A ghost imaging target reconstruction method based on FSD-GIRA

Abstract

The present invention discloses a ghost imaging target reconstruction method based on FSD-GIRA, and relates to the technical field of digital image processing. The technical solution of the present invention uses a fuzzy clustering algorithm to classify the eigenvalues ​​of the light field intensity measurement matrix of the optical path detector, reconstructs it through singular value decomposition, realizes the dimensionality reduction processing of the measurement data of the ghost imaging system, and proposes a WE-FOMP-CG algorithm. By combining generalized orthogonal matching pursuit, conjugate gradient method and multi-threshold wavelet denoising method, the recovery of sparse signals is optimized; the most relevant sensor matrix column is selected in each iteration, the linear equation system is solved by PCG, and the result is subjected to wavelet preprocessing and multi-threshold denoising, and the recovery estimate is updated. The computational efficiency and convergence speed are improved, and a more accurate recovery result is provided in a high noise environment. A WBDH algorithm is also proposed, which uses a dual denoising mechanism, including wavelet transform and BM3D method, to ensure that the restored image details and structure are retained, thereby further improving the reconstruction quality of the ghost imaging target.

Description

Technical Field

[0001] The present invention relates to the technical field of digital image processing, and in particular to a ghost imaging target reconstruction method based on FSD-GIRA. Background Art

[0002] Since the 20th century, the rapid development of quantum mechanics has triggered changes in many fields, including quantum computing and quantum communication. As an important branch of quantum communication and quantum information science, ghost imaging technology has attracted much attention due to its unique physical properties and wide application potential. Traditional optical imaging technology relies on the first-order correlation of light fields to obtain object information, such as cameras and telescopes. In contrast, ghost imaging uses the second-order or higher-order correlation of light fields to reconstruct its image without contacting the object. This non-local imaging method has the advantages of single-element imaging and lens-free imaging, and has therefore become one of the important research directions of quantum optics and classical optics.

[0003] Ghost imaging technology divides the light source into a detection beam and a reference beam, and achieves high-resolution coherent imaging by measuring the correlation between the detection beam and the reference beam after it passes through an object. This technology can provide clear visual information even in harsh environments, so it is widely used in the military field, such as evaluating the effectiveness of bombing and assisting soldiers in quickly identifying enemies and friends. At the same time, this technology can also overcome the limitations of traditional imaging technology in harsh weather conditions and provide more reliable images. In addition, in the field of optical information security, the implementation of ghost imaging technology has also played a positive role in improving the security of optical image encryption.

[0004] Although ghost imaging technology has important application value, it requires a large amount of measurement data in actual use, and too many measurements will increase the time for target reconstruction, making it difficult to achieve real-time processing. In addition, traditional ghost imaging technology has the problem of low measurement data utilization, making it difficult to completely obtain clear images. Therefore, how to improve the imaging signal-to-noise ratio and reduce the number of measurements are key issues that need to be solved in the practical application of this technology. Summary of the invention

[0005] The technical solution of the present invention to solve the above technical problem is to provide a ghost imaging target reconstruction method based on FSD-GIRA, comprising the following steps:

[0006] S1, collect reference light intensity to form measurement matrix A, collect observation values ​​to form observation vector B;

[0007] S2. Use a fuzzy clustering algorithm to classify the eigenvalues ​​of the optical path detector light field intensity measurement matrix, set the smaller eigenvalues ​​to zero, reconstruct it through singular value decomposition, reduce the dimension of the measurement data, and obtain the reduced-dimensional measurement matrix A' and bucket detector value B';

[0008] S3, initialization stage, the recovery signal θ is set to zero vector, the residual r n Initialized to observation vector B', number of iterations k;

[0009] In the iterative process, the sensor matrix Φ is calculated and each column is compared with the residual r n The inner product of the matrix is ​​constructed by selecting the S columns with the largest absolute value of the inner product. Use the conjugate gradient method (PCG) to solve the least squares problem and get the sparse coefficients When k≤10, the formula Update residual r n , k=k+1; when the number of iterations l>10, let Processed by multi-threshold wavelet denoising technology The multi-threshold wavelet denoising technology includes:

[0010] set up Ψ is represented by the discrete cosine coefficient transform matrix, which is used for the signal Perform the maximum overlap discrete wavelet transform MODWT, use the sym8 wavelet to transform the signal into a 6-layer wavelet, and get the transform coefficient wt:

[0011]

[0012] For each layer kk of the MODWT coefficient wt(kk,:), calculate the median absolute deviation MAD:

[0013]

[0014] Where median(|wt(kk,:)|) is the median of the absolute values ​​of the coefficients, and 0.6745 is the scaling factor of the MAD estimate, making it an unbiased estimate;

[0015] Based on MAD and signal length, calculate the threshold thr(kk) of each layer:

[0016]

[0017] Where N is the length of the signal, 2 kk is the scaling factor, adjusting the effect of the number of layers kk on the threshold;

[0018] Apply thresholding to the MODWT coefficients of each layer, using a soft threshold to process each coefficient wt(kk,:):

[0019] wt(kk,:)=sign(wt(kk,:))max(|wt(kk,:)|-thr(kk),0);

[0020] Where sign(x) is the sign function of x, max(|wt(kk,:)|-thr(kk),0) means when the absolute value of the coefficient is greater than the threshold, the threshold is subtracted, otherwise it is set to zero;

[0021] Use the processed MODWT coefficients wt to reconstruct the denoised signal

[0022]

[0023] pass The processed coefficients of and Ψ are transformed into coefficients as follows:

[0024]

[0025] make By formula Update residual r n , k=k+1;

[0026] If the selected column is the same as the previous column or the number of columns exceeds the number of rows N of the measurement matrix r , that is |S k |=|Pos θ |or|S k |=N r , the iteration is terminated, Then the multi-threshold wavelet denoising technique is used to The value is processed and the processing result is recorded as Indicates that the output is a vector of size M×1;

[0027] S4. The obtained Convert to m×n matrix M = m × n;

[0028] right Transpose 90° counterclockwise to flatten the matrix in column-major order Form a column vector

[0029] Applying the multi-threshold wavelet denoising technology to reduce noise on a single column of vectors in one-dimensional space;

[0030] The denoising result is transformed from M×1 to m×n, and we get right Transpose 90° clockwise to get Obtain the target image after noise reduction;

[0031] For the denoised target image The noise is estimated to obtain the noise intensity;

[0032] The BM3D filter is used to reconstruct the target image and reduce the noise according to the noise intensity to obtain a clear and restored target image.

[0033] Furthermore, the steps of using a fuzzy clustering algorithm to classify the eigenvalues ​​of the optical path detector light field intensity measurement matrix, setting the smaller eigenvalues ​​to zero, and then reconstructing it through singular value decomposition, reducing the dimension of the measurement data, and obtaining the reduced-dimensional measurement matrix A' and bucket detector value B' include:

[0034] Use singular value decomposition to process the light field intensity data of the measurement matrix A:

[0035] Decompose the measurement matrix A into three parts:

[0036] A=UΣV T ;

[0037] Among them, Σ is a diagonal matrix containing singular values, U is an orthogonal matrix, and V is also an orthogonal matrix;

[0038] Perform fuzzy clustering on the eigenvalue matrix, set the small eigenvalues ​​to zero, and obtain a new eigenvalue matrix

[0039] Will Multiply by the orthogonal matrix V T , (·) Τ represents the transpose of the matrix, and obtains the measurement matrix A' after dimensionality reduction;

[0040] Use U T Perform product operation with observation vector B;

[0041] Delete U T B The elements corresponding to the zero position in are obtained to obtain the reduced-dimensional measurement matrix A' and bucket detector value B'.

[0042] Furthermore, the denoised target image The noise is estimated and the noise intensity is obtained by the following steps:

[0043] Preprocessing: Apply horizontal and vertical filters to the image and calculate the square of the image gradient;

[0044] Covariance matrix: Calculate the covariance matrix of the image block through matrix operations;

[0045] Noise threshold: Based on the eigenvalues ​​of the covariance matrix, the initial noise threshold is calculated using the Gamma distribution;

[0046] Weak texture selection: gradually estimate the noise level by selecting pixel blocks smaller than the current threshold;

[0047] Noise level: Estimate the noise standard deviation, i.e., the noise intensity, by calculating the eigenvalues ​​of the covariance matrix.

