Multi-scene single-frame large-view-field scattering imaging method based on polarization coding and spatial multiplexing

Abstract

The invention discloses a multi-scene single-frame large-view-field scattering imaging method based on polarization coding and spatial multiplexing, and the method comprises the steps: building a reflection-type scattering imaging system and a transmission-type scattering imaging system, and respectively measuring the OME ranges of the reflection-type scattering imaging system and the transmission-type scattering imaging system; multiple spatial multiplexing speckles are collected through single exposure of a polarization camera, and a linear multiplexing model is constructed; a signal identification method based on a minimum mean square error and an N-FINDR algorithm are introduced to realize target number identification and polarization specificity speckle initial value extraction; designing a Laplacian regularization term constrained Cozishi non-negative matrix factorization algorithm, and analyzing polarization specific speckles of different OME regions by using the extracted target number and initial value iterative optimization; and reconstructing a speckle result by using a phase recovery algorithm, and hiding the target after recovering the scattering medium. According to the method, the view field range is expanded by 4.5 times in a transmission-type / reflection-type system, the fidelity of a demultiplexing result reaches 32dB, and hidden scene reconstruction without continuous acquisition is realized.

Description

Technical Field

[0001] The present invention relates to the field of scattering imaging, and in particular to a multi-scene single-frame large-field-of-view scattering imaging method based on polarization coding and spatial multiplexing. Background Art

[0002] Light propagates in a straight line through homogeneous media such as clean water and air, allowing traditional optical imaging systems to directly image it. However, when light passes through complex scattering media, such as clouds, smoke, frosted glass, turbid water, and biological tissue, it collides with particles in the scattering medium, causing multiple scattering and randomizing the photon propagation path. Conventional optical systems are unable to directly image the target. Current methods for scattering imaging include adaptive optics, wavefront shaping, transfer matrix measurement, and speckle correlation imaging. Speckle correlation imaging offers the advantage of achieving single-frame, non-invasive imaging without prior information. However, this method has a significant drawback: due to the limited range of the optical memory effect (OME), the imaging field of view (FOV) is narrow. Therefore, conventional speckle correlation imaging can only image a single target within the OME, severely hindering its application in multi-target detection beyond the FOV.

[0003] To expand the field of view of scatter imaging, researchers have proposed numerous solutions, which can be categorized into four categories: The first category utilizes prior information (such as the point spread function (PSF), target location, and number of targets) combined with spatial demultiplexing techniques to expand the imaging field of view. However, this approach generally requires intrusion into the imaging system, making it difficult to apply in practice. The second category utilizes mathematical methods to measure the transmission matrix and establish a connection between the input and output fields. However, this approach is generally computationally intensive and requires high stability of the scattering medium. The third category utilizes deep learning methods to train a network to decode speckle patterns, analyze the statistical correlation between targets and speckle patterns, and resolve unknown targets. However, this approach requires extensive dataset annotation and lengthy training, and suffers from slow model adaptation, making it difficult to apply in dynamic environments where scattering conditions evolve rapidly.

[0004] The fourth category focuses on extracting effective information from different OME regions from large field-of-view speckles through component analysis and feature separation, thereby weakening the limitation of the OME range. When multiple targets with a distance greater than the OME range are illuminated at the same time, the multiplexed speckles generated through the scattering medium can be regarded as a linear superposition of the speckles generated by each sub-target separately. Based on this principle, in 2020, the existing technology proposed a blind target position detection method based on a low-crosstalk area allocation strategy (Wang X, JinX, Li J. Blind position detection for large field-of-view scattering imaging[J / OL]. Photonics Research, 2020, 8(6): 920-928. DOI:10.1364 / PRJ.388522.), which can restore scenes with multiple isolated targets exceeding the OME range without the need for prior information. However, blind detection methods usually require complex inverse problem solving, especially in large field-of-view scenes. The increase in the number of targets and the increase in the field of view angle will lead to an exponential increase in the number of algorithm iterations and the amount of calculation. The following year, the existing technology proposed to use superposition and averaging algorithms to separate the speckles produced by two targets, one moving and one static, with a distance greater than OME, to achieve large field of view imaging (He W, Wei Y, Lu D, et al. Noninvasive imaging of two isolated objects through a thin scattering medium beyond the 3D optical memory effect by speckle-based differencestrategy[J]. Optics Letters, 2021, 46(23): 5954-5957.). However, this method is only applicable to specific scenarios and has strict requirements on the number of targets. In 2023, the existing technology improved this speckle separation-based method and introduced a mixed speckle simplex separation strategy (Wei Y, Guo E, Zhao Y, et al. Prior-free mixedspeckle simplex separation strategy for multi-object imaging through thinscattering media beyond the optical memory effect[J]. APL Photonics, 2023, 8(12).), which greatly improved the separation fidelity and solution capability.However, all of the above methods require continuous acquisition of speckle images multiple times, do not have single-frame imaging capabilities, and are difficult to meet application scenarios with high-speed imaging requirements. Summary of the Invention

[0005] In order to overcome the shortcomings of the prior art, the present invention provides a multi-scene single-frame large-field-of-view scattering imaging method based on polarization coding and spatial multiplexing.

[0006] The technical solution for achieving the purpose of the present invention is: a multi-scene single-frame large-field-of-view scattering imaging method based on polarization coding and spatial multiplexing, comprising:

[0007] Step 1: Build two scattering imaging systems, one reflective and one transmissive, and measure their OME ranges to verify the linear multiplexing relationship of polarization speckle.

[0008] Step 2: Use a polarization camera to collect multiple spatially multiplexed speckles in a single exposure and construct a linear multiplexing model;

[0009] Step 3: Introduce the minimum mean square error-based signal recognition method and the N-FINDR algorithm to respectively realize the number of polarization targets and extract the initial value of polarization-specific speckle;

[0010] Step 4: Design a Cauchy non-negative matrix factorization algorithm constrained by the Laplace canonical term. Use the number of targets extracted in Step 3 and the initial value of the polarization-specific speckle to iteratively optimize and parse the polarization-specific speckle patterns in different OME regions. Use the phase retrieval algorithm to reconstruct the speckle results and recover the targets hidden behind the scattering medium.

