CN111458300A - Sparse projection-based Nesterov homotopic perturbation iteration optical tomography reconstruction method and system - Google Patents

Sparse projection-based Nesterov homotopic perturbation iteration optical tomography reconstruction method and system Download PDF

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CN111458300A
CN111458300A CN202010256539.9A CN202010256539A CN111458300A CN 111458300 A CN111458300 A CN 111458300A CN 202010256539 A CN202010256539 A CN 202010256539A CN 111458300 A CN111458300 A CN 111458300A
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佟珊珊
毕波
唐锦萍
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Shaanxi Normal University
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Abstract

The invention discloses a Nesterov homotopy perturbation iteration optical tomography reconstruction method and a system based on sparse projection, wherein the method comprises the following steps: the method comprises the steps that a Nesterov homotopy perturbation iteration optical tomography reconstruction algorithm based on sparse projection adopts a radiation transmission equation model to describe the transmission process of photons in an object to be detected; establishing a measurement system of the optical tomography problem through multi-light source excitation and finite angle average measurement data; and adopting a Nesterov accelerated homotopic perturbation iterative regularization reconstruction algorithm, and performing sparse projection on each iteration result. In the invention, a Nesterov acceleration method is introduced on the basis of homotopy perturbation iterative regularization to realize further acceleration of the algorithm and improve the imaging speed of optical tomography; a sparse projection strategy is introduced, the sparse characteristic of a solved target is fully utilized, the detail information of an abnormal area can be effectively identified, and the imaging resolution is improved.

Description

Sparse projection-based Nesterov homotopic perturbation iteration optical tomography reconstruction method and system
Technical Field
The invention belongs to the technical field of optical tomography, and particularly relates to a Nesterov homotopic perturbation iteration optical tomography reconstruction method and system based on sparse projection.
Background
Optical tomography is a new technology developed in recent years, can realize qualitative and quantitative imaging on a detected object, and has important application in the aspects of detection, control and the like of industrial engineering, such as monitoring of atmospheric pollution, combustion conditions of internal combustion engines and the like.
Optical tomography is to reconstruct the distribution of optical parameters inside the detected object by combining boundary measurement data with a photon propagation model, and can be used to obtain structural and functional information inside the imaging region. Due to the limited measurement data, the complex propagation process of photons in the imaging region and the like, the optical parameter reconstruction presents serious ill-qualification, the quantization degree of the reconstructed image is poor, and the high-resolution imaging of the imaging object is difficult to obtain. Multiple light source excitation can increase measurement data and alleviate the problem of unsuitability to some extent, but multiple light source excitation strategies can significantly increase the amount of calculation of the problem, thus placing higher requirements on the reconstruction algorithm.
In optical tomography, an imaging object generally has locality, namely optical parameter distribution on an abnormal region is sparse compared with that of the whole imaging region, most of traditional nonlinear iterative algorithms for optical parameter identification are based on L andweber iterative regularization expansion, on one hand, L andweber iterative regularization calculation speed is low and is difficult to meet the requirements of people on fast imaging, on the other hand, a reconstruction solution has an excessive smoothness phenomenon and is difficult to reflect detail information in the imaging region, and therefore effective detection cannot be carried out.
In summary, a new method and system for reconstructing optical tomography based on sparse projection Nesterov homotopic perturbation iteration are needed.
Disclosure of Invention
The invention aims to provide a Nesterov homotopic perturbation iteration optical tomography reconstruction method and system based on sparse projection, and aims to solve the technical problems of low imaging speed and low imaging resolution in the existing optical tomography. The method and the system can rapidly and highly-distinguishably image the imaging area.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to a Nesterov homotopy perturbation iteration optical tomography reconstruction method based on sparse projection, which comprises the following steps of:
step 1, setting the distribution of optical parameters, excitation light sources and detectors of a region to be detected;
step 2, combining a photon propagation model and a finite element theory, and establishing a nonlinear relation between unknown optical parameters in an imaging region and measurement data; the method comprises the following steps of describing the transmission process of photons in an imaging region to be detected by adopting a radiation transmission equation model; establishing a measurement system of the optical tomography problem through multi-light source excitation and finite angle average measurement data;
3, based on the nonlinear relation established in the step 2, inverting the optical parameters by using a Nesterov acceleration homotopy perturbation iterative regularization method based on sparse projection to obtain a distribution image of the optical parameters in the region; and carrying out sparse projection on each iteration result to ensure the reconstruction quality.
