A light source reconstruction method based on adaptive nearest neighbor orthogonal least squares algorithm

Abstract

The present invention discloses a method for light source reconstruction based on an adaptive nearest neighbor orthogonal least squares algorithm, and the implementation steps are as follows: (1) obtaining measurement data; (2) normalizing surface data; (3) using an adaptive nearest neighbor orthogonal least squares algorithm to reconstruct and obtain an optimal solution; the present invention is suitable for optical molecular tomography that excites fluorescence molecular tomography to reconstruct a fluorescence source. The reconstruction based on the present invention adopts an adaptive nearest neighbor orthogonal least squares method for reconstruction, introduces an adaptive strategy to reduce the pathological nature of the reconstruction problem, uses the nearest neighbor strategy to select the optimal support set, effectively improves the reconstruction quality and spatial resolution of fluorescence molecular tomography, and has important application value in the fields of optical tomography three-dimensional reconstruction algorithms.

Description

Technical Field

[0001] The invention belongs to the field of molecular imaging, and in particular is a light source reconstruction method based on an adaptive nearest neighbor orthogonal least squares algorithm. Background Art

[0002] Fluorescence molecular tomography (hereinafter referred to as FMT) or fluorescence molecular tomography uses an external light source to excite fluorescent molecular probes in the body to make them emit light. The emitted fluorescence is collected by equipment outside the body, and the three-dimensional distribution of fluorescent probes inside the body can be inverted using light transmission models and mathematical methods. It is a non-invasive optical molecular imaging technology with strong specificity and sensitivity. Therefore, it has great potential in pre-clinical research on tumor detection, drug development and efficacy evaluation. However, the strong scattering of photons and the lack of surface measurement data make the reconstruction results of FMT unstable, and the quality of the reconstruction results needs to be improved, which further hinders the application of FMT in early tumor detection.

[0003] FMT 3D reconstruction is seriously ill-posed and is a typical inverse problem in mathematics. This is because near-infrared light has strong scattering characteristics in biological tissues. At the same time, the acquired surface fluorescence data is limited and there will be noise interference, which greatly increases the ill-posedness of the problem. In order to obtain a stable and accurate solution, various regularization methods are applied to FMT reconstruction.

[0004] The more popular regularization methods are mainly based on L2 norm, L1 norm and L0 norm. Among them, the L2 norm method is simple in design and fast in calculation, but its over-smoothness often leads to poor reconstruction resolution. A typical application of FMT is the early detection model of tumors, in which tumors have significant sparse characteristics relative to the imaging target. In order to utilize sparse prior information, L1 norm and L0 norm regularization methods began to be applied to this model. They effectively overcome the over-smoothing disadvantage of the L2 norm, and the sparsity of the solution is also greatly improved compared with the L2 norm. Therefore, it has received widespread attention and attention from researchers. Summary of the invention

[0005] In order to improve the quality of reconstruction results of fluorescence molecular tomography, the present invention proposes a light source reconstruction method based on an adaptive nearest neighbor orthogonal least squares algorithm to solve the regularization problem based on the L0 norm. The algorithm is a typical greedy algorithm. It does not need to know the sparsity of the variable in advance, but can adaptively obtain the sparsity. At the same time, the nearest neighbor strategy is used to select the optimal support set, which ultimately improves the reconstruction quality and spatial resolution of fluorescence molecular tomography.

[0006] The specific process includes:

[0007] A fluorescence molecular tomography method based on an adaptive nearest neighbor orthogonal least squares algorithm comprises the following steps:

[0008] Step 1: Obtain measurement data: collect surface fluorescence data and anatomical structure information of the target organism, perform finite element meshing on the reconstructed target organism, and then approximate the model based on the diffusion equation of the photon transmission model to establish a linear relationship between the surface fluorescence data and the distribution of fluorophores inside the reconstructed target;

[0009] Φ=ΑX (1);

[0010] Where Φ is the surface fluorescence data, Α represents the system matrix, and X is the distribution of the fluorophores inside the reconstructed target to be solved;

[0011] Step 2: Normalize the measured data: Convert the linear relationship in step 1 into an L0 norm minimization problem:

[0012]

[0013] ||X||0 is the 0 norm, indicating the number of non-zero elements, and ε is the given threshold;

[0014] Step 3: Use the adaptive nearest neighbor orthogonal least squares algorithm to reconstruct and obtain the optimal solution X.

