Compressed Sensing Reconstruction and Correction Method Based on Self-Embedding of RS Code Check Bit Statistical Features

Abstract

This invention relates to the fields of image processing and information security technology, specifically to a compressed sensing reconstruction and correction method based on the self-embedding of statistical features of RS code check bits. The method involves performing a Haar wavelet decomposition on the original image to extract LL subband statistical features, embedding these features into RS code check bits to obtain a chaotic keystream sequence, and encrypting the measured values. At the decryption end, the extracted statistical features are extracted by majority voting and then used for moment matching correction. In the reconstruction stage, a MUSR algorithm is designed, solved using the ADMM framework, and the penalty parameter and regularization coefficient are adaptively adjusted based on the ratio of the original residual to the dual residual. Compared with existing technologies, this invention achieves self-closed-loop correction of statistical features, improves the system's robustness to mixed interference, reduces the burden of manual parameter tuning, and enables high-quality, highly robust, and secure transmission of compressed sensing images.

Description

Technical Field

[0001] This invention belongs to the field of image processing and information security technology, specifically relating to a compressed sensing reconstruction and correction method based on the self-embedding of statistical features of RS code check bits. Background Technology

[0002] In the field of chaotic compressed sensing image encryption, existing solutions typically employ dual-chaotic or hyperchaotic systems to generate chaotic sequences, combine this with discrete wavelet transform to transform the image into the sparse domain, and then use the chaotic sequences to construct a measurement matrix for compression encryption. This is further supplemented by DNA-encoded block encryption and chaotic row and column permutations to achieve secure transmission. These solutions focus on the security and randomness of the encryption algorithm but do not utilize the statistical characteristics of the image itself to assist in correcting the reconstruction quality at the decryption end.

[0003] Regarding the combination of RS coding and compressed sensing, existing solutions use RS codes for channel-protected transmission of quantized compressed sensing measurements. At the receiving end, RS decoding is used to correct errors that occurred during transmission, and an iterative algorithm based on constraint sets is designed to reconstruct the original image. While this approach improves the system's error-correcting performance by leveraging the error-correcting capability of RS codes, the RS check symbols are only used for error control and not for carrying the image's own global statistical information. Furthermore, the decrypted reconstructed image lacks a moment-matching correction step based on statistical features. The redundant information carried in the RS check symbols is not utilized, and the system lacks a mechanism to transmit the image's own statistical features through coding redundancy and perform post-processing correction.

[0004] Regarding improvements to the robustness of compressed sensing reconstruction algorithms, previous studies have introduced the Huber loss function into the reconstruction fidelity term to replace the traditional least-squares loss. The Huber function uses a squared penalty for small residuals and a linear penalty for large residuals, effectively suppressing the interference of non-Gaussian noise and outliers on the reconstruction results, but it does not address the problem of large-scale measurement loss caused by pruning attacks. Other studies have proposed an adaptive penalty parameter strategy in the ADMM solution framework, dynamically adjusting the penalty term value during iteration based on the noise power of the input signal or the trend of residual changes to accelerate the convergence speed of ADMM. However, none of these schemes monitor the ratio of the original residual to the dual residual in real time to coordinate the adjustment of the penalty parameter and regularization coefficient, and they also lack a measurement recovery mechanism to address pruning attacks.

[0005] Therefore, the existing technologies have the following problems: in compressed sensing image encryption transmission technology, the decryption end lacks self-correction methods based on the statistical characteristics of the image itself when reconstructing the image; the redundancy of RS encoding verification symbols is not fully utilized; the reconstruction algorithm is not robust enough to outlier noise and cropping attacks; and the parameters in the ADMM solution framework depend on manual debugging and cannot dynamically adapt to the iterative convergence state. Summary of the Invention

[0006] Purpose of the invention: To address the problems pointed out in the prior art, this invention proposes a compressed sensing reconstruction and correction method based on the self-embedding of statistical features of RS code check bits. It integrates the extraction of RS code check bits and majority voting based on the self-embedding of statistical features, the MUSR reconstruction algorithm, and the residual balance adaptive ADMM for compressed sensing image encryption and reconstruction.