[0048] Furthermore, the step of using the BM3D filter to reconstruct the target image and reduce the noise according to the noise intensity to obtain a clear restored target image includes:

[0049] Basic estimation, first select a reference block from the input noisy image, and find similar blocks to form a 3D matrix; perform two-dimensional and one-dimensional transformations on the matrix, perform threshold processing to remove noise, and perform inverse transformation to obtain the denoised image block; the processed blocks are fused to the original image position through weighted averaging

[0050] The final estimation generates two 3D matrices: one from the noise image and the other from the basic estimation result; the two matrices are transformed into two dimensions and one dimensions respectively, and the coefficients of the noise image are adjusted by applying Wiener filtering according to the estimated noise intensity, and then weighted average synthesis is performed to complete the final denoising process, and finally a clear restored target image is obtained.

[0051] Compared with the prior art, the advantages of the present invention are as follows:

[0052] (1) The F-SVD-MB algorithm proposed in this application is a dimensionality reduction method for reference light intensity information and bucket detector values ​​by combining fuzzy C-means clustering (FCM) and singular value decomposition (SVD) technology. Compared with conventional dimensionality reduction methods, F-SVD-MB can accurately extract core information and avoid the influence of noise and interference in data acquisition, thereby effectively reducing data redundancy and equipment storage pressure under multiple measurements. By reducing the dimensionality of reference light intensity information and bucket detector values, F-SVD-MB achieves a higher data compression ratio while maintaining data accuracy and precision.

[0053] (2) The WE-FOMP-CG algorithm proposed in this application has significant advantages over the existing technology. It combines the sparse selection capability of generalized orthogonal matching pursuit (GOMP) and the efficient calculation of the conjugate gradient (PCG) method to improve the recovery accuracy and calculation speed. The conjugate gradient method effectively solves the linear equations and optimizes the efficiency of high-dimensional data processing. At the same time, the algorithm applies multi-threshold wavelet denoising technology in each iteration, which effectively reduces the influence of noise and further improves the quality of signal recovery. This enables WE-FOMP-CG to provide more accurate and robust recovery results when facing high noise and complex data environments. Compared with the commonly used ghost imaging target reconstruction algorithm, the WE-FOMP-CG algorithm has multiple advantages, including the ability to effectively remove background noise from the image, improve the signal-to-noise ratio of the reconstructed image, and have the ability to resist background light and bucket detector noise interference.

[0054] (3) The WBDH algorithm proposed in this application provides a more powerful and efficient denoising capability by combining multi-threshold denoising in the wavelet domain and the BM3D algorithm. Wavelet transform can accurately capture and remove noise in the frequency domain, especially in areas with small wavelet coefficients, which is particularly important for high-noise images. The BM3D algorithm further reduces noise and restores image details through block matching and three-dimensional filtering technology, thereby enhancing the clarity and naturalness of the image. The core advantage of the WBDH algorithm lies in its multi-level denoising strategy. This dual denoising mechanism effectively processes noise in different frequency and spatial domains, ensuring the retention of image details and structures. This makes the WBDH algorithm perform excellently in high-noise environments, and is particularly suitable for image processing tasks that require high-precision denoising, such as ghost imaging target recovery, which improves the accuracy and quality of image restoration. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0056] Figure 1 The simulation and experimental test results are shown in Figure 2.

[0057] Figure 2 This is a diagram of the dimension reduction structure of the detector measurement data based on F-SVD-MB in this application;

[0058] Figure 3 This is the structure diagram of the WE-FOMP-CG algorithm of this application;

[0059] Figure 4 This is the structure diagram of the WBDH algorithm for this application. DETAILED DESCRIPTION

[0060] The present invention proposes a ghost imaging target reconstruction method based on FSD-GIRA, aiming to design a ghost imaging target reconstruction method based on FSD-GIRA to improve the accuracy and quality of image restoration.

[0061] The ghost imaging target reconstruction method based on FSD-GIRA proposed by the present invention will be described below in a specific embodiment:

[0062] In the technical solution of this embodiment, a ghost imaging target reconstruction method based on FSD-GIRA includes the following steps:

[0063] S1, collect reference light intensity to form measurement matrix A, collect observation values ​​to form observation vector B;

[0064] It can be understood that the reference light path detector is used to collect the reference light intensity, and the bucket detector is used to collect the observation value.

