CN111458300B - Sparse projection-based Nesterov homotopic perturbation iteration optical tomography reconstruction method and system - Google Patents

Abstract

The invention discloses an optical tomography reconstruction method and system based on Nesterov homotopy perturbation iteration based on sparse projection. The transmission equation model describes the transmission process of photons in the object to be detected; the measurement system for optical tomography is established by means of multi-light source excitation and finite-angle averaged measurement data; the Nesterov-accelerated homotopy perturbation iterative regularization reconstruction algorithm is used, and the The result of each iteration is sparsely projected. In the present invention, the Nesterov acceleration method is introduced on the basis of the homotopy perturbation iterative regularization to realize further acceleration of the algorithm, which can improve the imaging speed of optical tomography; Effectively identify the details of abnormal areas and improve imaging resolution.

Description

Optical tomography reconstruction method and system based on Nesterov homotopy perturbation iteration based on sparse projection

technical field

The invention belongs to the technical field of optical tomography, and in particular relates to an iterative optical tomography reconstruction method and system based on Nesterov homotopy perturbation of sparse projection.

Background technique

Optical tomography is an emerging technology that has only been developed in recent years. It can achieve qualitative and quantitative imaging of the detected object. It has important applications in the detection and control of industrial engineering, such as monitoring air pollution and combustion of internal combustion engines. condition, etc.

Optical tomography is to reconstruct the distribution of optical parameters inside the detection object by combining the boundary measurement data with the photon propagation model, which can be used to obtain structural and functional information inside the imaging area. Due to the limited measurement data and the complex propagation process of photons in the imaging area, the optical parameter reconstruction presents serious ill-posedness and the quantification of the reconstructed image is poor, making it difficult to obtain high-resolution imaging of the imaging object. The multi-light source excitation can increase the measurement data and reduce the ill-posedness of the problem to a certain extent, but the multi-light source excitation strategy will significantly increase the computational load of the problem, so it puts forward higher requirements for the reconstruction algorithm.

In optical tomography, the imaging object generally has "locality", that is, the optical parameter distribution on the abnormal area is sparse compared to the entire imaging area. Most of the traditional nonlinear iterative algorithms for optical parameter identification are based on Landweber iterative regularization. On the one hand, the calculation speed of Landweber iterative regularization is slow, and it is difficult to meet people's needs for fast imaging; on the other hand, the reconstruction solution will appear excessively smooth. It is difficult to reflect the detailed information inside the imaging area, so that effective detection cannot be performed. In this context, the development of reconstruction algorithms with strong noise resistance, fast computation speed and high imaging accuracy has become one of the hot issues in optical tomography research.

In conclusion, there is an urgent need for a new iterative optical tomographic reconstruction method and system based on Nesterov homotopy perturbation based on sparse projection.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide an iterative optical tomography reconstruction method and system based on Nesterov homotopy perturbation of sparse projection, so as to solve the technical problems of slow imaging speed and low imaging resolution in current optical tomography . The method and system of the present invention can image the imaging region rapidly and with high resolution.

To achieve the above object, the present invention adopts the following technical solutions:

A kind of optical tomography reconstruction method based on Nesterov homotopy perturbation iteration based on sparse projection of the present invention comprises the following steps:

Step 1: Set the optical parameters of the area to be measured, the distribution of excitation light sources and detectors;

Step 2: Combine the photon propagation model and the finite element theory to establish a nonlinear relationship between the unknown optical parameters in the imaging area and the measurement data; wherein, the radiation transfer equation model is used to describe the photon transmission process in the imaging area to be inspected; excitation by multiple light sources and finite angle average measurement data to establish a measurement system for optical tomography problems;

Step 3: Based on the nonlinear relationship established in Step 2, use the Nesterov accelerated homotopy perturbation iterative regularization method based on sparse projection to invert the optical parameters, and obtain the distribution image of the optical parameters in the region; Sparse projection is used to ensure reconstruction quality.