[0007] Technical solution: This invention discloses a compressed sensing reconstruction and correction method based on the self-embedding of statistical features of RS code check bits, comprising:

[0008] Read the image file, divide it into blocks, and perform compressed sensing measurements on each block using a measurement matrix. Then, concatenate the measurement values ​​of all blocks into a column vector.

[0009] Each measurement value is RS encoded, the original image is decomposed once by Haar wavelet, the statistical features of the LL subband are extracted, the statistical features of the wavelet LL subband are embedded into the RS encoded check symbol LSB, and the metadata of the image size is encoded and spliced ​​to the front end of the measurement value.

[0010] The user password is used to generate 6 chaotic parameters using SHA-256. and 4 memory parameters This is fused into a 10-dimensional key K;

[0011] The chaotic system is initialized with a key, and after multiple pre-iterations, a chaotic sequence with matching length is generated. This sequence is then normalized to 0-255 and histogram equalization is performed to obtain the chaotic key stream sequence.

[0012] The measured values ​​are globally scrambled using the chaotic key stream sequence sorting index, and then the row and column are cyclically shifted based on the first two chaotic values ​​to obtain the shifted measured value vector;

[0013] The scrambled and shifted measurement vector is XORed bit by bit with the chaotic key stream sequence to complete the encryption. The encrypted vector is then reshaped into a two-dimensional image format and saved as an encrypted image file.

[0014] Furthermore, during the image encryption process, the measurement matrix and compression ratio are also preserved. Block size, RS encoding parameters, shift step size for row-column circular shift, scrambling index and metadata encoding length .

[0015] Furthermore, it also includes a decryption process, during which the encrypted image and the saved parameter file are loaded, the same 10-dimensional key K is generated using the same user password, and the same chaotic key stream sequence is generated.

[0016] Furthermore, the specific decryption process is as follows:

[0017] The chaotic key stream sequence is histogram equalized and then XORed with the encrypted data for decryption. Then, it is descrambled by reverse cyclic shift and reverse indexing.

[0018] The original image size is obtained by extracting metadata from the front end of the sequence, extracting RS encoded data, decoding each block of RS, and extracting statistical features from the majority vote of the LSB check symbol.

[0019] The decoded measurements are reconstructed into a block format, and the MUSR reconstruction algorithm is used to solve the reconstruction using the ADMM framework. During the iteration, the penalty parameter and regularization coefficient are adaptively adjusted according to the ratio of the original residual to the dual residual. The cropped measurements are iteratively restored, and the reconstruction result is converted into a two-dimensional image. The extracted statistical features are used for moment matching correction, and the final image is output.

[0020] Furthermore, the statistical features of the wavelet LL subband of the original image are self-embedded into the least significant bit of the RS-coded check symbol, specifically:

[0021] Perform a Haar wavelet decomposition on the original image to extract the LL subband. ,calculate:

[0022] ;

[0023] The three statistics are linearly quantized to 8-bit integers and clamped to [0, 255]:

[0024] ;

[0025] Convert each integer to 8 bits:

[0026]

[0027]

[0028] ;

[0029] Concatenate into a 24-bit string For each code block Take the first 24 positions of the check symbol and replace its least significant bit with This completes the self-embedding of statistical features; where B is the number of blocks. , , These are the mean, standard deviation, and skewness, respectively. , , These are the mean, standard deviation, and skewness values, respectively, after being quantified and clamped to [0, 255] and returned as 8-bit integers.

[0030] Furthermore, the process of obtaining the chaotic key stream sequence is as follows:

[0031] Let the vector to be encrypted be... The length is Using a key Initialize the chaotic system and set the initial state. And system parameters, first perform 100 pre-iterations to eliminate transient effects, then iteratively generate The chaotic state values, where the first one is... The two state values ​​after the second iteration are denoted as follows: and ,Pick The original chaotic sequence is obtained. ;

[0032] Normalize the sequence to the integer range [0, 255] to obtain And then Perform histogram equalization: statistics cumulative distribution function ,make Output an integer sequence , This is the chaotic key stream ultimately used for encryption.

