A light source reconstruction method based on residual guidance in an incomplete variable framework

Abstract

The present invention discloses a light source reconstruction method based on residual guidance under an incomplete variable framework, comprising the following steps: (1) solving the light source reconstruction problem using L1 regularization, and giving a smaller regularization parameter initial value and a maximum number of iterations; (2) determining the termination condition of the parameter search iteration; (3) bringing the regularization parameter into the incomplete variable truncated conjugate gradient method, and determining whether the KKT equivalent condition residual oscillates; (4) if the KKT equivalent condition residual oscillates, reducing and outputting the regularization parameter as the selected optimal regularization parameter for reconstruction; otherwise, increasing the regularization parameter and increasing the number of iterations by one to proceed to step (2). When determining whether the regularization parameter is appropriate, the present invention only requires a few iterations within the algorithm to obtain a result, which is conducive to quickly finding a suitable regularization parameter; no manual adjustment is required, thereby improving the feasibility of the algorithm application and the quality of the reconstruction result.

Description

Technical Field

[0001] The present invention belongs to the field of molecular imaging, specifically a residual-guided light source reconstruction method under an incomplete variable framework, which can be used for the regularization parameter selection of the incomplete variable algorithm in the inverse problem reconstruction of X-ray luminescence tomography. Background Art

[0002] X-ray luminescence tomography (XLCT) is a hybrid molecular imaging modality first proposed in the past decade. It combines the high spatial resolution of traditional X-ray imaging with the high measurement sensitivity of optical imaging and holds great potential for small animal imaging. As a key optical molecular imaging modality, XLCT utilizes external high-energy X-rays to detect objects. When nanophosphorescent particles in biological tissue are excited by X-rays, they generate visible or near-infrared (NIR) luminescence signals. After being captured by a CCD camera, reconstruction algorithms can be used to reconstruct the spatial distribution of the nanophosphorescent particles. Compared to other commonly used optical tomography techniques, such as fluorescence molecular tomography and bioluminescence tomography, XLCT avoids autofluorescence and background fluorescence and utilizes the X-ray excitation position as a priori information, achieving higher spatial resolution and sensitivity. However, due to the absorption and scattering of light in biological tissue and the limitations of prior information collected by optical instruments, the inverse problem of XLCT reconstruction is one in which the number of unknowns is far greater than the equation, making it a severely ill-posed and ill-posed problem. Sparse regularized reconstruction methods are commonly used to solve this type of ill-posed inverse problem. Solving large, sparse, ill-posed problems often involves the addition of a constrained regularization term to ensure a certain degree of immunity to sensitive data. However, the impact of this constrained regularization term on the solution depends heavily on the appropriate regularization parameter, which can balance the residual norm and the solution norm to achieve optimal results. Therefore, selecting the optimal regularization parameter has been a focus of much research. Summary of the Invention

[0003] In order to solve the problem of selecting regularization parameters for incomplete variable algorithms for solving the inverse problem of X-ray luminescence tomography, the present invention proposes a light source reconstruction method based on residual guidance in an incomplete variable framework. In order to select a suitable regularization parameter, the oscillation of the residual guides the iterative selection of the regularization parameter according to the KKT equivalent condition proposed in the incomplete variable framework, thereby improving the situation where the reconstruction result has large errors due to inappropriate regularization parameters.

[0004] The technical solution of the present invention is:

[0005] A light source reconstruction method based on residual guidance in an incomplete variable framework includes the following steps:

[0006] S1: Use L1 regularization to solve the reconstruction of the light source, giving the initial value of the regularization parameter τ0 and the maximum number of iterations k max ;

[0007] S2: Determine the termination condition of the parameter search iteration. The number of parameter search iterations is not less than k. max When , output the regularization parameter τ at this time;

[0008] S3: The output regularization parameter τ is brought into the incomplete variable truncated conjugate gradient method to determine whether the KKT equivalent condition residual oscillates; if the KKT equivalent condition residual oscillates, the regularization parameter is reduced and output as the selected optimal regularization parameter for reconstruction; otherwise, the regularization parameter is increased and the number of iterations is increased by one to go to step S2.

[0009] Optionally, the specific steps of S1 are:

[0010] (1a) collecting fluorescence data of the imaged object for optical data reconstruction, and collecting CT data of the imaged object for obtaining tissue structure information of the object;

[0011] (1b) constructing a three-dimensional finite element structure of the object based on the acquired CT data and mapping the acquired fluorescence data onto the imaged object;

[0012] (1c) Construct a linear relationship between the surface fluorescence distribution and the internal light source distribution, and use L1 regularization to solve the constructed linear relationship:

[0013]

[0014] Where τ is the regularization parameter, A is the system matrix composed of prior information, Φ is the surface spot distribution, and ρ is the internal light source distribution. The initial value of the regularization parameter τ0 is given for parameter search, and the maximum number of iterations k is max Used to terminate the iteration.