[0065] S2, using a fuzzy clustering algorithm to classify the eigenvalues ​​of the optical path detector light field intensity measurement matrix, setting the smaller eigenvalues ​​to zero, and then reconstructing it through singular value decomposition, reducing the dimension of the measurement data, and obtaining the reduced-dimensional measurement matrix A' and bucket detector value B';

[0066] Understandably, if Figure 2 As shown in the figure, this step uses the F-SVD-MB algorithm for dimensionality reduction. The key is to effectively optimize the processing of reference light intensity data and bucket detector observations by reducing the dimension and complexity of the data without affecting the quality of subsequent algorithm reconstruction. Such optimization not only saves computing resources, but also ensures the efficiency and accuracy of the imaging and analysis process, providing strong support for the performance improvement of optical imaging systems.

[0067] S3, initialization stage, the recovery signal θ is set to zero vector, the residual r n Initialized to observation vector B', number of iterations k;

[0068] In the iterative process, the sensor matrix Φ is calculated and each column is compared with the residual r n The inner product of the matrix is ​​constructed by selecting the S columns with the largest absolute value of the inner product. Use the conjugate gradient method (PCG) to solve the least squares problem and get the sparse coefficients When k≤10, the formula Update residual r n , k=k+1; when the number of iterations k>10, let Processed by multi-threshold wavelet denoising technology The multi-threshold wavelet denoising technology includes:

[0069] set up Ψ is represented by the discrete cosine coefficient transform matrix, which is used for the signal Perform the maximum overlap discrete wavelet transform MODWT, use the sym8 wavelet to transform the signal into a 6-layer wavelet, and get the transform coefficient wt:

[0070]

[0071] For each layer kk of the MODWT coefficient wt(kk,:), calculate the median absolute deviation MAD:

[0072]

[0073] Where median(|wt(kk,:)|) is the median of the absolute values ​​of the coefficients, and 0.6745 is the scaling factor of the MAD estimate, making it an unbiased estimate;

[0074] Based on MAD and signal length, calculate the threshold thr(kk) of each layer:

[0075]

[0076] Where N is the length of the signal, 2 kk is the scaling factor, adjusting the effect of the number of layers kk on the threshold;

[0077] Apply thresholding to the MODWT coefficients of each layer, using a soft threshold to process each coefficient wt(kk,:):

[0078] wt(kk,:)=sign(wt(kk,:))max(|wt(kk,:)|-thr(kk),0);

[0079] Where sign(x) is the sign function of x, max(|wt(kk,:)|-thr(kk),0) means when the absolute value of the coefficient is greater than the threshold, the threshold is subtracted, otherwise it is set to zero;

[0080] Use the processed MODWT coefficients wt to reconstruct the denoised signal

[0081]

[0082] pass The processed coefficients of and Ψ are transformed into coefficients as follows:

[0083]

[0084] make By formula Update residual r n , k=k+1;

[0085] If the selected column is the same as the previous column or the number of columns exceeds the number of rows N of the measurement matrix r , that is |S k |=|Pos θ |or|S k |=N r , the iteration is terminated, Then the multi-threshold wavelet denoising technique is used to The value is processed and the processing result is recorded as Indicates that the output is a vector of size M×1;