[0033] Furthermore, the specific process of extracting statistical features from the majority vote of the LSB for decoding each RS block is as follows:

[0034] For the Take the first 24 check symbols from the block. Extract its least significant bit:

[0035] ;

[0036] get A 24-bit bit vector, for each bit Conduct a majority vote:

[0037] ;

[0038] Where mode(·) represents taking the mode, that is, taking the majority vote among B bit values ​​and taking the bit that appears most frequently as the vote result for the i-th bit; Divide into 3 groups, each with 8 bits, and restore each group to three 8-bit integers. That is, each group of binary bit strings is expanded according to its weights and converted into a decimal integer with a value range of 0 to 255, and then dequantized to obtain the target statistic:

[0039] ;

[0040] in, The number of measurements per block, For the preset compression ratio, , , These are the target mean, target standard deviation, and target skewness, respectively.

[0041] Furthermore, the MUSR reconstruction algorithm is adopted and the ADMM framework is used to solve the reconstruction. The specific process is as follows:

[0042] Construct the MUSR model with the objective function as follows:

[0043] ;

[0044] in, Let each block be a column vector to be reconstructed. The floating-point measurement value recovered by dequantization. This is a block-diagonal measurement matrix. For weight The expanded weight vector, and These are the regularization coefficients for the MC penalty term and the TV penalty term, respectively. Penalized for Minimax Concave The total variation is solved using the ADMM framework, with auxiliary variables introduced. The augmented Lagrangian function is:

[0045] ;

[0046] in, As dual variables, This is the penalty parameter.

[0047] Furthermore, the original residual is calculated every certain number of iterations:

[0048] ;

[0049] And dual residuals:

[0050] ;

[0051] Calculate the ratio of the two. Set threshold ;

[0052] like This indicates that the original residuals are too large. Increasing the penalty parameter will accelerate the convergence of the original variables, i.e., let: And scale the dual variable accordingly. , ;

[0053] like This indicates that the dual residual is too large, so the penalty parameter should be reduced, i.e.: and scale dual variables , ;

[0054] in, and These are the upper and lower bounds of the penalty parameter, used to prevent over-adjustment of the parameter; and These are the increase and decrease coefficients for the penalty parameter, respectively;

[0055] At the same time, the regularization coefficient is adjusted according to the residual ratio, and is defined as follows: ,in, It is a very small positive number, used to prevent the denominator from being zero; then update , ,in, The adjustment step size for the regularization coefficient, and It is limited to the preset upper and lower bounds.

[0056] Furthermore, the reconstructed Each column is reshaped into a corresponding block, and then stitched together in its original arrangement to form a complete image. , Calculate the mean of the current image, given the original image size. and standard deviation Using the target standard deviation of extracted statistical features Perform linear correction: ,Will Truncate to [0, 255] and round down to obtain the final decrypted and reconstructed image. .

[0057] Beneficial effects:

[0058] 1. This invention achieves self-closed-loop transfer of statistical features between the encryption and decryption ends by embedding global statistical features such as the mean, standard deviation, and skewness of the wavelet LL subband of the original image into the least significant bit of the RS-encoded check symbol. At the decryption end, the features are extracted by majority voting and used for moment matching correction. This allows for the correction of contrast distortion of the reconstructed image without the need for an external reference image.

[0059] 2. In the reconstruction stage, this invention designs the MUSR algorithm, which integrates MC sparse prior, TV smooth prior and Huber weighted fidelity term to effectively suppress outlier noise interference, and iteratively recovers the large-area loss of measurement values ​​caused by pruning attacks, which significantly improves the reconstruction robustness under adverse channel conditions.

[0060] 3. This invention introduces an adaptive parameter adjustment strategy into the ADMM solution framework, which monitors the ratio of the original residual to the dual residual in real time and dynamically adjusts the penalty parameter and regularization coefficient, reducing the burden of manual parameter tuning and accelerating the convergence speed.

