogonal matrix; s is an L x L dimension diagonal matrix composed of singular values of Θ; v is represented by Θ T L×L-dimensional orthogonal matrix composed of eigenvectors of Θ T Is the transposed matrix of Θ; v (V) T Is the transposed matrix of V; generalized inverse matrix Θ of Θ -1 The method comprises the following steps:
Θ -1 ＝VS -1 U T (13)。
optionally, the reconstructing the light absorption energy distribution map on the cross section of the cavity according to the unattenuated photoacoustic signal specifically includes:
the light absorption energy distribution over the cavity cross section is:
Figure BDA0002033554600000042
wherein a (r) is the light absorption energy at position r in the cavity cross-section; p is p ideal (r m ,t k ') is a matrix P ideal M=1, 2, N, k=1, 2,; c (C) p Is the specific heat capacity of the tissue; c U (r) is the propagation velocity of the ultrasound wave at position r in the tissue; beta is the isobaric expansion coefficient of the tissue；l 0 Is the perpendicular distance from the tissue surface at position r.
In order to achieve the above object, the present invention further provides the following solutions:
a biological photoacoustic endoscopic image reconstruction system, the reconstruction system specifically comprising:
the measured value acquisition module is used for acquiring the photoacoustic signal measured value of the existing sound attenuation received by the ultrasonic transducer;
an association equation establishing module for establishing an association equation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal;
the discretization processing module is used for discretizing the association equation to obtain an association matrix;
the generalized inverse matrix calculation module is used for calculating the generalized inverse matrix of the correlation matrix by adopting a singular value decomposition method to obtain the correlation generalized inverse matrix;
the non-attenuation photoacoustic signal calculation module is used for calculating the non-attenuation photoacoustic signal of the imaging tissue according to the associated generalized inverse matrix and the photoacoustic signal measurement value to obtain an imaging non-attenuation photoacoustic signal;
and the light absorption energy distribution map reconstruction module is used for reconstructing a light absorption energy distribution map on the cross section of the cavity according to the unattenuated photoacoustic signal.
Optionally, the association equation establishing module specifically includes:
an association equation establishing unit for establishing an association equation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal as:
Figure BDA0002033554600000051
wherein FT [. Cndot.]Is a fourier transform; p (r, t) is a sound pressure measurement value of the photoacoustic signal with sound attenuation acquired by the ultrasonic transducer at the position r and at the moment t; i (t) is a function of time of the incident laser pulse; i is an imaginary unit; c 0 Is the reference phase velocity of the ultrasonic wave; omega is the angular frequency of the ultrasonic wave; sgn @ω) is a sign function; p is p ideal (r, t) is the sound pressure of the silence attenuation ideal photoacoustic signal acquired by the ultrasonic transducer at the position r and at the time t; alpha (ω) is the linear attenuation coefficient of an ultrasonic wave as it propagates in a lossy medium:
α(ω)＝α 0 |ω| n (2)
wherein ,α0 ≈(10 -7 /2π)cm -1 rad -1 s is a constant coefficient of linear attenuation of ultrasonic waves when the ultrasonic waves propagate in a lossy medium; n is a power, n=1 when ultrasound propagates in biological tissue;
and the middle sound pressure data module is used for carrying out inverse Fourier transform on the two ends of the formula (1) to obtain:
Figure BDA0002033554600000052
wherein ,FT-1 [·]Representing an inverse fourier transform; and (3) making:
Figure BDA0002033554600000053
wherein ,
Figure BDA0002033554600000054
is the intermediate sound pressure data obtained from p (r, t). Then formula (3) is rewritten as:
Figure BDA0002033554600000055
optionally, the discretization processing module specifically includes:
a two-dimensional discrete unit for the two-dimensional discrete form of formula (5) being:
Figure BDA0002033554600000056
wherein ,rm Is the mth measurement position of the ultrasonic transducer, m=1,2.., N; n is the number of measurement positions; t is t j Is the j-th moment, j=1, 2,., L; t is t k ' is the kth time, k=1, 2,. -%, L; l is the length of the photoacoustic pressure time series acquired at each measurement position;
the matrix form of formula (6) is:
Figure BDA0002033554600000061
parameter matrix establishing unit for matrix
Figure BDA0002033554600000062
Is an N x L dimensional parameter matrix of the correlation equation: />
Figure BDA0002033554600000063