A further improvement of the present invention is that step 1 specifically includes:

Set the distribution of optical parameters inside the area to be measured, including: the size of the imaging area and the number, location, and shape of abnormal areas inside;

Set the distribution of excitation light sources and detectors, including: using multi-light source excitation and multi-angle measurement strategies; wherein, the light source points and detectors are equidistant and staggered on the outer surface of the area to be measured.

A further improvement of the present invention is that step 2 specifically includes:

In step 2.1, the radiation transfer equation is used as the propagation model of photons in the imaging object, combined with the angle average data measured by the boundary, to construct a boundary value problem describing the optical tomography process; based on the finite element theory and RTE_2D_MATLAB software, the imaging area is discretized as N triangular elements, the boundary value problem is transformed into a nonlinear relationship between surface measurement data and internal optical parameters, and the expression is,

F _i (x)=y _i , i=1,...,N _s ,

是吸收系数，

为测量数据，N_d为探测器的个数，N_s为光源个数；In the formula,

is the absorption coefficient,

is the measurement data, N _d is the number of detectors, and N _s is the number of light sources;

The present invention is abbreviated as follows: F(x)=y;

Step 2.2, based on the optical parameter distribution preset in step 1, use RTE_2D_MATLAB software to perform forward problem calculation to obtain the real measurement data y;

In step 2.3, noise is added to the real measurement data obtained in step 2.2 to obtain measurement data y ^δ containing noise. The relationship between optical parameters and measurement data containing noise is expressed as,

F(x)=y ^δ ,

where ||y ^δ -y||≤δ, δ is the noise level.

A further improvement of the present invention is that step 3 specifically includes:

Nesterov参数α＝3；Step 3.1, take the absorption coefficient of the background of the imaging area as the initial value

Nesterov parameter α = 3;

Step 3.2, construct the Nesterov accelerated homotopy perturbation iterative regularization algorithm, and obtain the iterative result according to the regularization algorithm; the expression of the regularization algorithm is:

为Nesterov中间变量，

为

的伴随算子，s_k为搜索方向，迭代步长

Among them, α is the Nesterov parameter, k is the number of iteration steps,

is the Nesterov intermediate variable,

for

The adjoint operator of , _sk is the search direction, the iteration step size

Step 3.3, project the iterative result obtained in step 3.2 to the L ¹ -sphere of optical parameters B _R :={x:||x|| ₁ ≤R}B _R :={x:||x|| ₁ ≤R }, is used to improve the reconstruction accuracy of the abnormal area, the expression is,

为向球B_R的投影算子；in,

is the projection operator to the ball _BR ;

当满足

时，迭代停止；其中，τ为大于1的参数。Step 3.4, iterate through steps 3.2 and 3.3 to obtain the reconstruction result of the k-th iteration

when satisfied

, the iteration stops; where τ is a parameter greater than 1.

A further improvement of the present invention is that step 3.3 specifically includes:

中的元素的绝对值进行降序排列，得到一组新序列

(1) will

The absolute values of the elements in are sorted in descending order to obtain a new set of sequences

中的第n个元素，使其满足：(2) Search

The nth element in , so that it satisfies:

Among them, the threshold operator S is defined as

以及

则(3) Order

as well as

but

A further improvement of the present invention is, also includes:

In step 4, the real image of the optical parameter distribution is compared with the distribution image obtained in step 3 through the relative error or the sectional graph index, so as to evaluate the reconstruction result.

A further improvement of the present invention is that, in step 4, the reconstruction error expression is,

代表真实的吸收系数；where x represents the reconstructed absorption coefficient,

represents the true absorption coefficient;

At the 120th iteration of the Nesterov homotopy perturbation iterative optical tomography reconstruction method based on sparse projection, RE=0.1649.