The invention has the further improvement that the step 1 specifically comprises the following steps:
setting the distribution condition of the optical parameters in the region to be measured, including: the size of the imaging area and the number, position and shape of the internal abnormal area;
the method for setting the distribution of the excitation light sources and the detectors comprises the following steps: adopting multi-light source excitation and multi-angle measurement strategies; the light source points and the detectors are distributed on the outer surface of the area to be detected in an equidistant and staggered mode.
The invention has the further improvement that the step 2 specifically comprises the following steps:
step 2.1, using a radiation transmission equation as a propagation model of photons in an imaging object, combining angle average data of boundary measurement to construct an edge value problem for describing an optical tomography process, dispersing an imaging region into N triangular elements based on finite element theory and RTE-2D-MAT L AB software, converting the edge value problem into a nonlinear relation between surface measurement data and internal optical parameters, wherein the expression is as follows,
Fi(x)＝yi,i＝1,…,Ns，
in the formula (I), the compound is shown in the specification,
Figure BDA0002437557120000031
is the absorption coefficient of the water-soluble polymer,
Figure BDA0002437557120000032
for measuring data, NdIs the number of detectors, NsThe number of light sources;
the invention will be referred to as the following equation: f (x) y;
step 2.2, based on the optical parameter distribution condition preset in the step 1, utilizing RTE _2D _ MAT L AB software to calculate forward problems, and obtaining real measurement data y;
step 2.3, adding noise to the real measurement data obtained in step 2.2 to obtain measurement data y containing noiseThe relational expression of the optical parameter with respect to the measurement data containing noise is,
F(x)＝y,
wherein, | | y-y | | is less than or equal to the noise level.
The invention has the further improvement that the step 3 specifically comprises the following steps:
step 3.1, taking the absorption coefficient of the background of the imaging area as an initial value
Figure BDA0002437557120000033
Nesterov parameter α ═ 3;
step 3.2, constructing a Nesterov acceleration homotopy perturbation iteration regularization algorithm, and obtaining an iteration result according to the regularization algorithm; the expression of the regularization algorithm is as follows:
Figure BDA0002437557120000034
wherein α is a Nesterov parameter, k is the number of iteration steps,
Figure BDA0002437557120000035
is the intermediate variable of the Nesterov,
Figure BDA0002437557120000036
is composed of
Figure BDA0002437557120000037
Associated operator of skFor searching direction, iteration step size
Figure BDA0002437557120000038
Step 3.3, projecting the iteration result obtained in step 3.2 to L of optical parameters1Ball BR:＝{x:||x||1≤R}BR:＝{x:||x||1R is less than or equal to R, the reconstruction precision of the abnormal area is improved, the expression is,
Figure BDA0002437557120000039
wherein the content of the first and second substances,
Figure BDA0002437557120000041
is a heading ball BRThe projection operator of (3);
step 3.4, iteration is carried out through the step 3.2 and the step 3.3, and the reconstruction result of the kth iteration is obtained
Figure BDA0002437557120000042
When it is satisfied with
Figure BDA0002437557120000043
When so, the iteration stops; wherein tau is a parameter greater than 1.
A further improvement of the present invention is that step 3.3 specifically comprises:
(1) will be provided with
Figure BDA0002437557120000044
The absolute values of the elements in (1) are arranged in descending order to obtain a group of new sequences
Figure BDA0002437557120000045
(2) Searching
Figure BDA0002437557120000046
So that it satisfies:
Figure BDA0002437557120000047
wherein the threshold operator S is defined as
Figure BDA0002437557120000048
(3) Order to
Figure BDA0002437557120000049
And
Figure BDA00024375571200000410
then
Figure BDA00024375571200000411
The invention further improves the method and also comprises the following steps:
and 4, comparing the optical parameter distribution real image with the distribution image obtained in the step 3 through a relative error or sectional diagram index, and evaluating a reconstruction result.