[0061] In summary, this invention organically integrates statistical feature self-embedding, RS coding redundancy utilization, MUSR reconstruction, and adaptive ADMM to achieve self-closed-loop correction of statistical features. While ensuring encryption security, it significantly improves the system's resistance to mixed interference and the quality of reconstructed images, reduces the burden of manual parameter tuning, and achieves high-quality, robust, and secure transmission of compressed sensing images. Attached Figure Description

[0062] Figure 1 This is a block diagram of the encryption and decryption scheme of the present invention;

[0063] Figure 2 The original image is from an embodiment of the present invention;

[0064] Figure 3 The encrypted image is an embodiment of the present invention;

[0065] Figure 4 This is a normal decrypted image according to an embodiment of the present invention;

[0066] Figure 5 This is the encrypted image after being cut in half according to an embodiment of the present invention;

[0067] Figure 6 This is the decrypted image after being cut in half according to an embodiment of the present invention. Detailed Implementation

[0068] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0069] This invention discloses a compressed sensing reconstruction and correction method based on the self-embedding of statistical features of RS code check bits, which includes an encryption process and a decryption process. The encryption process is as follows:

[0070] 001 Read the original image to be encrypted, crop its size to a multiple of 16, and record the cropped image size as . .

[0071] 002 Divide the image into Non-overlapping blocks, number of blocks Vectorize each block using a measurement matrix. ( ) for the first The blocks are compressed and measured, and the number of measurements per block is... , To achieve the preset compression ratio, the measurement vectors of all blocks are obtained and concatenated into a total measurement vector. , length is ,remember For each The resulting block-diagonal measurement matrix.

[0072] 003 Calculation minimum value and maximum value ,Will Linear quantization to the integer range of 0-255:

[0073]

[0074] 004 will Reshape by block The matrix is ​​used to encode each measurement value using RS encoding, and the error correction capability is assumed to be... Code length ,get Encoding matrix.

[0075] Calculate the statistical characteristics of the original image:

[0076] Perform a Haar wavelet decomposition on the original image to extract the LL subband. ,calculate:

[0077] The three statistics are linearly quantized to 8-bit integers and clamped to [0, 255]:

[0078] Convert each integer to 8 bits:

[0079]

[0080] Concatenate into a 24-bit string .

[0081] For each code block Take the first 24 positions of the check symbol and replace its least significant bit with This completes the self-embedding of statistical features. Then, metadata such as image dimensions is encoded into octal and concatenated to the front end of the encoded data to obtain the final vector to be encrypted. Let the length of the encoded metadata vector be . .

[0082] 005 The user enters a password, which is then hashed using SHA-256. Six parameters are extracted from this hash to form the password. Extract 4 parameters to form fused into a 10-dimensional key .

[0083] 006 Let the vector to be encrypted be... The length is Using a key Initialize the chaotic system and set the initial state. And system parameters. First, perform 100 pre-iterations to eliminate transient effects, then iteratively generate... Each chaotic state value is taken as... The original chaotic sequence is obtained. Normalize the sequence to the integer range [0, 255]:

[0084]

[0085] Again Perform histogram equalization: statistics cumulative distribution function ,make Output an integer sequence , This is the chaotic key stream ultimately used for encryption.

[0086] 007 On chaotic key stream sequences Perform ascending sorting and record the sorted index vector. ,Right now Using this index to measure the vector Perform a global scramble:

[0087]

[0088] Pick The first two values Calculate the cyclic shift step size Then to Perform a row-direction circular shift:

[0089] 008. Perform a bitwise XOR operation between the shifted measurement vector and the chaotic key stream:

[0090]

[0091] in This indicates a bitwise XOR operation, which yields an encrypted integer vector. .

[0092] 009 Encryption vector Reconstruct the image into a 2D image format, save it as an encrypted image file, and simultaneously save the following parameters to the parameter file: measurement matrix. Compression ratio Segment size, quantization parameters and RS encoding parameters, cyclic shift step size Scramble the index Metadata encoding length wait.