wherein ,
Figure BDA0002033554600000064
is->
Figure BDA0002033554600000065
The element on the mth row j of (c) is calculated from the photoacoustic signal measurement value in the presence of acoustic attenuation according to equation (4), m=1, 2, N, j=1, 2,. -%, L; matrix P ideal Is an N x L dimensional matrix of silently attenuated photoacoustic signal data:
Figure BDA0002033554600000066
wherein ,pideal (r m ,t k ') is a matrix P ideal M=1, 2,..n, k=1, 2,..l; the matrix Θ is an association matrix in the l×l dimension:
Figure BDA0002033554600000067
according to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention provides a biological photoacoustic endoscopic image reconstruction method and a biological photoacoustic endoscopic image reconstruction system. The reconstruction method specifically comprises the following steps: acquiring a photoacoustic signal measured value of the existing sound attenuation received by the ultrasonic transducer; establishing an association equation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal; discretizing the association equation to obtain an association matrix; calculating a generalized inverse matrix of the association matrix by adopting a singular value decomposition method to obtain an association generalized inverse matrix; by establishing the incidence matrix and then calculating the incidence matrix, the distortion and the artifact caused by acoustic attenuation in the reconstructed image are reduced, and the focusing effect of the image is effectively improved; calculating an unattenuated photoacoustic signal of the imaging tissue according to the associated generalized inverse matrix and the photoacoustic signal measurement value to obtain an imaging unattenuated photoacoustic signal; and reconstructing a light absorption energy distribution diagram on the cross section of the cavity according to the unattenuated photoacoustic signal, so that the resolution of biological photoacoustic endoscopic imaging is improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a biological photoacoustic endoscopic image reconstruction method provided by the invention;
fig. 2 is a block diagram of a biological photoacoustic endoscopic image reconstruction system provided by the present invention;
FIG. 3 is a schematic diagram of a cross section of a cavity with acoustic attenuation characteristics and propagation of photoacoustic signals in tissue provided by the present invention;
fig. 4 is a schematic diagram of a linear scanning mode of photoacoustic endoscopic imaging provided by the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a biological photoacoustic endoscopic image reconstruction method and system capable of reducing image distortion, artifacts and the like caused by acoustic attenuation of imaging tissues.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
A biological optoacoustic endoscopic image reconstruction method specifically comprises the following steps:
step 100: acquiring a photoacoustic signal measured value of the existing sound attenuation received by the ultrasonic transducer;
step 200: establishing an association equation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal;
step 300: discretizing the association equation to obtain an association matrix;
step 400: calculating a generalized inverse matrix of the association matrix by adopting a singular value decomposition method to obtain an association generalized inverse matrix;
step 500: calculating an unattenuated photoacoustic signal of the imaging tissue according to the associated generalized inverse matrix and the photoacoustic signal measurement value to obtain an imaging unattenuated photoacoustic signal;
step 600: reconstructing a light absorption distribution diagram on the cross section of the cavity according to the unattenuated photoacoustic signal.
The step 200: establishing an association equation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal specifically includes:
as shown in fig. 3, the imaging catheter is located at the center of the cavity cross section, the ultrasound probe is disposed at the tip of the imaging catheter, the imaging catheter performs circumferential scanning on surrounding tissues during rotation, and the imaging plane is perpendicular to the imaging catheter. Taking the center of the imaging catheter as a coordinate origin, taking the horizontal rightward direction as an X-axis positive direction, taking the direction vertical to the X-axis direction as a Y-axis positive direction, and establishing an X-Y plane rectangular coordinate system on an imaging plane; the imaging catheter center outwards sequentially comprises an inner cavity 8, a catheter wall inner membrane 9 and a catheter wall outer membrane 10, an ultrasonic transducer 11 is arranged in the inner cavity 8, and an absorber 12 is arranged on the catheter wall outer membrane 10.