[0011] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the steps of the above method are implemented when the processor executes the program.

[0012] A computer-readable storage medium stores a computer program, which implements the steps of the above method when executed by a processor.

[0013] A computer program product comprises a computer program, which implements the steps of the above method when executed by a processor.

[0014] Compared with the prior art, the present invention has the following significant advantages:

[0015] (1) The present invention does not require multiple consecutive data acquisitions, and only requires a single exposure of the polarization camera to achieve full data acquisition;

[0016] (2) The method proposed in this paper can be applied to both imaging through scattering media and imaging around corners;

[0017] (3) The continuity and similarity of speckles with similar polarization angles are used to introduce the adjacency matrix and graph Laplace regularization term constraints into the specific speckle extraction process to guide the iterative direction of the NMF algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Schematic diagram of polarization-coded spatial multiplexing imaging method, where (a) is the transmission imaging system configuration, (b) is the reflection imaging system configuration, and (c) is the polarization-guided speckle demultiplexing framework.

[0019] Figure 2 Configuration of the optical system for large-field imaging beyond the OME range, where (a) is the transmissive imaging system; (b) is the reflective imaging system; (c) is the OME range measurement device; and (d) is the OME range measurement results of the reflective and transmissive systems, respectively.

[0020] Figure 3 To experimentally verify the spatial linear multiplexing relationship between the measured speckle and the speckles of different targets in different polarization states, (a) is a transmission system and (b) is a reflection system.

[0021] Figure 4 The experimental results of single-frame multi-target imaging through scattering media in a 2× OME range are shown, where (a) is the position of the target and polarization mask, (b) is the polarization-multiplexed speckle pattern captured by the polarization camera, (c) is the initial polarization-specific speckle demultiplexed by the N-FINDR algorithm and their respective autocorrelation results, (d) is the accurate polarization-specific speckle demultiplexed after optimization by the NMF algorithm and their respective autocorrelation results, (e) is the target structure reconstructed from the demultiplexed speckle using the HIO phase recovery algorithm, and (f) is the real target speckle and autocorrelation result as a control group.

[0022] Figure 5 Experimental results of single-frame multi-target imaging through scattering media at different target spacings: (a) 2.5× OME; (b) 3× OME; (c) 3.75× OME.

[0023] Figure 6 The experimental results of single-frame multi-target imaging in a 2.5× OME range angle scenario, (a) shows the position of the target and polarization mask; (b) shows the polarization multiplexed speckle pattern captured by the polarization camera; (c) shows the initial polarization-specific speckle demultiplexed by the N-FINDR algorithm and their respective autocorrelation results; (d) shows the accurate polarization-specific speckle demultiplexed after optimization by the NMF algorithm and their respective autocorrelation results; (e) shows the target structure reconstructed from the demultiplexed speckle using the HIO phase recovery algorithm; (f) shows the real target speckle and autocorrelation results as a control group.

[0024] Figure 7 These are the imaging experimental results of a single-frame multi-target corner scene at different target spacings, where (a) is 3× OME; (b) is 3.5× OME; (c) is 4× OME; and (d) is 4.5× OME. DETAILED DESCRIPTION

[0025] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0026] The core of this method is to extract differentiated speckle information from different OME regions within a large field of view to achieve individual reconstruction. By introducing a special polarization camera, speckle images in up to 181 polarization states can be calculated with a single exposure. Leveraging the polarization linear multiplexing relationship between the acquired speckle and the speckle corresponding to different OME regions, a polarization-guided speckle demultiplexing framework is constructed to resolve the polarization-specific speckle patterns in different OME regions. Initialization is performed first, using the minimum mean square error (MMSE) criterion to identify the number of targets, and the N-FINDR algorithm is used to estimate the initial value of the polarization-specific speckle. Furthermore, the polarization-specific speckle patterns corresponding to different OME regions are accurately demultiplexed using the truncated Cauchy non-negative matrix factorization (TCLF-NMF) algorithm based on neighborhood weighting and graph Laplace regularization terms. This method expands the field of view by 4.5 times in a transmissive / reflective system, achieving a demultiplexing fidelity of 32 dB, enabling reconstruction of hidden scenes without the need for continuous acquisition.

[0027] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0028] A multi-scene single-frame large-field-of-view scattering imaging method based on polarization coding and spatial multiplexing, comprising:

[0029] Step 1: Build two scattering imaging systems, one reflective and one transmissive, and measure their OME ranges to verify the linear multiplexing relationship of polarization speckle. Specifically:

[0030] Step 1-1, experimental system setup: Build both a reflective and a transmissive scattering imaging system. The difference between the two is that the scattering medium of the transmissive scattering imaging system is frosted glass, while the reflective scattering imaging system uses a ZnO-coated wall instead of frosted glass as the scattering medium. The light source and camera are distributed on both sides of the scattering medium and separated by a light-blocking baffle to prevent direct illumination.

[0031] Step 1-2, OME range measurement: A target plate with a 0.5mm×0.5mm pinhole cutout at its center is placed on a motorized translation stage to simulate a point light source. The stage controls the point light source to move perpendicular to the optical path with a 0.1mm step size, generating a speckle pattern for correlation calculation. The cross-correlation coefficient between each frame of the displaced speckle pattern and the central reference speckle pattern is calculated, and a correlation curve is plotted. The OME range is defined as the displacement range within which the speckle cross-correlation coefficient remains above 0.5. Therefore, the actual OME range for a transmissive system is 2.79mm. The same method can be used to measure the OME range of a reflective system to 1.60mm.

[0032] Steps 1-3, polarization-encoded target board design: Design a hollow target board containing multiple targets. Each target is affixed with linear polarization masks arranged at equal intervals in N directions. In the four-target experiment, the linear polarization masks are at 0°, 45°, 90°, and 135°, respectively.