In step 4, the reconstruction error is expressed as,
Figure BDA00024375571200000412
wherein x represents the reconstructed absorption coefficient,
Figure BDA00024375571200000413
represents the true absorption coefficient;
according to the sparse projection-based Nesterov homotopy perturbation iteration optical tomography reconstruction method, when the 120 th iteration is performed, RE is 0.1649.
The invention relates to a Nesterov homotopy perturbation iterative optical tomography reconstruction system based on sparse projection, which comprises:
the parameter presetting module is used for setting the distribution of optical parameters, excitation light sources and detectors of the area to be detected;
the nonlinear relation building module is used for building a nonlinear relation between the unknown optical parameters in the imaging region and the measured data by combining the photon propagation model and the finite element theory; the method comprises the following steps of describing the transmission process of photons in an imaging region to be detected by adopting a radiation transmission equation model; establishing a measurement system of the optical tomography problem through multi-light source excitation and finite angle average measurement data;
the reconstruction module is used for inverting the optical parameters by utilizing a Nesterov acceleration homotopy perturbation iteration regularization method based on sparse projection based on the established nonlinear relation to obtain a distribution image of the optical parameters in the region; and carrying out sparse projection on each iteration result to ensure the reconstruction quality.
Compared with the prior art, the invention has the following beneficial effects:
in the method, homotopic perturbation iteration regularization can be regarded as an acceleration algorithm of L and weber iteration regularization, and a Nesterov acceleration method is introduced on the basis to realize further acceleration of the algorithm, so that the iteration times required by imaging are remarkably reduced, and the imaging speed of optical tomography can be further improved1In the sphere, the sparse characteristic of the solved target is fully utilized, the detail information of the imaging area can be effectively identified, and the imaging resolution is improved. Aiming at the multi-light-source strategy, the calculation amount of each iteration in the reconstruction process is increased, and the method only needs relatively less iteration times to obtain the high-resolutionImaging information, thereby achieving the effect of saving the total calculated amount and the calculated time.
The optical tomography system provided by the invention can effectively improve the imaging speed and the imaging quality based on the method provided by the invention.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art are briefly introduced below; it is obvious that the drawings in the following description are some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.
FIG. 1 is a schematic block diagram of a flow of an optical tomography reconstruction method based on sparse projection and Nesterov accelerated homotopic perturbation iteration according to an embodiment of the present invention;
FIG. 2 is a schematic block diagram of a flow chart of a further optical tomography reconstruction method based on sparse projection and Nesterov accelerated homotopic perturbation iteration according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating the true distribution of absorption coefficients for a circular imaging region for numerical simulation in an embodiment of the present invention;
FIG. 4 is a comparison graph of the reconstruction of the absorption coefficient of a circular imaging region for numerical simulation in an embodiment of the present invention; fig. 4 (a) is a schematic reconstruction diagram of the method according to the embodiment of the present invention, and fig. 4 (b) is a schematic reconstruction diagram of a homotopic perturbation iterative algorithm.
Detailed Description
In order to make the purpose, technical effect and technical solution of the embodiments of the present invention clearer, the following clearly and completely describes the technical solution of the embodiments of the present invention with reference to the drawings in the embodiments of the present invention; it is to be understood that the described embodiments are only some of the embodiments of the present invention. Other embodiments, which can be derived by one of ordinary skill in the art from the disclosed embodiments without inventive faculty, are intended to be within the scope of the invention.
Referring to fig. 1, an optical tomography reconstruction method based on sparse projection nervov homotopic perturbation iteration in an embodiment of the present invention specifically includes the following steps:
s1 setting the optical parameters of the area to be detected, the distribution of the excitation light source and the detector;
s2, establishing a nonlinear relation to obtain measurement data;
s3, obtaining a two-dimensional optical parameter distribution image of an imaging region through an optical tomography reconstruction algorithm of Nesterov accelerated homoenergetic perturbation iteration based on sparse projection.
The method comprises the following steps of describing the transmission process of photons in an imaging region to be detected by adopting a radiation transmission equation model;
establishing a measurement system of the optical tomography problem through multi-light source excitation and finite angle average measurement data;
adopting a Nesterov accelerated homotopic perturbation iterative regularization reconstruction algorithm; wherein, the sparse projection is carried out on each iteration result, and the reconstruction quality is ensured.