The equation of correlation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal is:
Figure BDA0002033554600000081
wherein FT [. Cndot.]Is a fourier transform; p (r, t) is a sound pressure measurement value of the photoacoustic signal with sound attenuation acquired by the ultrasonic transducer at the position r and at the moment t; i (t) is a function of time of the incident laser pulse; i is an imaginary unit; c 0 Is the reference phase velocity of the ultrasonic wave; omega is the angular frequency of the ultrasonic wave; sgn (ω) is a sign function; p is p ideal (r, t) is the sound pressure of the silence attenuation ideal photoacoustic signal acquired by the ultrasonic transducer at the position r and at the time t; alpha (ω) is the linear attenuation coefficient of an ultrasonic wave as it propagates in a lossy medium:
α(ω)＝α 0 |ω| n (2)
wherein ,α0 ≈(10 -7 /2π)cm -1 rad -1 s is a constant coefficient of linear attenuation of ultrasonic waves when the ultrasonic waves propagate in a lossy medium; n is a power, n=1 when ultrasound propagates in biological tissue;
inverse fourier transform is performed on both ends of formula (1), resulting in:
Figure BDA0002033554600000082
wherein ,FT-1 [·]Representing an inverse fourier transform; and (3) making:
Figure BDA0002033554600000091
wherein ,
Figure BDA0002033554600000092
is the intermediate sound pressure data obtained from p (r, t). Then formula (3) is rewritten as:
Figure BDA0002033554600000093
the step 300: discretizing the association equation to obtain an association matrix specifically comprises:
the two-dimensional discrete form of formula (5) is:
Figure BDA0002033554600000094
wherein ,rm Is the m-th measurement position of the ultrasonic transducer, m=1, 2, N; n is the number of measurement positions; t is t j Is the j-th moment, j=1, 2,., L; t is t k ' is the kth time, k=1, 2,. -%, L; l is the length of the photoacoustic pressure time series acquired at each measurement position;
the matrix form of formula (6) is:
Figure BDA0002033554600000095
wherein the matrix
Figure BDA0002033554600000096
Is an N x L dimensional parameter matrix of the correlation equation:
Figure BDA0002033554600000097
wherein ,
Figure BDA0002033554600000098
is->
Figure BDA0002033554600000099
The element on the mth row j of (c) is calculated from the photoacoustic signal measurement value in the presence of acoustic attenuation according to equation (4), m=1, 2, N, j=1, 2,. -%, L; matrix P ideal Is an N x L dimensional matrix of silently attenuated photoacoustic signal data:
Figure BDA00020335546000000910
wherein ,pideal (r m ,t k ') is a matrix P ideal M=1, 2,..n, k=1, 2,..l; the matrix Θ is an association matrix in the l×l dimension:
Figure BDA0002033554600000101
the step 500: calculating the unattenuated photoacoustic signal of the imaged tissue from the associated generalized inverse matrix and the photoacoustic signal measurements specifically comprises:
obtaining a matrix of silence-attenuated ideal photoacoustic signal data according to equation (7):
Figure BDA0002033554600000102
wherein ,Θ-1 Is a generalized inverse matrix of Θ, and the specific calculation method is as follows:
singular value decomposition of matrix Θ:
Θ＝USV T (12)
wherein U is an L×L orthogonal matrix; s is an L x L dimension diagonal matrix composed of singular values of Θ; v is represented by Θ T L×L-dimensional orthogonal matrix composed of eigenvectors of Θ T Is the transposed matrix of Θ; v (V) T Is the transposed matrix of V; generalized inverse matrix Θ of Θ -1 The method comprises the following steps:
Θ -1 ＝VS -1 U T (13)。
the step 600: reconstructing a light absorption distribution diagram on the cross section of the cavity according to the unattenuated photoacoustic signal specifically comprises:
the light absorption energy distribution over the cavity cross section is:
Figure BDA0002033554600000103
wherein a (r) is the light absorption energy at position r in the cavity cross-section; p is p ideal (r m ,t k ') is a matrix P ideal M=1, 2, N, k=1, 2,; c (C) p Is the specific heat capacity of the tissue; c U (r) is the propagation velocity of the ultrasound wave at position r in the tissue; beta is the isobaric expansion coefficient of the tissue; as shown in fig. 4, l 0 Is the perpendicular distance from the tissue surface at position r.