[0015] Optionally, the step three specifically includes:

[0016] X=K i (S i );

[0017] K i =K i-1 +s, i is the number of iterations, s is the step size, Indicates rounding up, s0=K0=6;

[0018] S i =L i (E i-1 )∪S i-1 , L i (E i-1 ) indicates that from E i-1 Select L i nodes, find S i-1 Take the union of the nearest neighbor sets of all nodes in the , and the resulting set is recorded as the nearest neighbor set E i-1 , the process is described by the nearest neighbor operator N, then E i-1 =N(S i-1 );

[0019] i represents the number of iterations, with an initial value of 1; K represents the sparsity; S irepresents the support set;

[0020] Each iteration is performed once i=i+1 until the residual is less than a given threshold or the step length of the sparsity K changes to 1, and then the iteration stops.

[0021] Preferably, the step three specifically includes:

[0022] 3.1 Initialization parameters: i represents the number of iterations, initial value i = 1, sparsity K0 = 6, L0 = 10, initial residual r0 = Φ;

[0023] Element selection criteriaq j , in the iteration, select a new column index j m :

[0024]

[0025]

[0026]

[0027] in I is the column set, a j is the jth column of the system matrix A, u l are orthogonal basis vectors; according to the above formula (3), select L0 elements to form the initial support set S0;

[0028] 3.2 Adaptive step size adjustment: using nonlinear function To adjust the step size, the function is a monotonically decreasing function, and the step size is expressed as follows:

[0029]

[0030] Where s is the step size, denotes rounding upwards; let the support set S i The number of atoms added is L i , and its iteration formula is L i =L i-1 -s, where s0 = L0 = 10. As the number of iterations increases, the number of atoms added to the support set gradually decreases until the number of atoms becomes 1, then the iteration stops;

[0031] The sparsity iteration formula is set to K i =K i-1 +s, where s0=K0=6; as the number of iterations increases, the sparsity gradually increases, with a larger step size at the beginning of the increment and a smaller step size at the end, until it reaches 1;

[0032] 3.3 Support set update: Based on the finite element theory, the nearest neighbor node set is constructed according to the tetrahedral unit structure.i-1

[0033] is the support set generated by the i-1th iteration. Let any node G k ∈S i-1 , then the set of all nodes of the tetrahedron where the node is located is the nearest neighbor set, and S i-1 Take the union of the nearest neighbor sets of all nodes in the , and the resulting set is recorded as the nearest neighbor set E i-1 , the process is described by the nearest neighbor operator N, then E i-1 =N(S i-1 ), from E i-1 According to formula (3), select L i nodes into the support set S i-1 , forming a new support set S i , that is, S i =L i (E i-1 )∪S i-1 , L i (E i-1 ) indicates that from E i-1 Select L i nodes;

[0034] 3.4 Residual Update: Setting r i represents the residual vector generated by the i-th iteration. In addition, the residual vector r required for the next iteration i+1 for:

[0035] r i+1 =r i -u i+1 (7);

[0036] in,

[0037] Since each iteration needs to select L i nodes, so in the i-th iteration, we need to construct L i Linearly independent vectors

[0038] 3.5 Loop through steps 3.1-3.4: i = i + 1 for each loop until the residual r i <ε or the step length of the sparsity K is 1, the iteration stops; the first K columns of the final support set are the solution set, that is

[0039] X=K i (S i ) (8);

[0040] This solution is the solution to the minimization problem.

[0041] Furthermore, the result X is displayed using Tecplot imaging software.