A kind of optical tomography reconstruction system based on Nesterov homotopy perturbation iteration based on sparse projection of the present invention includes:

The parameter preset module is used to set the optical parameters of the area to be measured, the distribution of the excitation light source and the detector;

The nonlinear relationship building module is used to combine the photon propagation model and the finite element theory to establish the nonlinear relationship between the unknown optical parameters in the imaging area and the measurement data; the radiation transfer equation model is used to describe the photon transmission process in the imaging area to be inspected ;Establish a measurement system for optical tomography problems by means of multi-light source excitation and finite-angle averaging measurement data;

The reconstruction module is used to invert the optical parameters based on the established nonlinear relationship using the Nesterov accelerated homotopy perturbation iterative regularization method based on sparse projection, and obtain the distribution image of the optical parameters in the region; The results are sparsely projected to ensure reconstruction quality.

Compared with the prior art, the present invention has the following beneficial effects:

In the method of the present invention, the radiation transfer equation is used as the photon propagation model, which can describe the propagation process of photons in the imaging area more accurately than the traditional diffusion approximation equation, and can effectively reduce the model error; multi-light source excitation and multi-angle measurement are adopted. It can effectively slow down the pathological nature of the problem. In the method of the present invention, the iterative regularization of the homotopy perturbation can be regarded as an acceleration algorithm of the Landweber iterative regularization. On this basis, the Nesterov acceleration method is introduced to realize the further acceleration of the algorithm, which significantly reduces the number of iterations required for imaging. Further improve the imaging speed of optical tomography. In the present invention, a sparse projection strategy is introduced for the sparse characteristics of the distribution of optical parameters in the imaging area, and the obtained iterative results are projected into the L ¹ -sphere of the solution, which makes full use of the sparse characteristics of the solution target and can effectively identify the imaging area. detailed information and improve imaging resolution. For the multi-light source strategy, the calculation amount of each iteration in the reconstruction process is increased, and the method of the present invention only needs a relatively small number of iterations to obtain higher-resolution imaging information, thereby achieving the effect of saving the overall calculation amount and calculation time. .

The optical tomography system proposed by the present invention, based on the method of the present invention, can effectively improve the imaging speed and imaging quality.

Description of drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the accompanying drawings used in the description of the embodiments or the prior art; obviously, the accompanying drawings in the following description are For some embodiments of the present invention, for those of ordinary skill in the art, other drawings can also be obtained from these drawings without creative efforts.

1 is a schematic flow chart of an optical tomographic reconstruction method based on sparse projection and Nesterov accelerated homotopy perturbation iteration according to an embodiment of the present invention;

2 is a schematic flow chart of another optical tomography reconstruction method based on sparse projection and Nesterov accelerated homotopy perturbation iteration according to an embodiment of the present invention;

3 is a schematic diagram of the real distribution of the absorption coefficient of a circular imaging area used for numerical simulation in an embodiment of the present invention;

4 is a schematic diagram showing the comparison of the reconstruction results of the absorption coefficient of the circular imaging area used for numerical simulation in the embodiment of the present invention; wherein, (a) in FIG. 4 is a schematic diagram of reconstruction of the method according to the embodiment of the present invention, and FIG. (b) is the reconstruction diagram of the homotopy perturbation iterative algorithm.

Detailed ways

In order to make the purposes, technical effects and technical solutions of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention; are some embodiments of the present invention. Based on the embodiments disclosed in the present invention, other embodiments obtained by persons of ordinary skill in the art without creative work shall fall within the protection scope of the present invention.

Referring to FIG. 1 , an iterative optical tomographic reconstruction method based on Nesterov homotopy perturbation of sparse projection according to an embodiment of the present invention specifically includes the following steps:

S1 sets the optical parameters of the area to be detected, the distribution of excitation light sources and detectors;

S2 establishes a nonlinear relationship and obtains measurement data;

S3 obtains the two-dimensional optical parameter distribution image of the imaging area through the Nesterov accelerated homotopy perturbation iterative optical tomography reconstruction algorithm based on sparse projection.