In order to achieve the above object, the present invention further provides the following solutions:
as shown in fig. 2, the present invention provides a biological photoacoustic endoscopic image reconstruction system, which specifically includes:
a measured value acquisition module 1, configured to acquire a photoacoustic signal measured value of attenuation of a presence sound received by the ultrasonic transducer;
an association equation establishing module 2 for establishing an association equation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal;
the discretization processing module 3 is used for discretizing the correlation equation to obtain a correlation matrix;
the generalized inverse matrix calculation module 4 is used for calculating the generalized inverse matrix of the correlation matrix by adopting a singular value decomposition method to obtain the correlation generalized inverse matrix;
an unattenuated photoacoustic signal calculation module 5, configured to calculate an unattenuated photoacoustic signal of the imaged tissue according to the associated generalized inverse matrix and the photoacoustic signal measurement value, and obtain an imaged unattenuated photoacoustic signal;
and the light absorption energy distribution map reconstruction module 6 is used for reconstructing a light absorption energy distribution map on the cross section of the cavity according to the unattenuated photoacoustic signal.
The association equation establishing module 2 specifically includes:
an association equation establishing unit for establishing an association equation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal as:
Figure BDA0002033554600000111
wherein FT [. Cndot.]Is a fourier transform; p (r, t) is a sound pressure measurement value of the photoacoustic signal with sound attenuation acquired by the ultrasonic transducer at the position r and at the moment t; i (t) is a function of time of the incident laser pulse; i is an imaginary unit; c 0 Is the reference phase velocity of the ultrasonic wave; omega is the angular frequency of the ultrasonic wave; sgn (ω) is a sign function; p is p ideal (r, t) is the sound pressure of the silence attenuation ideal photoacoustic signal acquired by the ultrasonic transducer at the position r and at the time t; alpha (ω) is the linear attenuation coefficient of an ultrasonic wave as it propagates in a lossy medium:
α(ω)＝α 0 |ω| n (2)
wherein ,α0 ≈(10 -7 /2π)cm -1 rad -1 s is a constant coefficient of linear attenuation of ultrasonic waves when the ultrasonic waves propagate in a lossy medium; n is a power, n=1 when ultrasound propagates in biological tissue;
and the middle sound pressure data module is used for carrying out inverse Fourier transform on the two ends of the formula (1) to obtain:
Figure BDA0002033554600000112
wherein ,FT-1 [·]Representing an inverse fourier transform; and (3) making:
Figure BDA0002033554600000121
wherein ,
Figure BDA0002033554600000122
is the intermediate sound pressure data obtained from p (r, t). Then formula (3) is rewritten as:
Figure BDA0002033554600000123
the discretization processing module 3 specifically includes:
a two-dimensional discrete unit for the two-dimensional discrete form of formula (5) being:
Figure BDA0002033554600000124
wherein ,rm Is the m-th measurement position of the ultrasonic transducer, m=1, 2, N; n is the number of measurement positions; t is t j Is the j-th moment, j=1, 2,., L; t is t k ' is the kth time, k=1, 2,. -%, L; l is the length of the photoacoustic pressure time series acquired at each measurement position;
the matrix form of formula (6) is:
Figure BDA0002033554600000125
parameter matrix establishing unit for matrix
Figure BDA0002033554600000126
Is an N x L dimensional parameter matrix of the correlation equation: />
Figure BDA0002033554600000127
wherein ,
Figure BDA0002033554600000128
is->
Figure BDA0002033554600000129
The element on the mth row j of (c) is calculated from the photoacoustic signal measurement value in the presence of acoustic attenuation according to equation (4), m=1, 2, N, j=1, 2,. -%, L; matrix P ideal Is an N x L dimensional matrix of silently attenuated photoacoustic signal data:
Figure BDA00020335546000001210
wherein ,pideal (r m ,t k ') is a matrix P ideal M=1, 2,..n, k=1, 2,..l; the matrix Θ is an association matrix in the l×l dimension:
Figure BDA0002033554600000131
in the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.