[0042] The present invention has the following advantages:

[0043] The present invention is suitable for optical molecular tomography with the reconstruction of fluorescence sources as the goal. During the reconstruction process, the proposed adaptive nearest neighbor orthogonal least squares algorithm is used for reconstruction, which improves the spatial resolution and robustness while ensuring the accuracy, thereby ensuring the quality of the reconstruction result. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] 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 specific embodiments, they are used to explain the present disclosure but do not constitute a limitation of the present disclosure. In the accompanying drawings:

[0045] Figure 1 It is a flow chart of a light source reconstruction method based on an adaptive nearest neighbor orthogonal least squares algorithm according to the present invention;

[0046] Figure 2 It is a flow chart for realizing the light source reconstruction method based on the adaptive nearest neighbor orthogonal least squares algorithm of the present invention;

[0047] Figure 3 It is a flow chart of the implementation of the adaptive nearest neighbor orthogonal least squares algorithm based on the present invention;

[0048] Figure 4 A digital mouse model for simulation experiments based on the present invention;

[0049] Figure 5 This is the FMT reconstruction result based on the present invention, where the dark blue is the reconstructed fluorophore area, and this is the three-dimensional display of the reconstruction result of the dual targets;

[0050] Figure 6 The present invention is applied to FMT three-dimensional reconstruction, and is a reconstruction result obtained when using different amounts of projection data for reconstruction, and a dual light source is a reconstruction distribution map of a fluorescent target with a cross section of z=14 mm. DETAILED DESCRIPTION

[0051] The present invention will be further described in detail below in conjunction with the accompanying drawings. It should be noted that the described embodiments are only intended to facilitate the understanding of the present invention and do not have any limiting effect on the present invention.

[0052] In order to improve the quality of reconstruction results of fluorescence molecular tomography, the present invention proposes an orthogonal least squares algorithm based on adaptive nearest neighbor to solve the regularization problem based on L0 norm. This algorithm is a typical greedy algorithm. It does not need to know the sparsity of the variable in advance, but adaptively approximates the sparsity in the iterative process. At the same time, the nearest neighbor strategy is used to select the optimal support set, which ultimately improves the reconstruction quality and spatial resolution of fluorescence molecular tomography. The specific process includes:

[0053] Using a multimodal optical molecular imaging system, fluorescence data and anatomical information of the imaging object are collected, and the imaging target organism is meshed by finite element. Then, based on the diffusion approximation equation of the light transmission model, a linear relationship between the surface fluorescence data and the fluorophore inside the target is established. In order to obtain a stable and sparse solution, the L0 norm is used to construct the optimization problem, and the adaptive nearest neighbor orthogonal least squares method is used to quickly solve it, and finally the reconstruction results are displayed.

[0054] First, multiple positions are excited to obtain projection data at multiple angles, and the organism labeled with fluorescent probes is irradiated with excitation light of a specific wavelength. The fluorescence signal emitted by the fluorescent probe is collected on the body surface with a highly sensitive optical detector, and a diffusion equation based on finite element theory is constructed to establish a linear relationship between the fluorescence data and the distribution of fluorophores inside the reconstructed target.

[0055] Φ=ΑX (1);

[0056] Among them, Φ is the surface fluorescence data, Α represents the system matrix, and X is the distribution of the internal fluorophores of the imaging target to be solved. The above linear relationship is transformed into the L0 norm minimization problem:

[0057]

[0058] ||X||0 is the zero norm, indicating the number of non-zero elements, and ε is a given threshold. The present invention designs an orthogonal least squares algorithm with an adaptive nearest neighbor strategy to solve the above optimization problem.

[0059] The technical principles adopted in the present invention are as follows:

[0060] (a) Initialize the parameters: number of iterations i = 1, threshold ε, support set S i , sparsity K0 = 6, and L0 = 10, initial residual r0 = Φ, surface fluorescence distribution Φ,

[0061] Element selection criteriaq j Specifically, in an iteration, it selects a new column index j according to m :

[0062]

[0063]

[0064]

[0065] in I is the column set, a j is the jth column of the system matrix A, u l are orthogonal basis vectors.