Among them, the radiation transfer equation model is used to describe the photon transmission process in the imaging area to be inspected;

Establish a measurement system for optical tomography problems by means of multi-light source excitation and finite-angle average measurement data;

The Nesterov-accelerated homotopy perturbation iterative regularization reconstruction algorithm is used; the results of each iteration are sparsely projected to ensure the reconstruction quality.

Referring to FIG. 2 , an iterative optical tomography reconstruction method based on Nesterov homotopy perturbation based on sparse projection according to an embodiment of the present invention specifically includes the following steps:

Step 1, setting the information of the imaging area to be detected and the distribution of excitation light sources and detectors;

Step 2, combining the photon propagation model and the finite element theory, to establish the nonlinear relationship between the unknown optical parameters in the imaging area and the measurement data;

Step 3, for the nonlinear relationship established in step 2, use the Nesterov accelerated homotopy perturbation iterative regularization method based on sparse projection to invert the optical parameters to obtain a distribution image of the optical parameters in the region;

Optionally, the method further includes: step 4, displaying the result, comparing the real image of the optical parameter distribution with the reconstructed image through indicators such as relative error and cross-section diagram, and evaluating the reconstruction result.

Preferably, step 1 specifically includes:

Step 1.1, set the distribution of optical parameters inside the imaging area to be measured, that is, the size of the imaging area and the number, position, and shape of the internal abnormal areas;

Step 1.2, setting the distribution of light sources and detectors; wherein, a multi-light source excitation and multi-angle measurement strategy is adopted, and the light source points and the detectors are equidistantly and staggeredly distributed on the outer surface of the area to be detected.

Preferably, step 2 specifically includes:

Step 2.1, establishing a nonlinear relationship, including: using the radiation transfer equation as the propagation model of photons in the imaging object, and combining the angle average data measured by the boundary to construct a boundary value problem describing the optical tomography process; with the help of finite element theory and RTE_2D_MATLAB The software discretizes the imaging area into N triangular elements, and converts this boundary value problem into a nonlinear relationship between surface measurement data and internal optical parameters, and the expression is:

F _i (x)=y _i , i=1,...,N _s ,

是吸收系数，

为测量数据，N_d为探测器的个数，N_s为光源个数，本发明将此方程组简记为F(x)＝y；In the formula,

is the absorption coefficient,

is the measurement data, N _d is the number of detectors, N _s is the number of light sources, and the present invention abbreviated this equation system as F(x)=y;

Step 2.2, obtain measurement data: Knowing the preset optical parameter distribution, use RTE_2D_MATLAB software to perform forward problem calculation to obtain the real measurement data y;

Step 2.3, adding noise to the real measurement data to obtain measurement data y ^δ containing noise, the relationship between optical parameters and measurement data containing noise is expressed as:

F(x)=y ^δ ,

where ||y ^δ -y||≤δ, δ is the noise level.

Preferably, step 3 specifically includes:

Nesterov参数α＝3；Step 3.1, initial value and parameter selection: take the absorption coefficient of the background of the imaging area as the initial value

Nesterov parameter α = 3;

Step 3.2, construct Nesterov accelerated homotopy perturbation iterative regularization algorithm, the expression is:

为Nesterov中间变量，

为

的伴随算子，s_k为搜索方向，迭代步长

Among them, α is the Nesterov parameter, k is the number of iteration steps,

is the Nesterov intermediate variable,

for

The adjoint operator of , _sk is the search direction, the iteration step size

Step 3.3, project the above iteration result into the optical parameter L ¹ -sphere B _R :={x:||x|| ₁ ≤R} to improve the reconstruction accuracy of the abnormal area, the expression is,

为向球B_R的投影算子。in,

is the projection operator to the ball _BR .