Referring to fig. 2, an optical tomography reconstruction method based on sparse projection nervov homotopic perturbation iteration in an embodiment of the present invention specifically includes the following steps:
step 1, setting information of an imaging area to be detected and distribution conditions of an excitation light source and a detector;
step 2, combining a photon propagation model and a finite element theory, and establishing a nonlinear relation between unknown optical parameters in an imaging region and measurement data;
step 3, for the nonlinear relation established in the step 2, inverting the optical parameters by using a Nesterov acceleration homotopy perturbation iterative regularization method based on sparse projection to obtain a distribution image of the optical parameters in the region;
optionally, the method further includes: and 4, displaying a result, comparing the optical parameter distribution real image with the reconstructed image through indexes such as relative errors, a cross-sectional diagram and the like, and evaluating the reconstructed result.
Preferably, step 1 specifically comprises:
step 1.1, setting the distribution condition of optical parameters in an imaging area to be detected, namely the size of the imaging area and the number, position and shape of internal abnormal areas;
step 1.2, setting the distribution condition of the light source and the detector; the multi-light source excitation and multi-angle measurement strategy is adopted, and light source points and detectors are distributed on the outer surface of the region to be detected in an equidistant and staggered mode.
Preferably, step 2 specifically comprises:
step 2.1, establishing a nonlinear relation, which comprises the steps of adopting a radiation transmission equation as a propagation model of photons in an imaging object, combining angle average data of boundary measurement to construct and describe an edge value problem of the optical tomography process, dispersing an imaging region into N triangular elements by means of finite element theory and RTE-2D-MAT L AB software, converting the edge value problem into a nonlinear relation between surface measurement data and internal optical parameters, and expressing the nonlinear relation as follows:
Fi(x)＝yi,i＝1,…,Ns，
in the formula (I), the compound is shown in the specification,
Figure BDA0002437557120000081
is the absorption coefficient of the water-soluble polymer,
Figure BDA0002437557120000082
for measuring data, NdIs the number of detectors, NsFor the number of light sources, this equation set is abbreviated as f (x) y;
step 2.2, acquiring measurement data, namely acquiring known preset optical parameter distribution, and performing forward problem calculation by utilizing RTE-2D _ MAT L AB software to obtain real measurement data y;
step 2.3, adding noise to the real measurement data to obtain measurement data y containing noiseThe relational expression of the optical parameter and the measurement data containing noise is:
F(x)＝y,
wherein, | | y-y | | is less than or equal to the noise level.
Preferably, step 3 specifically comprises:
step 3.1, initial value andparameter selection: the absorption coefficient of the background of the imaging area is used as an initial value
Figure BDA0002437557120000083
Nesterov parameter α ═ 3;
step 3.2, constructing a Nesterov acceleration homotopy perturbation iterative regularization algorithm, wherein the expression is as follows:
Figure BDA0002437557120000084
wherein α is a Nesterov parameter, k is the number of iteration steps,
Figure BDA0002437557120000085
is the intermediate variable of the Nesterov,
Figure BDA0002437557120000086
is composed of
Figure BDA0002437557120000087
Associated operator of skFor searching direction, iteration step size
Figure BDA0002437557120000088
Step 3.3, projecting the iteration result to L of optical parameters1Ball BR:＝{x:||x||1R is less than or equal to R to improve the reconstruction precision of the abnormal area, the expression is,
Figure BDA0002437557120000089
wherein the content of the first and second substances,
Figure BDA00024375571200000810
is a heading ball BRThe projection operator of (2).
In the embodiment of the invention, the specific projection process is as follows:
firstly, the following components are mixed
Figure BDA0002437557120000091
The absolute values of the elements in (1) are arranged in descending order to obtain a group of new sequences
Figure BDA0002437557120000092
Second, search
Figure BDA0002437557120000093
So that it satisfies:
Figure BDA0002437557120000094
wherein the threshold operator S is defined as
Figure BDA0002437557120000095
Finally, let
Figure BDA0002437557120000096
And
Figure BDA0002437557120000097
then
Figure BDA0002437557120000098
Step 3.4, iteration is carried out through the steps 3.2 to 3.3 to obtain a reconstruction result of the kth iteration
Figure BDA0002437557120000099
When it is satisfied with
Figure BDA00024375571200000910
When so, the iteration stops; wherein tau is a parameter greater than 1.