[0066] According to the above formula (3), L0 elements are selected to form the initial support set S0.

[0067] (b) Adaptive adjustment of step size: using nonlinear function To adjust the step size, the function is a monotonically decreasing function. The step size is expressed as follows:

[0068]

[0069] Where i is the number of iterations, s is the step size, denotes rounding up. Assume that the support set S i The number of atoms added is L i , and its iteration formula is L i =L i-1 -s, where s0 = L0 = 10. As the number of iterations increases, the number of atoms added to the support set gradually decreases until the number of atoms reaches 1, and then the iteration stops. The sparsity iteration formula is set to K i =K i-1 +s, where s0 = K0 = 6. As the number of iterations increases, the sparsity gradually increases, with a larger step size at the beginning of the increment and a smaller step size at the end, until it reaches 1.

[0070] (c) Support set update: Based on the finite element theory, the nearest neighbor node set is constructed according to the tetrahedral unit structure. i-1 is the support set generated by the i-1th iteration. Let any node G k ∈S i-1 , then the set of all nodes of the tetrahedron where the node is located is the nearest neighbor set, and S i-1 Take the union of the nearest neighbor sets of all nodes in the , and the resulting set is recorded as the nearest neighbor set E i-1 , the process is described by the nearest neighbor operator N, then E i-1 =N(S i-1 ), from E i-1 According to formula (3), select L i nodes into the support set S i-1 , forming a new support set S i , that is, S i =L i (E i-1 )∪Si-1 , L i (E i-1 ) indicates that from E i-1 Select L i nodes.

[0071] (d) Residual update: Set r i represents the residual vector generated by the i-th iteration. In addition, the residual vector r required for the next iteration i+1 for:

[0072] r i+1 =r i -u i+1 (7);

[0073] in,

[0074] Since each iteration needs to select L i nodes, so in the i-th iteration, we need to construct L i Linearly independent vectors

[0075] (e) Repeat steps (b)-(d), with i=i+1 each time, until the residual r i <ε or the step length of the sparsity K is 1, the iteration stops. The first K columns of the final support set are the solution set, that is,

[0076] X=K i (S i ) (8);

[0077] This solution is the solution to the minimization problem (2).

[0078] (f) The results were displayed using Tecplot imaging software.

[0079] Embodiment 1:

[0080] See also Figure 1 , the process of the fluorescence tomography reconstruction method of the present invention is as follows:

[0081] (1) Obtain surface fluorescence measurement data and establish a linear relationship between the fluorescence data and the internal fluorescence target distribution:

[0082] (2) Use a multimodal imaging system to collect fluorescence data and anatomical information of the imaging object,

[0083] (3) Using a multimodal optical molecular imaging system, the fluorescence data and the anatomical structure information of the imaging object are collected, the imaging target organism is meshed by finite element method, and then the model is approximated based on the diffusion equation of the photon transport model.

[0084] Φ=ΑX

[0085] Among them, Φ is the surface fluorescence data, Α represents the system matrix, and X is the distribution of the internal fluorophores of the imaging target to be solved. The above linear relationship is transformed into the L0 norm minimization problem:

[0086]

[0087] ||X||0 is the 0 norm, expressing the number of non-zero elements, and ε is the given threshold.

[0088] (4) The reconstruction results were obtained using the adaptive nearest neighbor orthogonal least squares algorithm and displayed using Tecplot software.

[0089] See also Figure 2 The present invention is a flowchart of the fluorescence molecular tomography reconstruction implementation.

[0090] See also Figure 3 The figure is a flow chart for realizing the adaptive nearest neighbor orthogonal least squares algorithm based on the present invention.

[0091] Combination Figure 4-Figure 6 The reconstruction result based on the present invention is further described.