[0093] The decryption process is as follows:

[0094] 010 During decryption, read the encrypted image file and extract the encryption vector. The key length is the same as during encryption. Load the parameter file and obtain all necessary parameters. Using the same user password as the encryption end, regenerate the key according to step 005. Then generate the same chaotic sequence according to step 006. .

[0095] 011 First, perform XOR decryption:

[0096] Then reverse the circular shift:

[0097] Using the saved scrambled index Calculate inverted index ,satisfy Then perform the reverse scrambling:

[0098] Recover the measurement vector containing metadata and RS encoding. .

[0099] 012 From The former Extract metadata from each element, encode it, and decode it to obtain the original image size. The remaining part is based on codeword length. Number of blocks Remodeling into a matrix Each column corresponds to one RS code block.

[0100] Perform RS decoding on each block: Let the first block be... The block receive vector is Decoding output and return the number of error symbols. .like Then adopt As the measured value of this block, the weight Otherwise adopt As a measurement value, weight .

[0101] Extract statistical feature bits from the LSB of each code block:

[0102] For the Take the first 24 check symbols from the block. Extract its least significant bit:

[0103]

[0104] get A 24-bit bit vector. For each bit... Conduct a majority vote:

[0105]

[0106] Will Divide into 3 groups, each with 8 bits, and restore each group to three 8-bit integers. Inverse quantization yields the target statistic:

[0107]

[0108] 013 Combine the decoded measurement values ​​of each block into a matrix. Dequantization recovers floating-point measurements:

[0109]

[0110] Construct the MUSR model with the objective function as follows:

[0111]

[0112] in, Let each block be a column vector to be reconstructed. This is a block-diagonal measurement matrix. For weight The expanded weight vector, Penalized for Minimax Concave The total variation is represented. The ADMM framework is used for solving this problem, introducing auxiliary variables. The augmented Lagrangian function is:

[0113]

[0114] in, As dual variables, The penalty parameter is used. The iterative solution process is as follows:

[0115] First fix Update by solving the linear system :

[0116] Next, update the auxiliary variables. That is to Proximal operators that impose MC penalties:

[0117]

[0118] This proximal operator corresponds to the Firm threshold function, and its expression is:

[0119]

[0120] in , The shape parameters for the MC penalty. Then update. That is to Proximal operators that impose TV penalties:

[0121]

[0122] This operator is solved using the Chambolle projection algorithm. Finally, the dual variable is updated:

[0123]

[0124] During the ADMM iteration process, an adaptive parameter adjustment strategy is implemented simultaneously. The original residuals are calculated every few iterations:

[0125] And dual residuals:

[0126] Calculate the ratio of the two. Set a threshold ,like This indicates that the original residuals are too large, and the penalty parameter needs to be increased to accelerate the convergence of the original variables, that is, let: And scale the dual variable accordingly. , .like This indicates that the dual residual is too large, and the penalty parameter needs to be reduced, i.e.

[0127]

[0128] And scale the dual variable , Simultaneously, the regularization coefficient is adjusted based on the residual ratio, defined as follows:

[0129] Then update , and will It is limited to the preset upper and lower bounds.

[0130] For measurement loss caused by pruning attacks, detection is performed after every certain number of iterations. The positions marked as clipped are progressively filled using a weighted average of the current reconstructed measurements, i.e.:

[0131]

[0132] in, =0.3, For the set of cropping position indices, repeat until convergence or the maximum number of iterations is reached.

[0133] 014 The reconstructed result Each column in the middle is reshaped into The blocks are pieced together in their original arrangement to form a complete image. Calculate the mean of the current image. and standard deviation :

[0134]

[0135] Using the target standard deviation extracted in step 12 Perform linear correction:

[0136]

[0137] Will Truncate to [0, 255] and round down to obtain the final decrypted and reconstructed image. Output the image.