[0015] Optionally, the fluorescence data and CT data are collected using an X-ray optical platform dual-modality imaging system.

[0016] Optionally, the implementation process of S3 is:

[0017] Bring the current regularization parameter τ into the incomplete variable truncated conjugate gradient algorithm for calculation;

[0018]

[0019] Where γ is the oscillation factor, z * is the solution of the current iteration, Expressed as gradient, F is the original problem;

[0020] if It is considered that the residual is slowly decreasing at this time; if It is considered that the residual decreases and oscillation occurs at this time.

[0021] Optionally, reducing and outputting the regularization parameter as the selected optimal regularization parameter for reconstruction specifically includes: reducing and outputting the regularization parameter, that is, τ=τ-0.05*τ.

[0022] Optionally, the increased regularization parameter is τ=τ+0.1*τ.

[0023] Optionally, S4 is also included: Finally, the incomplete variable truncated conjugate gradient method is used to solve the inverse problem, and Tecplot is used to display the distribution of the light source reconstruction results.

[0024] The present invention has the following advantages:

[0025] First, when determining whether the regularization parameter is appropriate, the present invention only requires a few iterations within the algorithm to obtain the result, which is conducive to quickly finding the appropriate regularization parameter;

[0026] Second, the present invention adopts adaptive search for appropriate regularization parameters without manual adjustment, thereby improving the feasibility of algorithm application and the quality of reconstruction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The accompanying drawings are used to provide a further understanding of the present disclosure and constitute a part of the specification. Together with the following detailed description, they are used to explain the present disclosure but do not constitute a limitation of the present disclosure. In the accompanying drawings:

[0028] Figure 1 This is a flow chart of the light source reconstruction method based on residual guidance in an incomplete variable framework of the present invention;

[0029] Figure 2 The phantom model and surface fluorescence data from the simulation experiment; (a) shows the light source position; (b) shows the result of mapping the surface fluorescence data onto the grid;

[0030] Figure 3 The results after reconstruction using the initial regularization parameters, where (a) shows the three-dimensional display of the real target (red, cylinder) and the reconstructed target (blue, irregular body); (b) shows the two-dimensional cross-section of the reconstruction result at Z = 13mm (where the red circle is the position of the real light source);

[0031] Figure 4 is the result of reconstruction using the regularization parameter selection strategy based on incomplete variables, where (a)

[0032] The figure shows the three-dimensional display of the real target (red, cylinder) and the reconstructed target (blue, irregular body); (b) The figure shows the two-dimensional cross-section of the reconstruction result at Z = 13mm, where the red circle is the position of the real light source;

[0033] Figure 5 The reconstruction results obtained using the L-curve strategy with a regularization parameter of 1.04e-5, where (a) shows the three-dimensional display of the real target (red, cylinder) and the reconstructed target (blue, irregular body); (b) shows the two-dimensional cross-sectional view of the reconstruction result at Z = 13 mm, where the red circle indicates the position of the real light source. DETAILED DESCRIPTION

[0034] The present invention will be described in further detail below with reference to the accompanying drawings. It should be noted that the described embodiments are only intended to facilitate understanding of the present invention and do not have any limiting effect on the present invention.

[0035] The light source reconstruction method based on residual guidance in an incomplete variable framework of the present invention comprises the following steps:

[0036] S1: The light source reconstruction problem is solved using L1 regularization, and a small regularization parameter initial value τ0 and a maximum number of iterations k are given. max The initial value of the regularization parameter τ0 is set empirically based on the energy value of the surface spot.

[0037] S2: Determine the termination condition of the parameter search iteration. The number of parameter search iterations is not less than k. max When , output the regularization parameter τ at this time;

[0038] S3: The output regularization parameter τ is brought into the incomplete variable truncated conjugate gradient method to determine whether the KKT equivalent condition residual oscillates; if the KKT equivalent condition residual oscillates, the regularization parameter is reduced and output as the selected optimal regularization parameter for reconstruction; otherwise, the regularization parameter is increased and the number of iterations is increased by one to go to step S2; the increase and decrease coefficients determine the accuracy of finding the regularization parameter. The smaller the coefficient, the higher the accuracy. In this article, the increase coefficient is 0.1 and the decrease coefficient is 0.05.

[0039] The specific steps of step S1 are:

[0040] (1a) Using an X-ray optical platform dual-modality imaging system, fluorescence data of the imaging object is collected for optical data reconstruction, and CT data of the imaging object is collected to obtain the object's tissue structure information.