[0033] Step 1-4, linear multiplexing relationship verification: the relationship to be verified is , where I mix represents multiplexed speckle, I i represents the sub-target speckle in different OME areas, and N represents the number of polarization targets. A target plate with four hollow letters is placed on the object plane, and each target is equipped with a different polarizer (0°, 45°, 90°, 135°). First, all targets are collected to generate polarization multiplexing speckle I mea Then, the other three targets were covered with black light-shielding paper, and the polarization speckle patterns generated by the four targets were collected separately. i , will I i Perform linear superposition to obtain computational multiplexing speckle I mix ; will I mix with I mea Normalized difference analysis of the two speckle patterns shows that the difference between all pixels in the transmissive system is within the range [-0.14, 0.14], while the pixel-by-pixel difference results for the reflective system are all within the range [-0.1, 0.1]. This result fully demonstrates the validity of the spatial linear multiplexing model in polarization-coded speckle.

[0034] Step 2: Use a polarization camera to capture multiple spatially multiplexed speckles in a single exposure and construct a linear multiplexing model; specifically:

[0035] Data acquisition: Both the reflective and transmissive scattering imaging systems utilize the snapshot function of the polarization camera to achieve complete Stokes data acquisition. The polarization camera integrates a micropolarizer array with 0°, 45°, 90°, and 135° angles. Through the internal computational synthesis function, all polarization state speckle patterns are acquired in a single exposure. The acquisition step size of the polarization camera is set to 3°, and 61 polarization multiplexed speckle patterns are acquired in a single exposure.mk ;

[0036] Establishing a linear multiplexing model: Based on Muller matrix analysis, the polarization camera analyzer introduces a unique intensity modulation coefficient for each sub-target speckle , combined with the linear multiplexing relationship verified in step 1, we can get , where I mk represents the kth multiplexed speckle collected, , M is the number of multiplexed speckles collected by the polarization camera at different polarization angles, 0≤a i <1 and ; will I mk and I i Vectorize and normalize respectively to get b k and u i , from which we can get ; Among them, α k = [a1,a2,…,a N ] T is the intensity modulation coefficient a i A vector set; let A = [α1, α2,…,α M ] represents α k The vector set, B = [ b1,b2,…,b N ],U = [u1,u2,…,u N ] are the vectorized multiplexed speckle b k and different polarization target speckle u i The vector set constitutes a linear reuse model: .

[0037] The demultiplexing of different targets in different OME areas can be transformed into a mathematical linear solution model. The process is shown as follows: Figure 1 As shown in Figure 2, M multiplexed images captured by a polarization camera are analyzed using a polarization-guided speckle demultiplexing framework to resolve polarization-specific speckle patterns from N different targets. Once separated, a phase recovery algorithm is used to reconstruct the demultiplexed speckle patterns individually, restoring the true large-field-of-view scene.

[0038] Preferably, the number of spatially multiplexed speckles collected should be greater than 20, and in this embodiment, 61 are used.

[0039] Step 3: Introduce the minimum mean square error-based signal recognition method and the N-FINDR algorithm to respectively realize the number of polarization targets and extract the initial value of polarization-specific speckle. Step 3 is as follows:

[0040] Step 3-1, identify the number of polarization targets through MMSE: according to , that is, the covariance matrix R of matrix B B=R UA ; Among them, R B =BB T / M, then ,in Represents R UA The estimated value of Perform eigenvalue decomposition to obtain:

[0041] (1);

[0042] Where W = [e1,e2,…,e G ] is the characteristic matrix, G represents the number of elements in the polarization speckle, Σ is a diagonal matrix containing the eigenvalues ​​in descending order; the space is divided into two orthogonal subspaces, [e1,e2,…,e j ]determined by the j-dimensional subspace , and the (Gj)-dimensional subspace determined by other elements Based on the non-negative constraint of polarization multiplexing speckle, the projection of the mean value of B in any eigenvector direction should be non-zero. Therefore, the signal subspace is determined by finding the feature subset that best represents the least square mean of the data set. The mean value of the collected multiplexed polarization speckle intensity is defined as: , where 1 M is an M-dimensional all-one vector; let s j is s in the signal subspace Projection on The estimated value of Projection to Obtained above, that is , where P j = W j W j T is the projection matrix; then s and The mean square error MSE is:

[0043] (2);

[0044] Where E(·) represents the mathematical expectation, I represents the identity matrix; since the projection matrix P j is an idempotent matrix, and P j T =P j , P j 2 =P j , so (IP j ) T (IP j ) = (IP j ), so the above formula is simplified to:

[0045] (3);

[0046] in , represents the total signal energy, s T P j s represents the signal in the subspace Therefore, when mse(j) reaches its minimum value, the projection energy reaches its maximum value, and the subspace The order of is:

[0047] (4);

[0048] The obtained j is the number N of real target polarization speckles;

[0049] Step 3-2: Extract the initial polarization-specific speckle value using the N-FINDR algorithm. Each collected polarization-multiplexed speckle pattern can be represented as a linear combination of polarization-specific speckle patterns from different sub-targets in different OME regions. From a geometric perspective, the collection of all collected speckle patterns forms a convex polyhedron in high-dimensional space, with the independent polarization speckle pattern of each target located at a vertex of this convex polyhedron. Based on this idea, the speckle demultiplexing problem is transformed into a vertex identification problem.

[0050] The N-FINDR algorithm searches for vertices by maximizing the volume of a polyhedron. The entire process consists of four steps:

[0051] In the first step, in order to reduce the computational complexity and suppress noise interference, the speckle data is reduced in dimension by principal component analysis (PCA), the principal component information with the largest variance is retained, and the data is projected into (N-1)-dimensional space to generate M principal component multiplexed speckle vectors pb k ;

[0052] In the second step, N multiplexed speckles are randomly selected as candidate vertices to form an N×N augmented matrix H:

[0053] (5);

[0054] The third step is to calculate the volume V(H) of the polyhedron under the current vertex configuration according to the matrix determinant det(·):

[0055] (6);

[0056] Step 4: Fix (N-1) vertices and use the remaining pixels to replace the Nth vertex in sequence. If the volume of the polyhedron increases, the replacement is accepted;

[0057] Repeat steps 2 to 4 to iteratively optimize the volume of the polyhedron until the volume is maximized and the convergence condition is met. ,in 、 Respectively represent the volume of the polyhedron at the wth and w-1th updates, Indicates the convergence threshold. At this time, the N polarization multiplexing speckles corresponding to the vertices of the polyhedron are the initial values ​​of the target polarization speckle.