[0086] Understandably, if Figure 3 As shown in the figure, this step uses the WE-FOMP-CG algorithm for target reconstruction. The WE-FOMP-CG algorithm combines the sparse selection capability of generalized orthogonal matching pursuit (GOMP) and the efficient calculation of the conjugate gradient (PCG) method to improve the recovery accuracy and calculation speed. The conjugate gradient method effectively solves the linear equations and optimizes the efficiency of high-dimensional data processing. At the same time, the algorithm applies multi-threshold wavelet denoising technology in each iteration, which effectively reduces the influence of noise and further improves the quality of signal recovery. This enables WE-FOMP-CG to provide more accurate and robust recovery results when facing high noise and complex data environments. Compared with the commonly used ghost imaging target reconstruction algorithm, the WE-FOMP-CG algorithm has multiple advantages, including the ability to effectively remove the background noise of the image, improve the signal-to-noise ratio of the reconstructed image, and have the ability to resist background light and bucket detector noise interference. The core advantage of WE-FOMP-CG is that it uses the conjugate gradient method to solve the linear equations, thereby more effectively solving the sparse recovery problem. Specifically, the algorithm uses the conjugate gradient algorithm to solve the least squares problem in each iteration to accurately estimate the sparse coefficients. The introduction of the conjugate gradient algorithm greatly improves the computational efficiency and convergence speed, especially when processing high-dimensional data. WE-FOMP-CG also includes a multi-threshold wavelet denoising step, which further improves the quality of the recovery result by transforming the signal recovered in each iteration through a wavelet transform and denoising it. Wavelet denoising can effectively reduce the impact of noise, making the recovered signal closer to the real signal. This denoising process not only improves the clarity of the signal, but also enhances the robustness of the algorithm to a certain extent, especially in the face of strong noise interference. WE-FOMP-CG combines the sparsity selection advantage of orthogonal matching pursuit and the computational efficiency of the conjugate gradient method, while improving the accuracy of signal recovery through wavelet denoising. This makes the algorithm perform well in various application scenarios, especially in signal recovery tasks that require high accuracy and high robustness.

[0087] S4. The obtained Convert to m×n matrix M = m × n;

[0088] right Transpose 90° counterclockwise to flatten the matrix in column-major order Form a column vector

[0089] Applying the multi-threshold wavelet denoising technology to reduce noise on a single column of vectors in one-dimensional space;

[0090] The denoising result is transformed from M×1 to m×n, and we get right Transpose 90° clockwise to get Obtain the target image after noise reduction;

[0091] For the denoised target image The noise is estimated to obtain the noise intensity;

[0092] The BM3D filter is used to reconstruct the target image and reduce the noise according to the noise intensity to obtain a clear and restored target image.

[0093] Understandably, if Figure 4 As shown in the figure, this step uses the WBDH algorithm for denoising. The WBDH algorithm provides a more powerful and efficient denoising capability by combining multi-threshold denoising in the wavelet domain and the BM3D algorithm. Wavelet transform can accurately capture and remove noise in the frequency domain, especially in areas with small wavelet coefficients, which is particularly important for high-noise images. The BM3D algorithm further reduces noise and restores image details through block matching and three-dimensional filtering technology, thereby enhancing the clarity and naturalness of the image. The core advantage of the WBDH algorithm lies in its multi-level denoising strategy. This dual denoising mechanism effectively processes noise in different frequency and spatial domains, ensuring the retention of image details and structures. This makes the WBDH algorithm perform well in high-noise environments, and is particularly suitable for image processing tasks that require high-precision denoising, ghost imaging target recovery, and improves the accuracy and quality of image restoration.

[0094] Furthermore, the steps of using a fuzzy clustering algorithm to classify the eigenvalues ​​of the optical path detector light field intensity measurement matrix, setting the smaller eigenvalues ​​to zero, and then reconstructing it through singular value decomposition, reducing the dimension of the measurement data, and obtaining the reduced-dimensional measurement matrix A' and bucket detector value B' include:

[0095] Use singular value decomposition to process the light field intensity data of the measurement matrix A:

[0096] Decompose the measurement matrix A into three parts:

[0097] A=U∑V T ;

[0098] Among them, ∑ is a diagonal matrix containing singular values, U is an orthogonal matrix, and V is also an orthogonal matrix;

[0099] Perform fuzzy clustering on the eigenvalue matrix, set the small eigenvalues ​​to zero, and obtain a new eigenvalue matrix

[0100] Will Multiply by the orthogonal matrix V T , (·) Τ represents the transpose of the matrix, and obtains the measurement matrix A' after dimensionality reduction;

[0101] Use UT Perform product operation with observation vector B;

[0102] Delete U T B The elements corresponding to the zero position in are obtained to obtain the reduced-dimensional measurement matrix A' and bucket detector value B'.