In the embodiment of the invention, the radiation transmission equation is taken as a photon propagation model, and compared with the traditional diffusion approximation equation, the propagation process of photons in the imaging region can be more accurately described, so that the model error is effectively reduced. The problem discomfort is effectively relieved by adopting multi-light source excitation and multi-angle measurement. Homotopy takingThe dynamic iteration regularization can be regarded as an acceleration algorithm of L and weber iteration regularization, on the basis, a Nesterov acceleration method is introduced to realize further acceleration of the algorithm and improve the imaging speed of optical tomography, meanwhile, a sparse projection strategy is introduced according to the sparse distribution characteristic of an abnormal region in an imaging object, and the obtained iteration result is projected to L of a solution1In the sphere, the sparse characteristic of the solved target is fully utilized, the detail information of an abnormal area can be effectively identified, and the imaging resolution is improved. The optical tomography method based on the Nesterov acceleration homotopy perturbation iterative algorithm of sparse projection can effectively improve the imaging speed and the imaging quality.
The effect of the invention on the two-dimensional problem application is described in detail below with reference to the reconstruction result.
Referring to fig. 3, fig. 3 shows the actual distribution of the optical parameters of the region to be detected; the detected area is a circular area with the radius of 5cm and the origin as the center of a circle; the inside of the device comprises two circular abnormal areas with different sizes, wherein the radius of one circle center is 0.9mm at the (0,2.5mm) and the radius of one circle center is 1cm at the (0, -2.5 mm).
Dividing the image into 1666 elements by RTE-2D-MAT L AB software for forward solving, and distributing 12 light sources and 12 detectors at the boundary of a circular region in an equidistant and staggered manner, wherein the absorption coefficient of the background of the imaged object is 0.01mm-1The absorption coefficient of the two circular abnormal regions is 0.02mm-1。
Referring to fig. 4, fig. 4 is a comparison of reconstruction effects of homotopic perturbation method at different iteration times according to the present invention; wherein, (a) in fig. 4 is the reconstruction result of the algorithm of the present invention at different iteration times; fig. 4 (b) is a reconstruction result of the homotopic perturbation iteration algorithm at different times, in fig. 4, AHPI represents a sparse projection-based Nesterov accelerated homotopic perturbation iteration algorithm proposed by the present invention, and HIP represents a homotopic perturbation iteration algorithm. In the embodiment of the invention, the position and the shape of the abnormal region can be accurately identified by using the method of the embodiment of the invention in 120 iterations, and the reconstructed background is clear. And by adopting the homotopic perturbation iteration method, the background disturbance of the reconstruction result is obvious in 120 iterations, and information such as the position and the outline of an abnormal region is not clearly identified.
The reconstruction error is expressed as
Figure BDA0002437557120000101
Wherein x represents the reconstructed absorption coefficient,
Figure BDA0002437557120000102
representing the true absorption coefficient.
RE is 0.1649 at the 120 th iteration based on the reconstruction result of the present invention, and RE is 0.2158 at the 120 th iteration based on the reconstruction result of the homotopic perturbation iteration.
In summary, as can be seen from fig. 4, the positions, shapes, and the absorption coefficients of the abnormal regions identified according to the present invention are quantized very close to the real situation, and the iteration coefficients and reconstruction time required to achieve the reconstruction accuracy are significantly less than those of the homotopic perturbation iteration. Therefore, the method provided by the invention is an effective optical tomography method.
The invention relates to a Nesterov homotopy perturbation iterative optical tomography reconstruction system based on sparse projection, which comprises:
the parameter presetting module is used for setting the distribution of optical parameters, excitation light sources and detectors of the area to be detected;
the nonlinear relation building module is used for building a nonlinear relation between the unknown optical parameters in the imaging region and the measured data by combining the photon propagation model and the finite element theory; the method comprises the following steps of describing the transmission process of photons in an imaging region to be detected by adopting a radiation transmission equation model; establishing a measurement system of the optical tomography problem through multi-light source excitation and finite angle average measurement data;
the reconstruction module is used for inverting the optical parameters by utilizing a Nesterov acceleration homotopy perturbation iteration regularization method based on sparse projection based on the established nonlinear relation to obtain a distribution image of the optical parameters in the region; and carrying out sparse projection on each iteration result to ensure the reconstruction quality.