[0041] (1b) A three-dimensional finite element structure of the object is constructed based on the acquired CT data, and the acquired fluorescence data is mapped onto the imaged object.

[0042] (1c) Construct a linear relationship between the surface fluorescence distribution and the internal light source distribution, and use L1 regularization to solve the constructed linear relationship:

[0043]

[0044] Where A is the system matrix composed of prior information, Φ is the surface spot distribution, and ρ is the internal light source distribution. A small initial value of the regularization parameter τ0 is given for parameter search, and the maximum number of iterations k is max Used to terminate the iteration.

[0045] The implementation process of S3 is: bring the current regularization parameter τ into the incomplete variable truncated conjugate gradient algorithm for calculation, and judge whether the KKT equivalent condition residual in the incomplete variable framework oscillates to guide the calculation of the regularization parameter.

[0046]

[0047] Where γ is the oscillation factor, z * is the solution of the current iteration, Expressed as gradient, F is the original problem; if It is considered that the residual is slowly decreasing at this time; if It is considered that the residual decreases and oscillation occurs at this time.

[0048] When the KKT equivalent condition residual γ oscillates in step S3, the regularization parameter is reduced and output as the parameter selection result, that is, τ = τ - 0.05*τ; when the KKT equivalent condition residual γ slowly decreases in step S3, the regularization parameter is increased, that is, τ = τ + 0.1*τ, and the number of iterations is increased by one to go to step S2 until the KKT equivalent condition residual γ oscillates; finally, the incomplete variable truncated conjugate gradient method is used to solve the inverse problem, and the distribution of the results is displayed using Tecplot.

[0049] Example 1:

[0050] See also Figure 1 The process of the regularization parameter selection strategy based on incomplete variables of the present invention is as follows:

[0051] (1) L1 regularization is used to solve the light source reconstruction problem, and a small initial value of the regularization parameter and a maximum number of iterations are given:

[0052] (1a) Using the X-ray optical platform dual-modality imaging system, fluorescent material is placed in the cylindrical phantom, and CT image data at various angles are obtained through X-ray irradiation, fixed-angle rotation of the rotating table, and X-ray detection plate.

[0053] (1b) The cylindrical phantom is irradiated with cone-beam X-rays to make the fluorescent material inside the phantom emit light, and the fluorescence information on the surface of the phantom is collected by an ultra-low temperature CCD camera.

[0054] (1c) The three-dimensional finite element structure of the object is constructed using Amira software and the acquired CT data, and the acquired fluorescence data is mapped onto the finite element mesh of the imaged object.

[0055] (1d) Based on the light transmission model, a linear relationship between the surface fluorescence distribution and the internal light source distribution is constructed, and the constructed linear relationship is solved using L1 regularization:

[0056]

[0057] Where τ is the regularization parameter, A is the system matrix, ρ is the internal light source distribution, and Φ is the light spot distribution on the phantom surface.

[0058] (1e) A smaller initial value of the regularization parameter is given for parameter search, and the maximum number of iterations is used to terminate the iteration.

[0059] (2) Determine the termination condition of the parameter search iteration. When the number of parameter search iterations is not less than k max When , the iteration ends and the regularization parameter at this time is output and the incomplete variable truncated conjugate gradient algorithm is used to solve it.

[0060] (3) The current regularization parameter is brought into the incomplete variable truncated conjugate gradient method for calculation, and the KKT equivalent condition in the incomplete variable framework is used to guide the calculation of the regularization parameter to see whether the residual oscillates.

[0061]

[0062] Where γ is the oscillation factor, z * is the solution of the current iteration, Expressed as gradient, F is the original problem.

[0063] if It is considered that the residual is slowly decreasing. It is considered that the residual decreases and oscillation occurs at this time.

[0064] (4) When the KKT equivalent condition residual γ in step (3) oscillates, reduce the regularization parameter and output it as the parameter selection result, i.e., τ = τ - 0.05*τ. When the KKT equivalent condition residual γ in step (3) slowly decreases, increase the regularization parameter, i.e., τ = τ + 0.1*τ, and increase the number of iterations by one and go to step (2) until the KKT equivalent condition residual γ oscillates. Finally, the incomplete variable truncated conjugate gradient method is used to solve the inverse problem, and Tecplot is used to display the distribution of the result after image fusion.

[0065] The following combination Figure 2-Figure 4 The reconstruction results of the present invention are further described.

[0066] Figure 2 The phantom model used for simulation experiments. Figure (a) includes the phantom structure and the position and structure of the light source, while Figure (b) shows the distribution of the light spot on the phantom surface after stimulating the internal light source.