[0103] It can be understood that the fuzzy clustering of the eigenvalue matrix is ​​as follows:

[0104]

[0105] Where k is the number of clusters, which is set to 2. In the clustering algorithm design, the row elements corresponding to the data with smaller center values ​​in Σ are set to 0, and the corresponding index is index. That is, Σ[index, j] = 0, The new measurement matrix is ​​as follows:

[0106]

[0107] Because AT = B, T means that the target information is expressed in the form of a column vector, satisfying Therefore, U Τ The value of index index in B is set to 0, and B' is obtained. The ratio of the number of elements in B that are not set to 0 to the original element value in B is r, which is called the compression ratio. Without ensuring the reconstruction quality, a compression ratio of about 0.8 can be achieved.

[0108] Furthermore, the denoised target image The noise is estimated and the noise intensity is obtained by the following steps:

[0109] Preprocessing: Apply horizontal and vertical filters to the image and calculate the square of the image gradient;

[0110] Covariance matrix: Calculate the covariance matrix of the image block through matrix operations;

[0111] Noise threshold: Based on the eigenvalues ​​of the covariance matrix, the initial noise threshold is calculated using the Gamma distribution;

[0112] Weak texture selection: gradually estimate the noise level by selecting pixel blocks smaller than the current threshold;

[0113] Noise level: Estimate the noise standard deviation, i.e., the noise intensity, by calculating the eigenvalues ​​of the covariance matrix.

[0114] Furthermore, the step of using the BM3D filter to reconstruct the target image and reduce the noise according to the noise intensity to obtain a clear restored target image includes:

[0115] Basic estimation, first select a reference block from the input noisy image, and find similar blocks to form a 3D matrix; perform two-dimensional and one-dimensional transformations on the matrix, perform threshold processing to remove noise, and perform inverse transformation to obtain the denoised image block; the processed blocks are fused to the original image position through weighted averaging

[0116] The final estimation generates two 3D matrices: one from the noise image and the other from the basic estimation result; the two matrices are transformed into two dimensions and one dimensions respectively, and the coefficients of the noise image are adjusted by applying Wiener filtering according to the estimated noise intensity, and then weighted average synthesis is performed to complete the final denoising process, and finally a clear restored target image is obtained.

[0117] Understandably, the ghost imaging target recovery algorithm based on WBDH. This method mainly combines multi-threshold wavelet denoising and BM3D algorithm through denoising in the wavelet domain to improve the quality and denoising effect of the image. The core process of the WBDH algorithm includes denoising the recovered sparse coefficients through wavelet transform. The use of wavelet transform allows the algorithm to effectively capture and remove noise in the frequency domain, especially in areas with small wavelet coefficients. Subsequently, the image is re-filtered longitudinally to further optimize the image quality. The algorithm calculates the noise level and adjusts the noise standard deviation, and uses it for the BM3D algorithm to reduce image noise and restore image details through block matching and three-dimensional filtering. The application of BM3D further enhances the denoising effect, making the image recovery more accurate and natural. The main advantage of the WBDH algorithm lies in its multi-level denoising strategy. By combining wavelet transform and BM3D methods, the algorithm can effectively process noise in different frequency and spatial domains, ensuring the retention of image details and structures. Wavelet transform can remove noise in the wavelet domain, while BM3D provides powerful block matching and filtering capabilities. Such a dual denoising mechanism improves the clarity and quality of the restored image, especially in high-noise environments, and is suitable for various image processing tasks that require high-precision denoising.

[0118] Verification test:

[0119] like Figure 1 As shown in the figure, the test targets of this embodiment and the reconstruction results obtained using different target reconstruction algorithms. Among them, the test targets are two types: simulation and experimental targets, corresponding to three reconstruction methods OMP, GOMP and a ghost imaging target reconstruction method based on FSD-GIRA proposed in the present invention. In the simulation and experiment, the wavelength of the laser is set to 532nm, and the distance between the pseudothermal light source and the target is z 1 , the distance between the pseudothermal light source and the reference detector is z 2, both of which are set to 200mm. The key to the superiority of the reconstruction algorithm lies in improving the reconstruction quality, and the ultimate goal is to improve the signal-to-noise ratio SNR and reduce the reconstruction time. This experiment uses an ASUS desktop computer with an Intel Core i7-7700 CPU, a main frequency of 3.60GHz, and a memory of 16GB. In the experiment of 1500 measurements, the results obtained using different image reconstruction methods show significant differences.