Claims (4)

1. The biological photoacoustic endoscopic image reconstruction method is characterized by comprising the following steps of:
acquiring a photoacoustic signal measured value with sound attenuation received by an ultrasonic transducer;
establishing an association equation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal;
discretizing the association equation to obtain an association matrix;
calculating a generalized inverse matrix of the association matrix by adopting a singular value decomposition method to obtain an association generalized inverse matrix;
calculating unattenuated photoacoustic signals of imaging tissues according to the correlation generalized inverse matrix and the photoacoustic signal measurement values, and obtaining imaging unattenuated photoacoustic signals;
reconstructing a light absorption distribution diagram on the cross section of the cavity according to the unattenuated photoacoustic signal;
the establishing an equation of correlation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal specifically includes:
the equation of correlation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal is:
Figure FDA0004112073700000011
wherein FT [. Cndot.]Is a fourier transform; p (r, t) is a sound pressure measurement value of the photoacoustic signal with sound attenuation acquired by the ultrasonic transducer at the position r and at the moment t; i (t) is a function of time of the incident laser pulse; i is an imaginary unit; c 0 Is the reference phase velocity of the ultrasonic wave; omega is the angular frequency of the ultrasonic wave; sgn (ω) is a sign function; the target (r, t) is the sound pressure of the silence attenuation ideal photoacoustic signal acquired by the ultrasonic transducer at the position r and at the moment t; alpha (ω) is the linear attenuation coefficient of an ultrasonic wave as it propagates in a lossy medium:
α(ω)＝α 0 |ω| n (2)
wherein ,α0 ≈(10 -7 /2π)cm -1 rad -1 s is a constant coefficient of linear attenuation of ultrasonic waves when the ultrasonic waves propagate in a lossy medium; n is a power, n=1 when ultrasound propagates in biological tissue;
inverse fourier transform is performed on both ends of formula (1), resulting in:
Figure FDA0004112073700000012
wherein ,FT-1 [·]Representing an inverse fourier transform; and (3) making:
Figure FDA0004112073700000021
wherein ,
Figure FDA0004112073700000022
is the intermediate sound pressure data obtained from p (r, t); then formula (3) is rewritten as:
Figure FDA0004112073700000023
the discretizing the association equation to obtain an association matrix specifically includes:
the two-dimensional discrete form of formula (5) is:
Figure FDA0004112073700000024
wherein ,rm Is the m-th measurement position of the ultrasonic transducer, m=1, 2, N; n is the number of measurement positions; t is t j Is the j-th moment, j=1, 2,., L; t is t k ' is the kth time, k=1, 2,. -%, L; l is the length of the photoacoustic pressure time series acquired at each measurement position;
the matrix form of formula (6) is:
Figure FDA0004112073700000025
wherein the matrix
Figure FDA0004112073700000026
Is an association equationN x L dimensional parameter matrix of (c):
Figure FDA0004112073700000027
wherein ,
Figure FDA0004112073700000028
is->
Figure FDA0004112073700000029
The element on the mth row j of (c) is calculated from the photoacoustic signal measurement value in the presence of acoustic attenuation according to equation (4), m=1, 2, N, j=1, 2,. -%, L; matrix P ideal Is an N x L dimensional matrix of silently attenuated photoacoustic signal data:
Figure FDA0004112073700000031
wherein ,pideal (r m ,t k ') is a matrix P ideal M=1, 2,..n, k=1, 2,..l; the matrix Θ is an association matrix in the l×l dimension:
Figure FDA0004112073700000032
2. the method for reconstructing a biological photoacoustic endoscopic image according to claim 1, wherein said calculating unattenuated photoacoustic signals of said imaged tissue from said associated generalized inverse matrix and said photoacoustic signal measurements comprises in particular:
obtaining a matrix of silence-attenuated ideal photoacoustic signal data according to equation (7):
Figure FDA0004112073700000033
wherein ,Θ-1 Is a generalized inverse matrix of Θ, and the specific calculation method is as follows:
singular value decomposition of matrix Θ:
Θ＝USV T (12)
wherein U is an L×L orthogonal matrix; s is an L x L dimension diagonal matrix composed of singular values of Θ; v is represented by Θ T L×L-dimensional orthogonal matrix composed of eigenvectors of Θ T Is the transposed matrix of Θ; v (V) T Is the transposed matrix of V; generalized inverse matrix Θ of Θ -1 The method comprises the following steps:
Θ -1 ＝VS -1 U T (13)。
3. the method for reconstructing a biological photoacoustic endoscopic image according to claim 1, wherein said reconstructing a light absorption profile on a cross section of a cavity from said unattenuated photoacoustic signal comprises:
the light absorption energy distribution over the cavity cross section is:
Figure FDA0004112073700000041
wherein a (r) is the light absorption energy at position r in the cavity cross-section; p is p ideal (r m ,t k ') is a matrix P ideal M=1, 2, N, k=1, 2,; c (C) p Is the specific heat capacity of the tissue; c U (r) is the propagation velocity of the ultrasound wave at position r in the tissue; beta is the isobaric expansion coefficient of the tissue; l (L) 0 Is the perpendicular distance from the tissue surface at position r.