[0092] Figure 4 It is a digital mouse model used for simulation experiments. We only selected the torso of the mouse and segmented the main organs of the mouse, including the heart, lungs, liver, stomach, kidneys and muscle tissue.

[0093] Figure 5 This is the result of the FMT dual light source reconstruction at different edge-to-edge distances based on the present invention. The green area in the figure is the reconstruction result of each stage. It can be seen that the dual light source reconstruction result is better as the edge-to-edge distance increases.

[0094] Figure 6 The invention is applied to FMT 3D reconstruction, and the dual light source is a fluorescent target reconstruction distribution map at a z=14mm section under 6 projection points. The dual light source reconstruction can be completed when the edge-to-edge distance is 2mm to 4mm. The invention introduces a nonlinear function based on the greedy strategy. An adaptive strategy is used to approximate the true sparsity, and a nearest neighbor strategy is used to accurately select the support set, which can accurately and effectively reconstruct the image with high precision and high spatial resolution.

[0095] 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 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 belongs to the protection scope of the technical solution represented by the embodiments of the present invention.

Claims

1. A light source reconstruction method based on an adaptive nearest neighbor orthogonal least squares algorithm, characterized in that: The following steps are involved: Step 1: Obtain measurement data: collect surface fluorescence data and anatomical structure information of the target organism, perform finite element meshing on the reconstructed target organism, and then approximate the model based on the diffusion equation of the photon transmission model to establish a linear relationship between the surface fluorescence data and the distribution of fluorophores inside the reconstructed target; ； in, is the surface fluorescence data, represents the system matrix, is the distribution of fluorophores inside the reconstruction target to be solved; Step 2: Normalize the measured data: Convert the linear relationship in step 1 into Norm minimization problem: ； is the zero norm, indicating the number of non-zero elements, is a given threshold; Step 3: Use the adaptive nearest neighbor orthogonal least squares algorithm to reconstruct and obtain the optimal solution ; The step three specifically includes: 3.1 Initialization parameters: i represents the number of iterations, initial value =1, sparsity , , the initial residual ; Element selection criteria , in the iteration, select a new column index : ；（3） (4)； (5)； in , is a collection of columns, is the system matrix A List, and u i is the orthogonal basis vector of I; according to the above formula (3) The initial support set ; 3.2 Adaptive step size adjustment: using nonlinear function To adjust the step size, the function is a monotonically decreasing function, and the step size is expressed as follows: (6)； Where s is the step size, denotes rounding upwards; let the support set The number of atoms added is , and its iteration formula is ,in ,As the number of iterations increases, the number of atoms added to the support set gradually decreases, until the number of atoms becomes 1, then the iteration stops; The sparsity iteration formula is set as ,in ; As the number of iterations increases, the sparsity gradually increases, with a larger step size at the beginning of the increment and a smaller step size at the end, until it reaches 1; 3.3 Support set update: Based on the finite element theory, the nearest neighbor node set is constructed according to the tetrahedral unit structure; is the support set generated by the i-1th iteration, let any node , then the set of all nodes of the tetrahedron where the node is located is the nearest neighbor set. Find Take the union of the nearest neighbor sets of all nodes in the , and the resulting set is recorded as the nearest neighbor set , this process is represented by the nearest neighbor operator To describe, ,from According to formula (3), select Nodes are incorporated into the support set , forming a new support set ,Right now , Indicates from Select nodes; 3.4 Residual Update: Setting Representative The residual vector generated by the iteration, in addition, the residual vector required for the next iteration for: (7)； in, ; Since each iteration requires the selection nodes, so in the Iterations require construction Linearly independent vectors ; 3.5 Cycle steps 3.1-3.4: once per cycle , until the residual Or when the step length of the sparsity K changes to 1, the iteration stops; the first K columns of the final support set are the solution set, that is (8)； This solution is the solution to the minimization problem.

2. The light source reconstruction method based on the adaptive nearest neighbor orthogonal least squares algorithm according to claim 1, characterized in that: The results were analyzed using Tecplot imaging software. for display.

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