[0058] Step 4: Design a Cauchy non-negative matrix factorization algorithm constrained by the Laplace regularization term, and use the number of targets extracted in step 3 and the initial value of the polarization-specific speckle to iteratively optimize and parse the polarization-specific speckle in different OME regions; use the phase retrieval algorithm to reconstruct the speckle results and recover the target hidden behind the scattering medium. Specifically:

[0059] Step 4-1, truncated Cauchy loss function: To enhance the robustness of the model, the truncated Cauchy loss function is used instead of the least squares loss as the objective function of NMF; the expression of the truncated Cauchy loss function (TCLF) f(x) is:

[0060] (7);

[0061] Where r is the scale coefficient of the Cauchy distribution, c is a custom adjustable threshold, and x represents the loss function, which is the difference between the true value B and the decomposition result (B-AU). When the absolute value of x is greater than the threshold, the loss function is truncated to a fixed value, weakening the impact of excessively high values ​​on the objective function, thereby suppressing smooth noise and outliers and enhancing the robustness of the model.

[0062] The objective function J of the NMF model based on TCLF can be expressed as:

[0063] (8);

[0064] Where G represents the number of pixels in the speckle image, (B-UA) lk Represents the element value of the lth row and kth column of the matrix B-UA;

[0065] Step 4-2, graph Laplace regularization constraint: According to graph theory, all polarization multiplexed speckles are mapped into a complete undirected graph, with each speckle representing a vertex, to obtain an M×M adjacency matrix; the polarization speckle correlation shows a strong angular dependence, and the closer the camera polarization angles are, the closer the two multiplexed speckle patterns b are. m and b n The closer the modulation vectors α are, the stronger the similarity of the multiplexed speckles is, and the larger the weight value should be; conversely, the larger the difference between the polarization angles is, the closer the weight value should be to 0; According to the above relationship, the Gaussian kernel is used to weight the M images composed of multiplexed speckles, b m and b n Weight between Expressed as:

[0066] (9);

[0067] Where δ is the bandwidth of the Gaussian kernel;

[0068] Adjacent multiplexed speckles should have similar modulation vectors. By adding a penalty term to the modulation matrix A based on this relationship, adjacent modulation vectors are mutually constrained and corrected to avoid isolated and unrealistic estimates, guiding the iterative process toward a smoother direction within the modulation matrix. Graph Laplace regularization can be used to effectively transform the similarity relationship:

[0069] (10);

[0070] where tr(·) represents the trace of the matrix, , D represents a diagonal matrix, the diagonal elements , The weight coefficient The weight matrix is ​​composed of L, the Laplace matrix, and A m 、A n Respectively represent the mth and nth columns of the modulation coefficient matrix A, that is, α m , α n ;

[0071] In order to reduce the amount of calculation and improve the efficiency of operation, the adjacency matrix is ​​simplified by the local neighborhood weighting method; for any point b m , only considering the local neighborhood The weight coefficient within, t is the custom neighborhood radius; the weight coefficients between all non-adjacent point pairs (|mn| > t) are set to 0; point b m Local neighborhood range The sum of all points in the neighborhood and its weight value is defined as the neighborhood similarity coefficient , which can be expressed as:

[0072] (11);

[0073] In formula (11), For all The tensor polarization speckle adjacency matrix and the similarity measure vector generated by the weights can be expressed as In actual calculation, in order to meet the matrix matching requirements, the vector C is expanded into the matrix R:

[0074] (12);

[0075] The objective function of the NMF model after adding the adjacency matrix and graph Laplace regularization term can be expressed as:

[0076] (13);

[0077] ;

[0078] in is an N-dimensional full-row vector, is an M-dimensional full-row vector, T represents the transpose operation, and β is the regularization coefficient;

[0079] Step 4-3 Model solution: Since Equation (13) is nonlinear and non-convex, it is difficult to solve directly. Based on the principle of Half-Quadratic Optimization, we introduce auxiliary variables and use the convex conjugate theory to decompose the original problem into a series of more easily solvable sub-problems for solution. For the truncated Cauchy loss function, first, let , g(y) = -f(y), Convert to ; According to the Legendre-Fenchel transformation, two conjugate transformations of g(y) yield:

[0080] (14);

[0081] Where Z is the conjugate variable of y, express The conjugate function of g(y) takes its maximum value. ,in Represents the partial derivative of the function g(y) with respect to g. Substituting y into it, we can see that when U and A are fixed, the element value Z in the lth row and kth column of the matrix Z is lk Expressed as:

[0082] (15);

[0083] in, Represents the modulus of the element value in the lth row and kth column of the matrix B-UA. When Z is fixed, the goal is an optimization problem involving two variables, U and A. The most common solution is to use the alternating direction method of multipliers (ADMM) to transform the original problem into several simple subproblems containing only one variable, and alternately optimize each subproblem to approach the optimal solution of the original problem. The two subproblems after transformation are:

[0084] (16); (17);

[0085] in 、 is the Lagrange multiplier, represents dot product;

[0086] Under the Karush-Kuhn-Tucker condition, the optimal solution of formula (16) is obtained, and the update rule of A is:

[0087] (18);

[0088] in The mth column of , , represents the point division operation; for the objective function (17), under the KKT condition, the update rule of U can be obtained:

[0089] (19);

[0090] By alternately iteratively updating matrices A, Z, and U until convergence, the polarization-specific speckles of different targets can be separated. Subsequently, the phase recovery algorithm can be used to reconstruct multiple targets beyond the OME range hidden behind the scattering medium.

[0091] Alternately iterate and update matrices A, Z, and U until the convergence conditions are met , where J q 、J q-1 denote the values ​​of the objective function at the qth and q-1th updates, respectively, and tol represents the convergence threshold. This allows the polarization-specific speckle patterns of different targets to be separated. Subsequently, a phase recovery algorithm can be used to reconstruct multiple targets beyond the OME range hidden behind the scattering medium. The specific process is shown in Table 1.