Wherein, in the nonlinear relation construction module,
the method adopts a radiation transmission equation as a propagation model of photons in an imaging object, combines angle average data of boundary measurement to construct and describe an edge value problem of the optical tomography process, disperses an imaging area into N triangular elements based on finite element theory and RTE-2D-MAT L AB software, converts the edge value problem into a nonlinear relation between surface measurement data and internal optical parameters, and has the expression,
Fi(x)＝yi,i＝1,…,Ns，
in the formula (I), the compound is shown in the specification,
Figure BDA0002437557120000111
is the absorption coefficient of the water-soluble polymer,
Figure BDA0002437557120000112
for measuring data, NdIs the number of detectors, NsFor the number of light sources, this equation set is abbreviated as f (x) y;
based on the preset optical parameter distribution condition, utilizing RTE-2D-MAT L AB software to perform forward problem calculation to obtain real measurement data y;
adding noise to the obtained real measurement data to obtain measurement data y containing noiseThe relational expression of the optical parameter with respect to the measurement data containing noise is,
F(x)＝y,
wherein, | | y-y | | is less than or equal to the noise level.
Wherein, in the reconstruction module,
the absorption coefficient of the background of the imaging area is used as an initial value
Figure BDA0002437557120000113
Nesterov parameter α ═ 3;
constructing a Nesterov acceleration homotopy perturbation iteration regularization algorithm, and obtaining an iteration result according to the regularization algorithm; the expression of the regularization algorithm is as follows:
Figure BDA0002437557120000121
wherein α is a Nesterov parameter, k is the number of iteration steps,
Figure BDA0002437557120000122
is the intermediate variable of the Nesterov,
Figure BDA0002437557120000123
is composed of
Figure BDA0002437557120000124
Associated operator of skFor searching direction, iteration step size
Figure BDA0002437557120000125
L projecting the obtained iteration result to optical parameters1Ball BR:＝{x:||x||1R is less than or equal to R, the reconstruction precision of the abnormal area is improved, the expression is,
Figure BDA0002437557120000126
wherein the content of the first and second substances,
Figure BDA0002437557120000127
is a heading ball BRThe projection operator of (3);
the iteration obtains the reconstruction result of the kth iteration
Figure BDA0002437557120000128
When it is satisfied with
Figure BDA0002437557120000129
When so, the iteration stops; wherein tau is a parameter greater than 1.
In summary, the invention discloses an optical tomography reconstruction algorithm and system based on sparse projection Nesterov accelerated homotopic perturbation iteration, which adopts a radiation transmission equation model to describe the transmission process of photons in an object to be detected; establishing a measurement system of the optical tomography problem through multi-light source excitation and finite angle average measurement data; and adopting a Nesterov accelerated homotopic perturbation iterative regularization reconstruction algorithm, and performing sparse projection on each iteration result. The invention can effectively improve the imaging speed and the imaging quality: the radiation transmission equation is used as a photon propagation model, the propagation process of photons in the imaging object is more accurately described, and model errors are effectively reduced. And the multi-light source excitation and multi-angle measurement are adopted, so that the ill-posed problem is effectively alleviated. A Nesterov acceleration method is introduced on the basis of homotopy perturbation iterative regularization, so that further acceleration of an algorithm is realized, and the imaging speed of optical tomography is improved. Meanwhile, aiming at the sparse distribution characteristic of an abnormal region in an imaging object, a sparse projection strategy is introduced, the sparse characteristic of a solved target is fully utilized, the detail information of the abnormal region can be effectively identified, and the imaging resolution is improved.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can make modifications and equivalents to the embodiments of the present invention without departing from the spirit and scope of the present invention, which is set forth in the claims of the present application.

Claims (10)

1. A Nesterov homotopic perturbation iteration optical tomography reconstruction method based on sparse projection is characterized by comprising the following steps:
step 1, setting the distribution of optical parameters, excitation light sources and detectors of a region to be detected;
step 2, combining a photon propagation model and a finite element theory, and establishing a nonlinear relation between unknown optical parameters in an imaging region and measurement data; the method comprises the following steps of describing the transmission process of photons in an imaging region to be detected by adopting a radiation transmission equation model; establishing a measurement system of the optical tomography problem through multi-light source excitation and finite angle average measurement data;
3, based on the nonlinear relation established in the step 2, inverting the optical parameters by using a Nesterov acceleration homotopy perturbation iterative regularization method based on sparse projection to obtain a distribution image of the optical parameters in the region; and carrying out sparse projection on each iteration result to ensure the reconstruction quality.