[0138] See Figures 2-6 The present invention is based on Figure 2 The original image was tested and encrypted using the encryption process described in the above embodiment to obtain... Figure 3 The encrypted image is decrypted using the decryption process described in the above embodiments to obtain... Figure 4 The normally decrypted image is shown. This verifies that the present invention can completely recover the original image under interference-free conditions, and the encrypted image visually exhibits a uniform noise-like distribution with no leakage of original image information. Furthermore, the decrypted image shows no significant visual difference from the original image, indicating that the encryption and decryption process of the present invention is reversible and faithful to the original.

[0139] See Figure 5 This invention performs a random 1 / 2 region cropping attack on encrypted images, obtaining cropped encrypted images. The same decryption process of this invention is then used to... Figure 5 Decrypt and reconstruct to obtain Figure 6 The decrypted image shown. (By...) Figure 6 As can be seen, even if half of the ciphertext is lost, the present invention can still recover identifiable image content, proving that the present invention has good robustness against large-area cropping attacks.

[0140] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent transformations or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A compressed sensing reconstruction and correction method based on the self-embedding of statistical features of RS code check bits, characterized in that, include: Read the image file, divide it into blocks, and perform compressed sensing measurements on each block using a measurement matrix. Then, concatenate the measurement values ​​of all blocks into a column vector. Each measurement value is RS encoded, the original image is decomposed once by Haar wavelet, the statistical features of the LL subband are extracted, the statistical features of the wavelet LL subband are embedded into the RS encoded check symbol LSB, and the metadata of the image size is encoded and spliced ​​to the front end of the measurement value. The user password is used to generate 6 chaotic parameters using SHA-256. and 4 memory parameters This is fused into a 10-dimensional key K; The chaotic system is initialized with a key, and after multiple pre-iterations, a chaotic sequence with matching length is generated. This sequence is then normalized to 0-255 and histogram equalization is performed to obtain the chaotic key stream sequence. The measured values ​​are globally scrambled using the chaotic key stream sequence sorting index, and then the row and column are cyclically shifted based on the first two chaotic values ​​to obtain the shifted measured value vector; The scrambled and shifted measurement vector is XORed bit by bit with the chaotic key stream sequence to complete the encryption. The encrypted vector is then reshaped into a two-dimensional image format and saved as an encrypted image file.

2. The compressed sensing reconstruction and correction method based on the self-embedding of RS code check bit statistical features according to claim 1, characterized in that, During the image encryption process, the measurement matrix and compression ratio are also preserved. Block size, RS encoding parameters, shift step size for row-column circular shift, scrambling index and metadata encoding length .

3. The compressed sensing reconstruction and correction method based on the self-embedding of RS code check bit statistical features according to claim 2, characterized in that, It also includes a decryption process, during which the encrypted image and the saved parameter file are loaded, the same 10-dimensional key K is generated using the same user password, and the same chaotic key stream sequence is generated.

4. The compressed sensing reconstruction and correction method based on the self-embedding of RS code check bit statistical features according to claim 3, characterized in that, The specific decryption process is as follows: The chaotic key stream sequence is histogram equalized and then XORed with the encrypted data for decryption. Then, it is descrambled by reverse cyclic shift and reverse indexing. The original image size is obtained by extracting metadata from the front end of the sequence, extracting RS encoded data, decoding each block of RS, and extracting statistical features from the majority vote of the LSB check symbol. The decoded measurements are reconstructed into a block format, and the MUSR reconstruction algorithm is used to solve the reconstruction using the ADMM framework. During the iteration, the penalty parameter and regularization coefficient are adaptively adjusted according to the ratio of the original residual to the dual residual. The cropped measurements are iteratively restored, and the reconstruction result is converted into a two-dimensional image. The extracted statistical features are used for moment matching correction, and the final image is output.

5. The compressed sensing reconstruction and correction method based on the self-embedding of statistical features of RS code check bits according to claim 1, characterized in that, The statistical features of the wavelet LL subband of the original image are self-embedded into the least significant bit of the RS-coded check symbol, specifically: Perform a Haar wavelet decomposition on the original image to extract the LL subband. ,calculate: ； The three statistics are linearly quantized to 8-bit integers and clamped to [0, 255]: ； Convert each integer to 8 bits: ； ； ； Concatenate into a 24-bit string For each code block Take the first 24 positions of the check symbol and replace its least significant bit with This completes the self-embedding of statistical features; where B is the number of blocks. , , These are the mean, standard deviation, and skewness, respectively. , , These are the mean, standard deviation, and skewness values, respectively, after being quantified and clamped to [0, 255] and returned as 8-bit integers.