[0092] Table 1 Framework of polarization-guided speckle demultiplexing

[0093]

[0094] The present invention designs two experimental configurations for large-field imaging beyond the OME range, namely a transmissive system for penetrating scattering media and a reflective system for corner imaging. Figure 2(a) shows the model of the transmission experiment system. Natural light from a xenon lamp (Beijing PerfectLight, PLS-SXE300E) passes through a pupil (Thorlabs, ID25SS / M, 10 mm diameter) and is homogenized by a rotating frosted glass. The light then passes through two collimating lenses to form a collimated beam. This beam then passes through a narrowband filter with a central wavelength of 520 nm to form unpolarized monochromatic light, which is then applied to the center of the target. The target is affixed with N equally spaced linear polarization masks (Changcheng Advanced Materials, T4-1825TP). In the four-target experiment, the linear polarization masks are angled at 0°, 45°, 90°, and 135°, respectively. Linearly polarized light from multiple targets is scattered through ground glass (Thorlabs, DG100X100-220, 220 grit) and captured by a polarization camera (The Imaging Source DYK 33UX250, 2448×2048 pixels) equipped with integrated micropolarizers at 0°, 45°, 90°, and 135°. The polarization camera's internal computational synthesis function allows the acquisition of speckle patterns from all polarization states in a single exposure. Figure 2 Figure (b) shows the model of the reflective experimental system. The optical paths before scattering are identical for both the reflective and transmissive systems. The difference is that the scattering medium in the transmissive system is frosted glass, while the reflective system uses a ZnO-coated wall instead of frosted glass. The light source and camera are located on either side of the scattering medium, separated by a light-blocking baffle to prevent direct illumination. Both systems utilize the snapshot function of the polarization camera to achieve complete Stokes data acquisition.

[0095] To verify the feasibility of imaging beyond the scope of OME, the specific scope of OME must be clarified first. Figure 2 (c) shows the experimental setup for measuring the OME range using a transmission imaging system. A target plate with a 0.5mm×0.5mm pinhole cutout in the center is placed on a motorized translation stage to simulate a point light source. The translation stage controls the point light source to move perpendicular to the optical path with a step size of 0.1mm, generating a speckle pattern for correlation calculation. The correlation coefficient between the displacement speckle pattern and the central reference speckle pattern is calculated for each frame, and plotted as shown in the figure. Figure 2 The correlation curve is shown in (d) in Figure 3. The OME range is defined as the displacement range in which the speckle cross-correlation coefficient remains above 0.5, i.e. Figure 2 The area within the two blue dotted lines in (d) indicates that the actual OME range of the transmissive system is 2.79 mm. The OME range of the reflective system measured using the same method is 1.60 mm.

[0096] exist Figure 2Based on the optical system shown, the present invention conducted three experimental verifications: linear multiplexing relationship verification, single-frame multi-target imaging through scattering media, and single-frame multi-target imaging at corners. These experiments collectively verified the feasibility of the proposed large-field-of-view imaging method beyond the OME range.

[0097] (1) Linear multiplexing relationship verification

[0098] In order to verify the spatial linear multiplexing model (Equation (5)), rigorous verification experiments were set up for both experimental devices. Figure 3 Figure (a) shows the verification process of the transmissive system. A target plate with four cutouts of the letters 'L', 'Z', '7', and 'V' is placed on the object plane. Each target is equipped with a different polarizer (0°, 45°, 90°, and 135°). The size of each cutout letter is 1.5 mm, and the distance between each target is 7 mm (2.5× OME range). Natural light passes through the four-way linear polarization mask and the target plate to form four beams of linearly polarized light. After being scattered by frosted glass, polarization-multiplexed speckle is generated. Then, the other three targets were covered with black light-shielding paper, and the polarization speckles generated by the four targets were collected separately. ,Will Perform linear superposition to obtain computational multiplexing speckle .Will and By comparing, we found that the intensity distribution of the two images is highly similar. The two speckle images were subjected to normalized difference analysis. The results showed that the difference of all pixels was between [-0.14, 0.14], and the difference of most pixels was within [-0.1, 0.1], which confirmed the measurement of multi-target speckle. and different target speckles with different polarization states A linear multiplexing relationship is established between them.

[0099] Figure 3 Figure (b) shows the verification process of the reflective imaging system. The distance between the targets is 4mm (2.5×OME range). The verification method is the same as that of the transmission system. The results are basically consistent with the experimentally obtained multi-target speckle intensity distribution, and the pixel-by-pixel difference results are all within the range of [-0.1, 0.1]. These results fully demonstrate the validity of the spatial linear multiplexing model in polarization-coded speckle.

[0100] (2) Single-frame multi-target imaging through scattering media

[0101] This embodiment builds a transmission single-frame multi-target imaging experimental system and designs a four-target imaging experiment with target spacing exceeding different degrees of OME range. Figure 4As shown in (a), each target is 1.5 mm in size, and the distance between each target is 5.5 mm (2× OME range). Natural light passes through a target with a four-way polarization mask, generating four linearly polarized beams containing target information in different OME regions. After passing through a scattering medium (ground glass), these beams spatially mix, resulting in a multiplexed speckle pattern captured by a polarization camera. Because the polarization camera has a built-in micropolarizer array and computational synthesis module, multiplexed speckle patterns in all polarization states can be acquired in a single exposure, applying different intensity modulation coefficients to the polarization speckle patterns of different targets.

[0102] The acquisition step of the polarization camera is set to 3°, and 61 polarization multiplexed speckle images are acquired in one exposure. ,like Figure 4 First, the number of targets N is obtained by MMSE algorithm, and then the N-FINDR method is used to obtain Extract the N speckles with the lowest degree of multiplexing as the initial value of polarization-specific speckle ,like Figure 4 However, since each speckle image actually collected contains at least (N-1) polarization components of the target, There is still interference from other speckles, which can be seen in their respective autocorrelation structures. To overcome this limitation, the present invention uses the designed Cauchy NMF algorithm, combined with the graph Laplace regularization constraint, to find the exact solution for different target speckles. Through multiple iterative optimizations, the demultiplexed polarization speckle is obtained. ,like Figure 4 As shown in (d) in the figure, the demultiplexed polarization-specific speckle structure is significantly purified, and its autocorrelation result is and Finally, the HIO phase recovery algorithm is used to Reconstruct the hidden target results separately ,like Figure 4 As shown in (e) in .