2. The optical tomography reconstruction method based on sparse projection Nesterov homotopic perturbation iteration as claimed in claim 1, wherein step 1 specifically comprises:
setting the distribution condition of the optical parameters in the region to be measured, including: the size of the imaging area and the number, position and shape of the internal abnormal area;
the method for setting the distribution of the excitation light sources and the detectors comprises the following steps: adopting multi-light source excitation and multi-angle measurement strategies; the light source points and the detectors are distributed on the outer surface of the area to be detected in an equidistant and staggered mode.
3. The optical tomography reconstruction method based on sparse projection Nesterov homotopic perturbation iteration as claimed in claim 1, wherein the step 2 specifically comprises:
step 2.1, using a radiation transmission equation as a propagation model of photons in an imaging object, combining angle average data of boundary measurement to construct an edge value problem for describing an optical tomography process, dispersing an imaging region into N triangular elements based on finite element theory and RTE-2D-MAT L AB software, converting the edge value problem into a nonlinear relation between surface measurement data and internal optical parameters, wherein the expression is as follows,
Fi(x)＝yi,i＝1,…,Ns，
in the formula (I), the compound is shown in the specification,
Figure FDA0002437557110000021
is the absorption coefficient of the water-soluble polymer,
Figure FDA0002437557110000028
for measuring data, NdIs the number of detectors, NsThe number of light sources;
the above expression is abbreviated as f (x) y;
step 2.2, based on the optical parameter distribution condition preset in the step 1, utilizing RTE _2D _ MAT L AB software to calculate forward problems, and obtaining real measurement data y;
step 2.3, adding noise to the real measurement data obtained in step 2.2 to obtain measurement data y containing noiseThe relational expression of the optical parameter with respect to the measurement data containing noise is,
F(x)＝y,
wherein, | | y-y | | is less than or equal to the noise level.
4. The sparse projection-based Nesterov homotopic perturbation iterative optical tomography reconstruction method according to claim 3, wherein the step 3 specifically comprises:
step 3.1, taking the absorption coefficient of the background of the imaging area as an initial value
Figure FDA0002437557110000023
Nesterov parameter α ═ 3;
step 3.2, constructing a Nesterov acceleration homotopy perturbation iteration regularization algorithm, and obtaining an iteration result according to the regularization algorithm; the expression of the regularization algorithm is as follows:
Figure FDA0002437557110000024
wherein α is a Nesterov parameter, k is the number of iteration steps,
Figure FDA0002437557110000025
is a Nesterov intermediate variable, skFor searching direction, iteration step size
Figure FDA0002437557110000026
Is composed of
Figure FDA0002437557110000027
The companion operator of (a);
step 3.3, projecting the iteration result obtained in step 3.2 to L of optical parameters1Ball BR:＝{x:||x||1R is less than or equal to R, the reconstruction precision of the abnormal area is improved, the expression is,
Figure FDA0002437557110000031
wherein the content of the first and second substances,
Figure FDA0002437557110000032
is a heading ball BRThe projection operator of (3);
step 3.4, iteration is carried out through the step 3.2 and the step 3.3, and the reconstruction result of the kth iteration is obtained
Figure FDA0002437557110000033
When it is satisfied with
Figure FDA0002437557110000034
When so, the iteration stops; wherein tau is a parameter greater than 1.
5. The sparse projection-based Nesterov homotopic perturbation iterative optical tomography reconstruction method according to claim 4, wherein the step 3.3 specifically comprises:
(1) will be provided with
Figure FDA0002437557110000035
The absolute values of the elements in (1) are arranged in descending order to obtain a group of new sequences
Figure FDA0002437557110000036
(2) Searching
Figure FDA0002437557110000037
So that it satisfies:
Figure FDA0002437557110000038
wherein the threshold operator S is defined as
Figure FDA0002437557110000039
(3) Order to
Figure FDA00024375571100000310
And
Figure FDA00024375571100000311
then
Figure FDA00024375571100000312
6. The sparse projection-based Nesterov homotopic perturbation iterative optical tomography reconstruction method according to claim 1, further comprising:
and 4, comparing the optical parameter distribution real image with the distribution image obtained in the step 3 through a relative error or sectional diagram index, and evaluating a reconstruction result.