4. A biological photoacoustic endoscopic image reconstruction system, comprising:
the measured value acquisition module is used for acquiring the photoacoustic signal measured value with sound attenuation received by the ultrasonic transducer;
an association equation establishing module for establishing an association equation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal;
the discretization processing module is used for discretizing the association equation to obtain an association matrix;
the generalized inverse matrix calculation module is used for calculating the generalized inverse matrix of the correlation matrix by adopting a singular value decomposition method to obtain the correlation generalized inverse matrix;
the non-attenuation photoacoustic signal calculation module is used for calculating non-attenuation photoacoustic signals of imaging tissues according to the associated generalized inverse matrix and the photoacoustic signal measurement values to obtain imaging non-attenuation photoacoustic signals;
the light absorption energy distribution map reconstruction module is used for reconstructing a light absorption energy distribution map on the cross section of the cavity according to the unattenuated photoacoustic signal;
the association equation establishing module specifically comprises:
an association equation establishing unit for establishing an association equation between the photoacoustic signal measurement value and the unattenuated photoacoustic signal as:
Figure FDA0004112073700000042
wherein FT [. Cndot.]Is a fourier transform; p (r, t) is a sound pressure measurement value of the photoacoustic signal with sound attenuation acquired by the ultrasonic transducer at the position r and at the moment t; i (t) is a function of time of the incident laser pulse; i is an imaginary unit; c 0 Is the reference phase velocity of the ultrasonic wave; omega is the angular frequency of the ultrasonic wave; sgn (ω) is a sign function; the target (r, t) is the sound pressure of the silence attenuation ideal photoacoustic signal acquired by the ultrasonic transducer at the position r and at the moment t; alpha (ω) is the linear attenuation coefficient of an ultrasonic wave as it propagates in a lossy medium:
α(ω)＝α 0 |ω| n (2)
wherein ,α0 ≈(10 -7 /2π)cm -1 rad -1 s is a constant coefficient of linear attenuation of ultrasonic waves when the ultrasonic waves propagate in a lossy medium; n is a power, n=1 when ultrasound propagates in biological tissue; intermediate sound pressureAnd the data module is used for carrying out inverse Fourier transform on the two ends of the formula (1) to obtain:
Figure FDA0004112073700000051
wherein ,FT-1 [·]Representing an inverse fourier transform; and (3) making:
Figure FDA0004112073700000052
wherein ,
Figure FDA0004112073700000053
is the intermediate sound pressure data obtained from p (r, t); then formula (3) is rewritten as: />
Figure FDA0004112073700000054
The discretization processing module specifically comprises:
a two-dimensional discrete unit for obtaining a two-dimensional discrete form of formula (5):
Figure FDA0004112073700000055
wherein ,rm Is the m-th measurement position of the ultrasonic transducer, m=1, 2, N; n is the number of measurement positions; t is t j Is the j-th moment, j=1, 2,., L; t is t k ' is the kth time, k=1, 2,. -%, L; l is the length of the photoacoustic pressure time series acquired at each measurement position;
the matrix form of formula (6) is:
Figure FDA0004112073700000056
parameter matrix creation listElements for use in which the matrix
Figure FDA0004112073700000057
Is an N x L dimensional parameter matrix of the correlation equation:
Figure FDA0004112073700000061
wherein ,
Figure FDA0004112073700000062
is->
Figure FDA0004112073700000063
The element on the mth row j of (c) is calculated from the photoacoustic signal measurement value in the presence of acoustic attenuation according to equation (4), m=1, 2, N, j=1, 2,. -%, L; matrix P ideal Is an N x L dimensional matrix of silently attenuated photoacoustic signal data:
Figure FDA0004112073700000064
wherein ,pideal (r m ,t k ') is a matrix P ideal M=1, 2,..n, k=1, 2,..l; the matrix Θ is an association matrix in the l×l dimension:
Figure FDA0004112073700000065
/>
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