6. The compressed sensing reconstruction and correction method based on the self-embedding of RS code check bit statistical features according to claim 1, characterized in that, The process of obtaining the chaotic key stream sequence is as follows: Let the vector to be encrypted be... The length is Using a key Initialize the chaotic system and set the initial state. And system parameters, first perform 100 pre-iterations to eliminate transient effects, then iteratively generate The chaotic state value, the th chaotic state value, The two state values ​​after the second iteration are denoted as follows: and ,Pick The original chaotic sequence is obtained. ; Normalize the sequence to the integer range [0, 255] to obtain And then Perform histogram equalization: statistics cumulative distribution function ,make Output an integer sequence , This is the chaotic key stream ultimately used for encryption.

7. The compressed sensing reconstruction and correction method based on the self-embedding of statistical features of RS code check bits according to claim 4, characterized in that, The specific process of extracting statistical features from the majority vote of the LSB for decoding each RS block is as follows: For the Take the first 24 check symbols from the block. Extract its least significant bit: ； get A 24-bit bit vector, for each bit Conduct a majority vote: ； Where mode(·) represents taking the mode, that is, taking the majority vote among B bit values ​​and taking the bit that appears most frequently as the vote result for the i-th bit; Divide into 3 groups, each with 8 bits, and restore each group to three 8-bit integers. That is, each group of binary bit strings is expanded according to its weights and converted into a decimal integer with a value range of 0 to 255, and then dequantized to obtain the target statistic: ； in, The number of measurements per block, For the preset compression ratio, , , These are the target mean, target standard deviation, and target skewness, respectively.

8. The compressed sensing reconstruction and correction method based on the self-embedding of RS code check bit statistical features according to claim 4, characterized in that, The MUSR reconstruction algorithm is used and the ADMM framework is employed to solve the reconstruction problem. The specific process is as follows: Construct the MUSR model with the objective function as follows: ; in, Let each block be a column vector to be reconstructed. The floating-point measurement value recovered by dequantization. This is a block-diagonal measurement matrix. For weight The expanded weight vector, and These are the regularization coefficients for the MC penalty term and the TV penalty term, respectively. Penalized for Minimax Concave The total variation is solved using the ADMM framework, with auxiliary variables introduced. The augmented Lagrangian function is: ； in, As dual variables, This is the penalty parameter.

9. The compressed sensing reconstruction and correction method based on the self-embedding of RS code check bit statistical features according to claim 8, characterized in that, The original residual is calculated after every certain number of iterations: ； And dual residuals: ； Calculate the ratio of the two. Set threshold ; like This indicates that the original residuals are too large. Increasing the penalty parameter will accelerate the convergence of the original variables, i.e., let: And scale the dual variable accordingly. , ; like This indicates that the dual residual is too large, so the penalty parameter should be reduced, i.e.: and scale dual variables , ; in, and These are the upper and lower bounds of the penalty parameter, used to prevent over-adjustment of the parameter; and These are the increase and decrease coefficients for the penalty parameter, respectively; At the same time, the regularization coefficient is adjusted according to the residual ratio, and is defined as follows: ,in, It is a very small positive number, used to prevent the denominator from being zero; then update , ,in, The adjustment step size for the regularization coefficient, and It is limited to the preset upper and lower bounds.

10. The compressed sensing reconstruction and correction method based on the self-embedding of statistical features of RS code check bits according to claim 9, characterized in that, The reconstructed Each column is reshaped into a corresponding block, and then stitched together in its original arrangement to form a complete image. , Calculate the mean of the current image, given the original image size. and standard deviation Using the target standard deviation of extracted statistical features Perform linear correction: ,Will Truncate to [0, 255] and round down to obtain the final decrypted and reconstructed image. .

Images