7. The optical tomography reconstruction method of Nesterov homotopic perturbation iteration based on sparse projection as claimed in claim 6, wherein in step 4, the reconstruction error expression is,
Figure FDA00024375571100000313
wherein x represents the reconstructed absorption coefficient,
Figure FDA00024375571100000314
represents the true absorption coefficient;
according to the sparse projection-based Nesterov homotopy perturbation iteration optical tomography reconstruction method, when the 120 th iteration is performed, RE is 0.1649.
8. An optical tomography reconstruction system based on Nesterov homotopy perturbation iteration of sparse projection is characterized by comprising the following components:
the parameter presetting module is used for setting the distribution of optical parameters, excitation light sources and detectors of the area to be detected;
the nonlinear relation building module is used for building a nonlinear relation between the unknown optical parameters in the imaging region and the measured data by combining the photon propagation model and the finite element theory; the method comprises the following steps of describing the transmission process of photons in an imaging region to be detected by adopting a radiation transmission equation model; establishing a measurement system of the optical tomography problem through multi-light source excitation and finite angle average measurement data;
the reconstruction module is used for inverting the optical parameters by utilizing a Nesterov acceleration homotopy perturbation iteration regularization method based on sparse projection based on the established nonlinear relation to obtain a distribution image of the optical parameters in the region; and carrying out sparse projection on each iteration result to ensure the reconstruction quality.
9. The sparse projection-based Nesterov homotopic perturbation iterative optical tomography reconstruction system according to claim 8, characterized in that in the nonlinear relation construction module,
the method adopts a radiation transmission equation as a propagation model of photons in an imaging object, combines angle average data of boundary measurement to construct and describe an edge value problem of the optical tomography process, disperses an imaging area into N triangular elements based on finite element theory and RTE-2D-MAT L AB software, converts the edge value problem into a nonlinear relation between surface measurement data and internal optical parameters, and has the expression,
Fi(x)＝yi,i＝1,…,Ns，
in the formula (I), the compound is shown in the specification,
Figure FDA0002437557110000041
is the absorption coefficient of the water-soluble polymer,
Figure FDA0002437557110000042
for measuring data, NdIs the number of detectors, NsThe number of light sources;
the expression is summarized as: f (x) y;
based on the preset optical parameter distribution condition, utilizing RTE-2D-MAT L AB software to perform forward problem calculation to obtain real measurement data y;
adding noise to the obtained real measurement data to obtain measurement data y containing noiseThe relational expression of the optical parameter with respect to the measurement data containing noise is,
F(x)＝y,
wherein, | | y-y | | is less than or equal to the noise level.
10. The sparse projection-based Nesterov homotopic perturbation iterative optical tomography reconstruction system according to claim 8, wherein in the reconstruction module,
the absorption coefficient of the background of the imaging area is used as an initial value
Figure FDA0002437557110000051
Nesterov parameter α ═ 3;
constructing a Nesterov acceleration homotopy perturbation iteration regularization algorithm, and obtaining an iteration result according to the regularization algorithm; the expression of the regularization algorithm is as follows:
Figure FDA0002437557110000052
wherein α is a Nesterov parameter, k is the number of iteration steps,
Figure FDA0002437557110000053
is a Nesterov intermediate variable, skFor searching direction, iteration step size
Figure FDA0002437557110000054
Is composed of
Figure FDA0002437557110000055
The companion operator of (a);
l projecting the obtained iteration result to optical parameters1Ball BR:＝{x:||x||1R is less than or equal to R, the reconstruction precision of the abnormal area is improved, the expression is,
Figure FDA0002437557110000056
wherein the content of the first and second substances,
Figure FDA0002437557110000057
is a heading ball BRThe projection operator of (3);
the iteration obtains the reconstruction result of the kth iteration
Figure FDA0002437557110000058
When it is satisfied with
Figure FDA0002437557110000059
When so, the iteration stops; wherein tau is a parameter greater than 1.
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