[0103] The demultiplexed speckle image and autocorrelation results are compared with Figure 4 (f) shows the real reference speckle images collected separately from targets with different polarization angles. and autocorrelation results For comparison, it can be seen that the initial value extracted by N-FINDR and The target structure is recognizable, but it also shows obvious target crosstalk. Especially the autocorrelation of the polarization-specific speckle at 45° In the image, although the main component is '2', it still contains residual speckle from the 0° polarization target 'L' and the 90° polarization target 'X'. Since the crosstalk speckle components are relatively small and the speckle itself is disordered, the impact of crosstalk is difficult to directly determine. In this embodiment, the polarization-specific speckle demultiplexed before and after optimization by the NMF algorithm is calculated separately. 、 The PSNR between the real target reference speckle I is used to quantitatively represent the crosstalk effect. The results are shown in Table 2, where 0°-L represents the 0° polarization target 'L', 45°-2 represents the 45° polarization target '2', 90°-X represents the 90° polarization target 'X', and 135°-D represents the 135° polarization target 'D'. It can be seen that for each separation result, the PSNR between FS and I is significantly improved compared to the PSNR between IS and I. The PSNRs of IS and I are all below 30dB, with an average of 29.0238dB, while the average PSNR between FS and I is 32.1052 dB. The autocorrelation structure analysis further confirms the optimization effect of the constrained NMF algorithm: compared with IA, FA has a stronger correlation signal peak and clearer structural contrast. Although there is still a slight loss of details compared with AC, as shown in the figure, Figure 4 (e) in the figure shows that after the NMF algorithm is optimized, the demultiplexed It is enough to reconstruct the target with clear and distinguishable structure.

[0104] Table 2 Figure 4 PSNR between the demultiplexed speckle and the true reference speckle

[0105]

[0106] In order to evaluate the fidelity of speckle demultiplexing results under different target spacing, the demultiplexing speckle was performed under 2.5×, 3×, and 3.5× OME ranges. and reconstruction results Respectively as Figure 5 As shown in (a)-(c) of the figure. The PSNR between the demultiplexed FS and the corresponding real target reference speckle of the three experimental groups is generally high, with average values ​​of 32.2887 (2.5×OME), 33.7435 (3×OME), and 30.9994 (3.5×OME), respectively. Phase recovery is performed, and the results can produce reconstruction results RO with clear and recognizable structures, indicating that the method proposed in the present invention is robust in a large field of view.

[0107] The transmission imaging system constructed in this embodiment successfully demonstrated the feasibility of single-frame multi-target scattering imaging beyond the OME range through polarization encoding and spatial demultiplexing technology, expanding the effective field of view of the system to 3.75 times the original.

[0108] (3) Single-frame multi-target imaging in corner scenes

[0109] Based on the verification of the above-mentioned transmission model, this embodiment also extends the feasibility assessment to Figure 2 In the reflective system shown in (b) in Figure 1, since the backscattered light from the ZnO wall still retains the same imaging mechanism as the transmission mode, there is an optical memory effect, and the hidden target can be reconstructed using the speckle correlation imaging method. Based on this underlying similarity, the method can be directly transferred. The feasibility verification process of the reflective imaging system is as follows: Figure 6 As shown, the size of a single target remains 1.5 mm, and the distance between targets is 2.5 × OME. Polarized light containing target information from different OME regions is reflected by the ZnO wall, generating multiplexed speckle patterns that are captured by a polarization camera in a single exposure. The entire recovery process, from speckle demultiplexing to phase recovery, is identical to the transmission-based verification process, demonstrating the robustness of this method across diverse scattering scenarios.

[0110] The results of quantitative verification using PSNR are shown in Table 3, where 0°-C represents the 0° polarization target 'C', 45°-K represents the 45° polarization target 'K', 90°-H represents the 90° polarization target 'H', and 135°-7 represents the 135° polarization target '7'. This result demonstrates the high structural fidelity between the demultiplexed speckle pattern and the real target reference speckle. All calculated results are above 25dB, and for each target corresponding to the polarization direction, the final value is Compared with the initial results extracted by the N-FINDR algorithm , the effect is always improved by more than 3dB, which shows that the designed iterative NMF algorithm can effectively suppress the mutual interference between different targets. The autocorrelation structure also shows obvious differences, although and Both have the target structure in AC, but Problems such as edge curvature degradation may lead to imbalanced reconstruction intensity and loss of structure. For example, the autocorrelation result of the target 'C' with 0° polarization is shown in the figure. There is almost no curvature on the left and right ends. While preserving the full edge curvature, the detail resolution is improved, achieving a high fidelity. These demultiplexed speckles can be reconstructed with high quality using the HIO phase recovery algorithm, successfully recovering all targets in the reflective configuration.

[0111] Table 3 Calculation results of 2.5ME target PSNR for reflective system

[0112]

[0113] In order to evaluate the feasibility of this method in different viewing ranges, this embodiment sets up four groups of experiments with target spacings of 4.8mm, 5.6mm, 6.4mm, and 7.2mm respectively. The results are as follows: Figure 7 Polarization-specific speckles demultiplexed from four experimental groups The PSNR results between the real target reference speckle I are all above 30dB, with average values ​​of 30.4873dB, 30.7070dB, 30.2723dB, and 30.1941dB, respectively, proving that the demultiplexing accuracy is high under different target spacings. Phase recovery is performed, and although some distortions and discontinuities are caused by the inevitable estimation errors of the reconstruction algorithm, the complete target reconstruction can still be achieved.

[0114] In summary, the experiments above demonstrate that the proposed polarization encoding and spatial multiplexing method can efficiently demultiplex the polarization-specific speckle patterns of targets with different OME regions from the multiplexed speckle pattern, successfully reconstructing target structures within a large field of view beyond the OME range. This method, in both reflective and transmissive configurations, breaks through the limitations of the OME range, achieving at least a 4.5-fold increase in field of view in a single acquisition.