[0120] Specifically, in this simulation, the orthogonal matching pursuit (OMP) method was used to reconstruct the target letter "JLAU", with a signal-to-noise ratio (SNR) of 7.9392dB and a reconstruction time of 20.718577 seconds. The SNR of the generalized orthogonal matching pursuit (GOMP) method is slightly higher, at 8.1325dB, but its reconstruction time is longer, at 45.557383 seconds. The method of the present invention performs well in both signal-to-noise ratio and reconstruction time, with an SNR of 9.3691dB and a reconstruction time of only 13.371924 seconds. Detailed analysis shows that the method of the present invention is 1.2366dB higher than GOMP and 1.4309dB higher than OMP. On the other hand, in terms of processing speed, the method of the present invention performs well, with the shortest reconstruction time of only 13.371924 seconds. This is much better than GOMP's 45.557383 seconds and OMP's 20.718577 seconds, showing the significant advantages of the method of the present invention in computational efficiency. This high efficiency can significantly reduce processing time and is suitable for application scenarios that require fast real-time reconstruction. The simulation experiment verified that the method of the present invention not only surpasses the traditional OMP and GOMP methods in reconstruction quality, but also shows obvious advantages in computational efficiency. In order to verify the application effect of the proposed method in practice, the test target is the letter "GI", and the SNR values ​​of the three algorithms (OMP, GOMP and the algorithm proposed in the present invention) in the reconstruction target are specifically SNR = 3.7168dB, SNR = 2.5400dB and SNR = 4.7921dB. Compared with the OMP and GOMP algorithms, the algorithm proposed in the present invention has a higher SNR value for the reconstruction target. This shows that the proposed algorithm can reconstruct the target signal more clearly and has a stronger anti-noise ability. At the same time, it can be seen that the GOMP algorithm has poor anti-noise ability and its SNR is low. The actual experiment verifies that the algorithm proposed in the present invention has strong robustness and can maintain stable performance when interfered by external environment or noise. Since noise interference is often difficult to avoid in actual situations, a robust algorithm is more conducive to ensuring the accuracy of the reconstruction result. In this regard, the algorithm proposed in the present invention has better performance, its SNR value is relatively stable, and even in the presence of noise, it can still accurately restore the original signal.

[0121] Therefore, the algorithm proposed in the present invention has certain advantages over the OMP and GOMP algorithms in terms of performance, and can effectively improve the signal-to-noise ratio and reconstruction quality. At the same time, in practical applications, the algorithm also has strong robustness and accuracy, and can be applied to signal processing and reconstruction in more complex and high-noise environments.

[0122] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A ghost imaging target reconstruction method based on FSD-GIRA, characterized in that: The following steps are involved: S1, collect reference light intensity to form measurement matrix A, collect observation values ​​to form observation vector B; S2. Use a fuzzy clustering algorithm to classify the eigenvalues ​​of the optical path detector light field intensity measurement matrix, set the smaller eigenvalues ​​to zero, reconstruct it through singular value decomposition, reduce the dimension of the measurement data, and obtain the reduced-dimensional measurement matrix A′ and bucket detector value B′; S3, initialization stage, the recovery signal θ is set to zero vector, the residual r n Initialized to bucket detector value B′, iteration number k; In the iterative process, the sensor matrix Φ is calculated and each column is compared with the residual r n The inner product of the matrix is ​​constructed by selecting the S columns with the largest absolute value of the inner product. Use the conjugate gradient method to solve the least squares problem and get the sparse coefficients When k≤10, the formula Update residual r n , k=k+1; when the number of iterations k>10, let Processed by multi-threshold wavelet denoising technology The multi-threshold wavelet denoising technology includes: set up Where, Ψ represents the discrete cosine coefficient transform matrix, for the signal Perform the maximum overlap discrete wavelet transform MODWT, use the sym8 wavelet to transform the signal into a 6-layer wavelet, and get the transform coefficient wt: For each layer kk of the MODWT coefficient wt(kk,:), calculate the median absolute deviation MAD: Where median(|wt(kk,:)|) is the median of the absolute values ​​of the coefficients, and 0.6745 is the scaling factor of the MAD estimate, making it an unbiased estimate; Based on MAD and signal length, calculate the threshold thr(kk) of each layer: Where N is the length of the signal, 2 kk is the scaling factor, adjusting the effect of the number of layers kk on the threshold; Apply thresholding to the MODWT coefficients of each layer, using a soft threshold to process each coefficient wt(kk,:): wt(kk,:)=sign(wt(kk,:))max(|wt(kk,:)|-thr(kk),0); Where sign(x) is the sign function of x, max(|wt(kk,:)|-thr(kk),0) means when the absolute value of the coefficient is greater than the threshold, the threshold is subtracted, otherwise it is set to zero; Use the processed MODWT coefficients wt to reconstruct the denoised signal pass The processed coefficients of and Ψ are transformed into coefficients as follows: make By formula Update residual r n , k=k+1; If the selected column is the same as the previous column or the number of columns exceeds the number of rows N of the measurement matrix r , that is |S k |=|Pos θ |or|S k |=N r , the iteration is terminated, Then the multi-threshold wavelet denoising technique is used to The value is processed and the processing result is recorded as Indicates that the output is a vector of size M×1; S4. The obtained Convert to m×n matrix M = m × n; right Transpose 90° counterclockwise to flatten the matrix in column-major order Form a column vector Applying the multi-threshold wavelet denoising technology to reduce noise on a single column of vectors in one-dimensional space; The denoising result is transformed from M×1 to m×n, and the right Transpose 90° clockwise to get Obtain the target image after noise reduction; For the denoised target image The noise is estimated to obtain the noise intensity; The BM3D filter is used to reconstruct the target image and reduce the noise according to the noise intensity to obtain a clear and restored target image.