In the embodiment of the present invention, the specific projection process is as follows:

中的元素的绝对值进行降序排列，得到一组新序列

First, put

The absolute values of the elements in are sorted in descending order to obtain a new set of sequences

中的第n个元素，使其满足：Second, search

The nth element in , so that it satisfies:

Among them, the threshold operator S is defined as

以及

则Finally, let

as well as

but

当满足

时，迭代停止；其中，τ为大于1的参数。Step 3.4, iterate through steps 3.2-3.3 to obtain the reconstruction result of the k-th iteration

when satisfied

, the iteration stops; where τ is a parameter greater than 1.

In the embodiment of the present invention, the radiation transfer equation is used as the photon propagation model, which can describe the propagation process of photons in the imaging area more accurately than the traditional diffusion approximation equation, and effectively reduces the model error. The use of multi-light source excitation and multi-angle measurement effectively alleviates the ill-posedness of the problem. Hotopy perturbation iterative regularization can be regarded as an acceleration algorithm of Landweber iterative regularization. On this basis, the Nesterov acceleration method is introduced to further accelerate the algorithm and improve the imaging speed of optical tomography. At the same time, according to the sparse distribution characteristics of abnormal areas in the imaging object, a sparse projection strategy is introduced, and the obtained iterative results are projected into the L ¹ -sphere of the solution. Detail information to improve imaging resolution. The optical tomography imaging method based on the Nesterov accelerated homotopy perturbation iterative algorithm based on the sparse projection proposed by the invention can effectively improve the imaging speed and imaging quality.

The application effect of the present invention in a two-dimensional problem will be described in detail below in conjunction with the reconstruction result.

Please refer to Fig. 3, Fig. 3 is the actual distribution of optical parameters of the area to be detected; wherein, the detected area is a circular area with a radius of 5cm with the origin as the center; its interior contains two circular abnormal areas of different sizes, A circle centered at (0,2.5mm) has a radius of 0.9mm, and a circle centered at (0,-2.5mm) has a radius of 1cm.

Using RTE_2D_MATLAB software, it is divided into 1666 elements for forward solution, and 12 light sources and 12 detectors are equidistantly distributed on the boundary of the circular region. The absorption coefficient of the imaged object background is 0.01 mm ^-1 , and the absorption coefficient of the two circular anomalous areas is 0.02 mm ^-1 .

Please refer to Fig. 4, Fig. 4 is a comparison of the reconstruction effect based on the present invention and the homotopy perturbation method at different iteration times; wherein, (a) in Fig. 4 is the reconstruction result of the present invention's algorithm at different iteration times (b) in Fig. 4 is to utilize the reconstruction result of homotopy perturbation iterative algorithm at different times, in Fig. 4, AHPI represents the Nesterov accelerated homotopy perturbation iterative algorithm based on sparse projection proposed by the present invention, HIP stands for the homotopy perturbation iterative algorithm. In the embodiment of the present invention, by using the method of the embodiment of the present invention, the position and shape of the abnormal area can be more accurately identified in 120 iterations, and the reconstructed background is clear. However, using the homotopy perturbation iterative method, in 120 iterations, the background perturbation of the reconstruction result is obvious, and the location, contour and other information of the abnormal area are not clearly identified.

The reconstruction error is expressed as

代表真实的吸收系数。where x represents the reconstructed absorption coefficient,

represents the true absorption coefficient.

The reconstruction result based on the present invention is RE=0.1649 at the 120th iteration, and the reconstruction result based on the homotopy perturbation iteration is RE=0.2158 at the 120th iteration.

To sum up, it can be seen from Fig. 4 that the location, shape and quantification of absorption coefficient of the abnormal area identified based on the present invention are very close to the real situation, and the iterative coefficient and reconstruction time required to achieve this reconstruction accuracy are significantly less than Homotopy perturbation iteration. Therefore, the method proposed by the present invention is an effective optical tomography method.