[0115] This paper proposes a polarization encoding and spatial multiplexing method that overcomes the limitations of the OME range in transmission / reflection scattering imaging and enables single-frame multi-target imaging beyond the OME range. Through rigorous physical modeling and algorithmic polarization multiplexing mapping, a polarization-guided speckle demultiplexing framework is established to analyze and reconstruct polarization-specific speckle in different OME regions. The framework mainly consists of two stages: the first is the initialization stage, which uses the MMSE algorithm to identify the number of hidden targets and the N-FINDR algorithm to estimate polarization-specific speckle; followed by the precise demultiplexing stage, which proposes a TCLF-guided NMF algorithm that uses local neighborhood weighting and graph Laplacian regularization terms. Transmission and reflection experiments have shown that the proposed method can expand the field of view by 4.5 times while maintaining a demultiplexing fidelity of 32dB. The compatibility of the proposed method for single-frame imaging beyond the OME range opens up the possibility of applying speckle correlation imaging methods in actual dynamic scenes.

Claims

1. A multi-scene single-frame large field of view scattering imaging method based on polarization coding and spatial multiplexing, characterized in that: include: Step 1: Build a reflective and transmissive scattering imaging system, measure their OME ranges, and verify the linear multiplexing relationship of polarization speckle. Step 2: Use a polarization camera to collect multiple spatially multiplexed speckles in a single exposure and construct a linear multiplexing model; Step 3: Introduce the minimum mean square error-based signal recognition method and the N-FINDR algorithm to respectively realize the number of polarization targets and extract the initial value of polarization-specific speckle; Step 4: Design a Cauchy non-negative matrix factorization algorithm constrained by the Laplace canonical term. Use the number of targets extracted in step 3 and the initial value of the polarization-specific speckle pattern for iterative optimization to parse the polarization-specific speckle patterns in different OME regions. Use the phase retrieval algorithm to reconstruct the speckle pattern results and recover the target hidden behind the scattering medium.

2. The multi-scene single-frame large-field-of-view scattering imaging method based on polarization coding and spatial multiplexing according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1-1, experimental system setup: Build both a reflective and a transmissive scattering imaging system. The difference between the two is that the scattering medium of the transmissive scattering imaging system is frosted glass, while the reflective scattering imaging system uses a ZnO-coated wall instead of frosted glass as the scattering medium. The light source and camera are distributed on both sides of the scattering medium and separated by a light-blocking baffle to prevent direct illumination. Step 1-2, OME range measurement: A target plate with a 0.5mm×0.5mm pinhole cutout at its center is placed on a motorized translation stage to simulate a point light source. The stage controls the point light source to move perpendicular to the optical path with a 0.1mm step size, generating a speckle pattern for correlation calculation. The cross-correlation coefficient between each frame of the displaced speckle pattern and the central reference speckle pattern is calculated, and a correlation curve is plotted. The OME range is defined as the displacement range within which the speckle cross-correlation coefficient remains above 0.

5. Steps 1-3, polarization-encoded target board design: Design a hollow target board containing multiple targets. Each target is affixed with linear polarization masks arranged at equal intervals in N directions. In the four-target experiment, the linear polarization masks are at 0°, 45°, 90°, and 135°, respectively. Step 1-4, linear multiplexing relationship verification: the relationship to be verified is , where I mix represents multiplexed speckle, I i represents the sub-target speckle in different OME areas, and N represents the number of polarization targets. A target plate with four hollow letters is placed on the object plane, and each target is equipped with a different polarizer. First, all targets are collected to generate polarization multiplexing speckle I mea Then, the other three targets were covered with black light-shielding paper, and the polarization speckle patterns generated by the four targets were collected separately. i , will I i Perform linear superposition to obtain computational multiplexing speckle I mix ; will I mix with I mea The two speckle patterns were subjected to normalized difference analysis.

3. The multi-scene single-frame large-field-of-view scattering imaging method based on polarization coding and spatial multiplexing according to claim 2, characterized in that: In step 2, the number of spatial multiplexing speckle patterns collected must be greater than 20.

4. The multi-scene single-frame large-field-of-view scattering imaging method based on polarization coding and spatial multiplexing according to claim 2, characterized in that: The step 2 is specifically as follows: Data acquisition: Both the reflective and transmissive scattering imaging systems utilize the snapshot function of the polarization camera to achieve complete Stokes data acquisition. The polarization camera integrates a micropolarizer array with 0°, 45°, 90°, and 135° angles. Through the internal computational synthesis function, all polarization state speckle patterns are acquired in a single exposure. The acquisition step size of the polarization camera is set to 3°, and 61 polarization multiplexed speckle patterns are acquired in a single exposure. mk ; Establish a linear multiplexing model: Based on the Muller matrix analysis, the polarization camera analyzer introduces an intensity modulation coefficient for each sub-target speckle , combined with the linear multiplexing relationship verified in step 1, we can get , where I mk represents the kth multiplexed speckle collected, , M is the number of multiplexed speckles collected by the polarization camera at different polarization angles, 0≤a i <1 and ; will I mk and I i Vectorize and normalize respectively to get b k and u i , from which we can get ; Among them, α k = [a1,a2,…,a N ] T is the intensity modulation coefficient a i A vector set; let A =[α1, α2,…,α M ] represents α k The vector set, B = [ b1,b2,…,b N ],U = [u1,u2,…,u N ] are the vectorized multiplexed speckle b k and different polarization target speckle u i The vector set constitutes a linear reuse model: .