[0067] Figure 3 The results of reconstruction using the initial regularization parameter 1e-10, where (a) shows the three-dimensional display of the real target (red) and the reconstructed target (blue); (b) shows the two-dimensional cross-sectional view of the reconstruction result at Z = 13mm, where the red circle indicates the position of the real light source.

[0068] The center position of the real light source is (0, 7.5, 13) mm. After removing the artifacts, the position error of the reconstructed target is:

[0069]

[0070] Figure 4 The reconstruction results with a regularization parameter of 6.22e-4 are obtained using the regularization parameter selection strategy based on incomplete variables, where (a) shows the three-dimensional display of the real target (red) and the reconstructed target (blue); (b) shows the two-dimensional cross-sectional view of the reconstruction result at Z = 13 mm, where the red circle indicates the position of the real light source.

[0071] The center position of the real light source is (0, 7.5, 13) mm, and the position error of the reconstructed target is:

[0072]

[0073] Figure 5 The reconstruction results obtained using the L-curve strategy with a regularization parameter of 1.04e-5, where (a) shows the three-dimensional display of the real target (red) and the reconstructed target (blue); (b) shows the two-dimensional cross-sectional view of the reconstruction result at Z = 13 mm, where the red circle indicates the position of the real light source.

[0074] The center position of the real light source is (0, 7.5, 13) mm, and the position error of the reconstructed target is:

[0075]

[0076] It can be seen that the light source reconstruction method based on residual guidance in the incomplete variable framework provided by the present invention has an error of less than 1 mm after reconstruction, which improves the accuracy of the light source reconstruction method and has a small result error.

[0077] The above is a detailed discussion of the best embodiment in conjunction with the accompanying drawings, which is not intended to limit the present invention. The various specific technical features described above can be combined in any suitable form without contradiction, and the present invention does not go into details one by one. Any person skilled in the art may adopt simple modifications or modifications such as arbitrary combination or equivalent replacement of the technical solution without departing from the scope of the technical solution, which does not affect the essence of the technical solution and still falls within the scope of protection of the technical solution represented by the various embodiments of the present invention.

Claims

1. A light source reconstruction method based on residual guidance in an incomplete variable framework, characterized in that: The following steps are involved: S1: Use L1 regularization to solve the reconstruction of the light source, giving the initial value of the regularization parameter τ0 and the maximum number of iterations k max ; S2: Determine the termination condition of the parameter search iteration. The number of parameter search iterations is not less than k. max When , output the regularization parameter τ at this time; S3: Substitute the current regularization parameter τ into the incomplete variable truncated conjugate gradient method to determine whether the KKT equivalent condition residual oscillates; if the KKT equivalent condition residual oscillates, reduce the regularization parameter and output it as the selected optimal regularization parameter for reconstruction; otherwise, increase the regularization parameter and increase the number of iterations by one to go to step S2; The implementation process of S3 is: Bring the current regularization parameter τ into the incomplete variable truncated conjugate gradient algorithm for calculation; Where γ is the oscillation factor, z * is the solution of the current iteration, Expressed as gradient, F is the original problem; if It is considered that the residual is slowly decreasing at this time; if It is considered that the residual decreases and oscillation occurs at this time; k represents the number of iterations; S4: Finally, the incomplete variable truncated conjugate gradient method is used to solve the inverse problem, and Tecplot is used to display the distribution of the light source reconstruction results.

2. The light source reconstruction method based on residual guidance in an incomplete variable framework according to claim 1, characterized in that: The specific steps of S1 are: (1a) collecting fluorescence data of the imaged object for optical data reconstruction, and collecting CT data of the imaged object for obtaining tissue structure information of the object; (1b) constructing a three-dimensional finite element structure of the object based on the acquired CT data and mapping the acquired fluorescence data onto the imaged object; (1c) Construct a linear relationship between the surface fluorescence distribution and the internal light source distribution, and use L1 regularization to solve the constructed linear relationship: Where τ is the regularization parameter, A is the system matrix composed of prior information, Φ is the surface spot distribution, and ρ is the internal light source distribution. The initial value of the regularization parameter τ0 is given for parameter search, and the maximum number of iterations k is max Used to terminate the iteration.

3. The light source reconstruction method based on residual guidance in an incomplete variable framework according to claim 2, characterized in that: The fluorescence data and CT data are collected using an X-ray optical platform dual-modality imaging system.

4. The light source reconstruction method based on residual guidance in an incomplete variable framework according to claim 1, 2 or 3, characterized in that: Reducing and outputting the regularization parameter as the selected optimal regularization parameter for reconstruction specifically includes: reducing and outputting the regularization parameter, that is, τ=τ-0.05*τ.

5. The light source reconstruction method based on residual guidance in an incomplete variable framework according to claim 1, 2 or 3, characterized in that: The increased regularization parameter is τ=τ+0.1*τ.

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