A kind of optical tomography reconstruction system based on Nesterov homotopy perturbation iteration based on sparse projection of the present invention includes:

The parameter preset module is used to set the optical parameters of the area to be measured, the distribution of the excitation light source and the detector;

The nonlinear relationship building module is used to combine the photon propagation model and the finite element theory to establish the nonlinear relationship between the unknown optical parameters in the imaging area and the measurement data; the radiation transfer equation model is used to describe the photon transmission process in the imaging area to be inspected ;Establish a measurement system for optical tomography problems by means of multi-light source excitation and finite-angle averaging measurement data;

The reconstruction module is used to invert the optical parameters based on the established nonlinear relationship using the Nesterov accelerated homotopy perturbation iterative regularization method based on sparse projection, and obtain the distribution image of the optical parameters in the region; The results are sparsely projected to ensure reconstruction quality.

Among them, in the nonlinear relationship building block,

The radiation transfer equation is used as the propagation model of photons in the imaging object, combined with the angle-averaged data of boundary measurement, the boundary value problem describing the optical tomography process is constructed; based on the finite element theory and RTE_2D_MATLAB software, the imaging area is discretized into N triangles element, the boundary value problem is transformed into a nonlinear relationship between surface measurement data and internal optical parameters, which is expressed as,

F _i (x)=y _i , i=1,...,N _s ,

是吸收系数，

为测量数据，N_d为探测器的个数，N_s为光源个数，本发明将此方程组简记为F(x)＝y；In the formula,

is the absorption coefficient,

is the measurement data, N _d is the number of detectors, N _s is the number of light sources, and the present invention abbreviated this equation system as F(x)=y;

Based on the preset optical parameter distribution, use RTE_2D_MATLAB software to calculate the forward problem to obtain the real measurement data y;

Add noise to the real measurement data obtained to obtain measurement data y ^δ containing noise, the relationship between optical parameters and measurement data containing noise is expressed as,

F(x)=y ^δ ,

where ||y ^δ -y||≤δ, δ is the noise level.

Wherein, in the reconstruction module,

Nesterov参数α＝3；Take the absorption coefficient of the background of the imaging area as the initial value

Nesterov parameter α = 3;

A Nesterov accelerated homotopy perturbation iterative regularization algorithm is constructed, and an iterative result is obtained according to the regularization algorithm; the expression of the regularization algorithm is:

为Nesterov中间变量，

为

的伴随算子，s_k为搜索方向，迭代步长

Among them, α is the Nesterov parameter, k is the number of iteration steps,

is the Nesterov intermediate variable,

for

The adjoint operator of , _sk is the search direction, the iteration step size

The obtained iterative result is projected into the optical parameter L ¹ -sphere B _R :={x:||x|| ₁ ≤R}, which is used to improve the reconstruction accuracy of the abnormal area, and the expression is,

为向球B_R的投影算子；in,

is the projection operator to the ball _BR ;

当满足

时，迭代停止；其中，τ为大于1的参数。Iterate to get the reconstruction result of the kth iteration

when satisfied

, the iteration stops; where τ is a parameter greater than 1.

To sum up, the present invention discloses an optical tomography reconstruction algorithm and system based on Nesterov accelerated homotopy perturbation iteration based on sparse projection, which adopts the radiation transfer equation model to describe the transmission process of photons in the object to be detected; Multi-light source excitation and finite-angle average measurement data are used to establish a measurement system for optical tomography problems; Nesterov-accelerated homotopy perturbation iterative regularization reconstruction algorithm is used, and the results of each iteration are sparsely projected. The invention can effectively improve the imaging speed and imaging quality: the radiation transfer equation is used as the photon propagation model, the photon propagation process in the imaging object is more accurately described, and the model error is effectively reduced. The use of multi-light source excitation and multi-angle measurement effectively alleviates the morbidity of the problem. Based on the iterative regularization of homotopy perturbation, the Nesterov acceleration method is introduced to further accelerate the algorithm and improve the imaging speed of optical tomography. At the same time, according to the sparse distribution characteristics of abnormal areas in the imaging object, a sparse projection strategy is introduced to make full use of the sparse characteristics of the solution target, which can effectively identify the details of abnormal areas and improve the imaging resolution.