2. The ghost imaging target reconstruction method based on FSD-GIRA according to claim 1, characterized in that: The steps of using a fuzzy clustering algorithm to classify the eigenvalues ​​of the optical path detector light field intensity measurement matrix, setting the smaller eigenvalues ​​to zero, and then reconstructing it through singular value decomposition, reducing the dimension of the measurement data, and obtaining the reduced-dimensional measurement matrix A′ and bucket detector value B′ include: Use singular value decomposition to process the light field intensity data of the measurement matrix A: Decompose the measurement matrix A into three parts: A=U∑V T ; Among them, ∑ is a diagonal matrix containing singular values, U is an orthogonal matrix, and V is also an orthogonal matrix; Perform fuzzy clustering on the eigenvalue matrix, set the small eigenvalues ​​to zero, and obtain a new eigenvalue matrix Will Multiply by the orthogonal matrix V T , represents the transpose of the matrix, and obtains the measurement matrix A' after dimensionality reduction; Use U T Perform product operation with observation vector B; Delete U T B The elements corresponding to the zero position in are obtained to obtain the reduced-dimensional measurement matrix A′ and bucket detector value B′.

3. The ghost imaging target reconstruction method based on FSD-GIRA according to claim 1, characterized in that: The target image after denoising The noise is estimated and the noise intensity is obtained by the following steps: Preprocessing: Apply horizontal and vertical filters to the image and calculate the square of the image gradient; Covariance matrix: Calculate the covariance matrix of the image block through matrix operations; Noise threshold: Based on the eigenvalues ​​of the covariance matrix, the initial noise threshold is calculated using the Gamma distribution; Weak texture selection: gradually estimate the noise level by selecting pixel blocks smaller than the current threshold; Noise level: Estimate the noise standard deviation, i.e., the noise intensity, by calculating the eigenvalues ​​of the covariance matrix.

4. The ghost imaging target reconstruction method based on FSD-GIRA according to claim 1, characterized in that: The step of using the BM3D filter to reconstruct the target image and reduce the noise according to the noise intensity to obtain a clear restored target image comprises: Basic estimation: select reference blocks from the input noisy image and find similar blocks to form a 3D matrix; perform two-dimensional and one-dimensional transformations on the 3D matrix, perform threshold processing to remove noise, and perform inverse transformation to obtain denoised image blocks; denoised image blocks are fused to the original image position through weighted averaging; Finally, two 3D matrices are generated: one 3D matrix comes from the noise image, and the other 3D matrix comes from the basic estimation result. The two 3D matrices are transformed into two dimensions and one dimensions respectively. According to the estimated noise intensity, the coefficients of the noise image are adjusted by applying Wiener filtering, and then weighted average synthesis is performed to complete the denoising process and obtain a clear restored target image.

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