5. The multi-scene single-frame large-field-of-view scattering imaging method based on polarization coding and spatial multiplexing according to claim 4, characterized in that: The step 3 is specifically as follows: Step 3-1, identify the number of polarization targets through MMSE: according to , the covariance matrix R of matrix B B =R UA ; Among them, R B =BB T / M, then ,in Represents R UA The estimated value of Perform eigenvalue decomposition to obtain: (1)； Where W = [e1,e2,…,e G ] is the characteristic matrix, G represents the number of elements in the polarization speckle, Σ is a diagonal matrix containing the eigenvalues ​​in descending order; the space is divided into two orthogonal subspaces, [e1,e2,…,e j ]determined by the j-dimensional subspace , and the (Gj)-dimensional subspace determined by other elements Based on the non-negative constraint of polarization multiplexing speckle, the projection of the mean value of B in any eigenvector direction should be non-zero. Therefore, the signal subspace is determined by finding the feature subset that best represents the least square mean of the data set. The mean value of the collected multiplexed polarization speckle intensity is defined as: , where 1 M is an M-dimensional all-one vector; let s j is s in the signal subspace The projection on The estimated value of Projection to Obtained above, that is , where P j = W j W j T is the projection matrix; then s and The mean square error MSE is: (2)； Where E(·) represents the mathematical expectation, I represents the identity matrix; since the projection matrix P j is an idempotent matrix, and P j T =P j , P j 2 =P j , so (IP j ) T (IP j ) = (IP j ), so the above formula is simplified to: (3)； in Represents the total signal energy, s T P j s represents the signal in the subspace Therefore, when mse(j) reaches its minimum value, the projection energy reaches its maximum value, and the subspace The order of is: (4)； The obtained j is the number N of real target polarization speckles; Step 3-2: Extract the initial value of the polarization-specific speckle pattern using the N-FINDR algorithm: Each collected polarization-multiplexed speckle pattern can be represented as a linear combination of the polarization-specific speckle patterns of different sub-targets in different OME regions. All collected speckle patterns are aggregated in a high-dimensional space to form a convex polyhedron, with the independent polarization speckle pattern of each target located at a vertex of this convex polyhedron. This transforms the speckle demultiplexing problem into a vertex identification problem. The N-FINDR algorithm searches for vertices by maximizing the volume of a polyhedron. The entire process consists of four steps: In the first step, the speckle data is reduced in dimension by principal component analysis, the principal component information with the largest variance is retained, and the data is projected into (N-1)-dimensional space to generate M principal component multiplexed speckle vectors pb k ; In the second step, N multiplexed speckles are randomly selected as candidate vertices to form an N×N augmented matrix H: (5)； The third step is to calculate the volume V(H) of the polyhedron under the current vertex configuration according to the matrix determinant det(·): (6)； Step 4: Fix (N-1) vertices and use the remaining pixels to replace the Nth vertex in sequence. If the volume of the polyhedron increases, the replacement is accepted; Repeat steps 2 to 4 to iteratively optimize the volume of the polyhedron until the volume is maximized and converged. The replacement cycle terminates. At this time, the N polarization multiplexing speckles corresponding to the vertices of the polyhedron are the initial values ​​of the target polarization speckle.

6. The multi-scene single-frame large-field-of-view scattering imaging method based on polarization coding and spatial multiplexing according to claim 5, characterized in that: The step 4 is specifically as follows: In step 4-1, the truncated Cauchy loss function is used instead of the least squares loss as the objective function of NMF; the expression of the truncated Cauchy loss function f(x) is: (7)； Where r is the scale coefficient of the Cauchy distribution, c is a custom adjustable threshold, and x represents the loss function, which is the difference between the true value B and the decomposition result (B-AU). When the absolute value of x is greater than the threshold, the loss function is truncated to a fixed value. The objective function J of the NMF model based on the truncated Cauchy loss function is expressed as: (8)； Where G represents the number of pixels in the speckle image, (B-UA) lk Represents the element value of the lth row and kth column of the matrix B-UA; Step 4-2, graph Laplace regularization constraint: According to image theory, all polarization multiplexed speckles are mapped into a complete undirected graph, with each speckle representing a vertex, to obtain an M×M adjacency matrix; the closer the camera polarization angles, the closer the two multiplexed speckles b m and b n The closer the modulation vectors α are, the stronger the similarity of the multiplexed speckles is, and the larger the weight value is; conversely, the larger the difference between the polarization angles is, the closer the weight value is to 0; Gaussian kernel is used to weight the M multiplexed speckle images, b m and b n Weight between Expressed as: (9)； Where δ is the bandwidth of the Gaussian kernel; The similarity relationship is transformed through graph Laplace regularization: (10)； where tr(·) represents the trace of the matrix, , D represents a diagonal matrix, the diagonal elements , The weight coefficient The weight matrix is ​​composed of L, the Laplace matrix, and A m 、A n Respectively represent the mth and nth columns of the modulation coefficient matrix A, that is, α m , α n ; The adjacency matrix is ​​simplified by the local neighborhood weighting method; for any point b m , only considering the local neighborhood The weight coefficient within, t is the custom neighborhood radius; the weight coefficients between all non-adjacent point pairs are set to 0; point b m Local neighborhood range The sum of all points in the neighborhood and its weight value is defined as the neighborhood similarity coefficient , expressed as: (11)； In formula (11), ; For all The tensor polarization speckle adjacency matrix and the similarity measure vector generated by the weights are expressed as In actual calculation, in order to meet the matrix matching requirements, the vector C is expanded into the matrix R: (12)； The objective function of the NMF model after adding the adjacency matrix and graph Laplace regularization term is expressed as: (13)； ； in is an N-dimensional full-row vector, is an M-dimensional full-row vector, T represents the transpose operation, and β is the regularization coefficient; Step 4-3, model solution: Based on the principle of semi-quadratic optimization, introduce auxiliary variables and use convex conjugate theory to decompose the original problem into multiple sub-problems for solution; for the truncated Cauchy loss function, first, let , g(y) = -f(y), Convert to According to the Legendre-Fenchel transformation, two conjugate transformations of g(y) yield: (14)； Where Z is the conjugate variable of y, express The conjugate function of g(y) takes its maximum value. ,in Represents the partial derivative of the function g(y) with respect to g. Substituting y into it, we can see that when U and A are fixed, the element value Z in the lth row and kth column of the matrix Z is lk Expressed as: (15)； in, Represents the modulus of the element value in the lth row and kth column of the matrix B-UA. When Z is fixed, the goal is an optimization problem involving two variables, U and A. The alternating direction multiplier method is used to transform the original problem into several simple subproblems containing only one variable. Each subproblem is optimized alternately to approach the optimal solution of the original problem. The two subproblems after transformation are: (16)； (17)； in 、 is the Lagrange multiplier, represents dot product; Under the Karush-Kuhn-Tucker condition, we find the optimal solution of Equation (16) and obtain the update rule of A as follows: (18)； in The mth column of , , represents the point division operation; for the objective function (17), under the KKT condition, the update rule of U can be obtained: (19)； The matrices A, Z, and U are updated alternately and iteratively until convergence, and the polarization-specific speckles of different targets are separated. Subsequently, the phase recovery algorithm is used to reconstruct multiple targets beyond the OME range hidden behind the scattering medium.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the method according to any one of claims 1 to 6 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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