As will be appreciated by those skilled in the art, the embodiments of the present application may be provided as a method, a system, or a 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, etc.) 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 present application. It will be understood that each flow and/or block in the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to the processor of a general purpose computer, special purpose computer, embedded processor or other programmable data processing device to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing device produce Means for implementing the functions specified in a flow or flow of a flowchart and/or a block or blocks of a block diagram.

These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory result in an article of manufacture comprising instruction means, the instructions The apparatus implements the functions specified in the flow or flow of the flowcharts and/or the block or blocks of the block diagrams.

These computer program instructions can also be loaded on a computer or other programmable data processing device to cause a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process such that The instructions provide steps for implementing the functions specified in the flow or blocks of the flowcharts and/or the block or blocks of the block diagrams.

The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art can still modify or equivalently replace the specific embodiments of the present invention. , any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention are all within the protection scope of the claims of the present invention for which the application is pending.

Claims (5)

1. a kind of optical tomography reconstruction method based on the Nesterov homotopy perturbation iteration of sparse projection, is characterized in that, comprises the following steps: Step 1: Set the optical parameters of the area to be measured, the distribution of excitation light sources and detectors; Step 2: Combine the photon propagation model and the finite element theory to establish a nonlinear relationship between the unknown optical parameters in the imaging area and the measurement data; wherein, the radiation transfer equation model is used to describe the photon transmission process in the imaging area to be inspected; excitation by multiple light sources and finite angle average measurement data to establish a measurement system for optical tomography problems; Step 3: Based on the nonlinear relationship established in Step 2, use the Nesterov accelerated homotopy perturbation iterative regularization method based on sparse projection to invert the optical parameters, and obtain the distribution image of the optical parameters in the region; Perform sparse projection to ensure reconstruction quality; Wherein, step 2 specifically includes: In step 2.1, the radiation transfer equation is used as the propagation model of photons in the imaging object, combined with the angle average data measured by the boundary, to construct a boundary value problem describing the optical tomography process; based on the finite element theory and RTE_2D_MATLAB software, the imaging area is discretized as N triangular elements, the boundary value problem is transformed into a nonlinear relationship between surface measurement data and internal optical parameters, and the expression is, F _i (x)=y _i , i=1,...,N _s , In the formula,

is the absorption coefficient,

is the measurement data, N _d is the number of detectors, and N _s is the number of light sources; The above expression is abbreviated as, F(x)=y; Step 2.2, based on the optical parameter distribution preset in step 1, use RTE_2D_MATLAB software to perform forward problem calculation to obtain the real measurement data y; In step 2.3, noise is added to the real measurement data obtained in step 2.2 to obtain measurement data y ^δ containing noise. The relationship between optical parameters and measurement data containing noise is expressed as, F(x)=y ^δ , where ||y ^δ -y||≤δ, δ is the noise level; Step 3 specifically includes: Step 3.1, take the absorption coefficient of the background of the imaging area as the initial value

Nesterov parameter α = 3; Step 3.2, construct the Nesterov accelerated homotopy perturbation iterative regularization algorithm, and obtain the iterative result according to the regularization algorithm; the expression of the regularization algorithm is:

Among them, α is the Nesterov parameter, k is the number of iteration steps,

is the Nesterov intermediate variable, _sk is the search direction, the iteration step size

for

the adjoint operator of ; Step 3.3, project the iterative result obtained in step 3.2 into L ¹ -sphere B _R :={x:||x|| ₁ ≤R} of optical parameters, to improve the reconstruction accuracy of the abnormal area, the expression is ,

in,

is the projection operator to the ball _BR ; Step 3.4, iterate through steps 3.2 and 3.3 to obtain the reconstruction result of the k-th iteration

when satisfied

When , the iteration stops; where τ is a parameter greater than 1; Step 3.3 specifically includes: (1) will

The absolute values of the elements in are sorted in descending order to obtain a new set of sequences

(2) Search

The nth element in , so that it satisfies:

Among them, the threshold operator S is defined as

(3) Order

as well as

but

2. a kind of optical tomography reconstruction method based on Nesterov homotopy perturbation iteration based on sparse projection according to claim 1, is characterized in that, step 1 specifically comprises: Set the distribution of optical parameters inside the area to be measured, including: the size of the imaging area and the number, location, and shape of abnormal areas inside; Set the distribution of excitation light sources and detectors, including: using multi-light source excitation and multi-angle measurement strategies; wherein, the light source points and detectors are equidistant and staggered on the outer surface of the area to be measured. 3. a kind of optical tomography reconstruction method based on Nesterov homotopy perturbation iteration based on sparse projection according to claim 1, is characterized in that, also comprises: In step 4, the real image of the optical parameter distribution is compared with the distribution image obtained in step 3 through the relative error or the sectional graph index, so as to evaluate the reconstruction result. 4. a kind of optical tomography reconstruction method based on Nesterov homotopy perturbation iteration based on sparse projection according to claim 3, is characterized in that, in step 4, reconstruction error expression is,

where x represents the reconstructed absorption coefficient,

represents the true absorption coefficient; At the 120th iteration of the Nesterov homotopy perturbation iterative optical tomography reconstruction method based on sparse projection, RE=0.1649. 5. An iterative optical tomography reconstruction system based on Nesterov homotopy perturbation of sparse projection, characterized in that, comprising: The parameter preset module is used to set the optical parameters of the area to be measured, the distribution of the excitation light source and the detector; The nonlinear relationship building module is used to combine the photon propagation model and the finite element theory to establish the nonlinear relationship between the unknown optical parameters in the imaging area and the measurement data; the radiation transfer equation model is used to describe the photon transmission process in the imaging area to be inspected ;Establish a measurement system for optical tomography problems by means of multi-light source excitation and finite-angle averaging measurement data; The reconstruction module is used to invert the optical parameters based on the established nonlinear relationship using the Nesterov accelerated homotopy perturbation iterative regularization method based on sparse projection to obtain the distribution image of the optical parameters in the region; The result is sparsely projected to ensure reconstruction quality; Among them, in the nonlinear relationship building block, The radiation transfer equation is used as the propagation model of photons in the imaging object, combined with the angle average data measured by the boundary, the boundary value problem describing the optical tomography process is constructed; based on the finite element theory and RTE_2D_MATLAB software, the imaging area is discretized into N triangles element, the boundary value problem is transformed into a nonlinear relationship between surface measurement data and internal optical parameters, which is expressed as, F _i (x)=y _i , i=1,...,N _s , In the formula,

is the absorption coefficient,

is the measurement data, N _d is the number of detectors, and N _s is the number of light sources; The expression is abbreviated as: F(x)=y; Based on the preset optical parameter distribution, use RTE_2D_MATLAB software to calculate the forward problem to obtain the real measurement data y; Add noise to the real measurement data obtained to obtain measurement data y ^δ containing noise, the relationship between optical parameters and measurement data containing noise is expressed as, F(x)=y ^δ , where ||y ^δ -y||≤δ, δ is the noise level; In the reconstruction module, Take the absorption coefficient of the background of the imaging area as the initial value

Nesterov parameter α = 3; A Nesterov accelerated homotopy perturbation iterative regularization algorithm is constructed, and an iterative result is obtained according to the regularization algorithm; the expression of the regularization algorithm is:

Among them, α is the Nesterov parameter, k is the number of iteration steps,

is the Nesterov intermediate variable, _sk is the search direction, the iteration step size

for

the adjoint operator of ; The obtained iterative result is projected into the optical parameter L ¹ -sphere B _R :={x:||x|| ₁ ≤R}, which is used to improve the reconstruction accuracy of the abnormal area, and the expression is,

in,

is the projection operator to the ball _BR ; Iterate to get the reconstruction result of the kth iteration

when satisfied

, the iteration stops; where τ is a parameter greater than 1.

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