Single-bit image restoration method, device, terminal and medium

Abstract

The present invention discloses a single-bit image restoration method, device, terminal, and medium, relating to the field of image processing. The method employs a non-zero quantization threshold to single-bit quantize an image to be restored, determining an initial image quantization model; employs a smooth hyperbolic tangent function to replace the sign function in the initial image quantization model, and performs low-rank matrix decomposition on the image to be restored, determining a target image quantization model; determines an initial optimization model based on a truncated least squares function and the target image quantization model; employs a semi-quadratic minimization method to transform the initial optimization model and determine a target optimization model; employs a proximal block coordinate descent algorithm to solve the target optimization model to obtain low-dimensional submatrices and a noise matrix; and utilizes the low-dimensional submatrices to determine a reconstructed image. This method effectively addresses the problem that prior art cannot effectively suppress quantization noise, thereby affecting image restoration accuracy.

Description

Technical Field

[0001] The present invention relates to the field of image processing, and in particular to a single-bit image recovery method, device, terminal and medium. Background Art

[0002] Images are often affected by noise during wireless transmission or suffer degradation due to bit loss during signal acquisition. Low-rank matrix recovery techniques are widely used in image processing because they exploit the low-rank structure inherent in the noise-corrupted observation matrix to effectively reconstruct the original low-dimensional information.

[0003] Single-bit low-rank matrix recovery technology is a technology that uses a single-bit high-resolution analog-to-digital converter (ADC) to quantize data, retains only the data symbol information, and recovers the low-rank data matrix based on the data symbol information. It can improve the efficiency of system resource utilization while ensuring the accuracy of image data recovery.

[0004] Existing image restoration methods based on single-bit low-rank matrix recovery primarily rely on maximum likelihood estimation based on the Gaussian assumption or equivalent loss functions. However, because single-bit quantization preserves sign information but loses amplitude information, the fitting error often deviates from the Gaussian assumption, making it impossible to effectively suppress quantization noise, thus affecting the accuracy of image restoration.

[0005] Therefore, the existing technology still needs to be improved and developed. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a single-bit image restoration method, device, terminal and medium in response to the above-mentioned defects of the prior art, aiming to solve the problem that the prior art cannot effectively suppress quantization noise, thereby affecting the image restoration accuracy.

[0007] The technical solutions adopted by the present invention to solve the problem are as follows:

[0008] In a first aspect, an embodiment of the present invention provides a single-bit image restoration method, wherein the method includes:

[0009] Acquire an image to be restored, perform single-bit quantization on the image to be restored using a non-zero quantization threshold, and determine an initial image quantization model;

[0010] A smooth hyperbolic tangent function is used to replace the sign function in the initial image quantization model, and a low-rank matrix decomposition is performed on the image to be restored to determine a target image quantization model;

[0011] determining an initial optimization model according to a truncated least squares function and the target image quantization model;

[0012] The initial optimization model is transformed using a semi-quadratic minimization method to determine a target optimization model;

[0013] A proximal block coordinate descent algorithm is used to solve the target optimization model to determine the low-dimensional sub-matrices and the noise matrix corresponding to the image to be restored;

[0014] A reconstructed image is determined using each of the low-dimensional sub-matrices.

[0015] In one implementation method, single-bit quantization is performed on the image to be restored using a non-zero quantization threshold to determine an initial image quantization model, including:

[0016] Performing single-bit quantization on the image to be restored using a single-bit low-rank matrix restoration model based on a non-zero quantization threshold to determine an image quantization model;

[0017] The noise matrix in the image quantization model is extracted outside the sign function to determine the initial image quantization model:

[0018] ,

[0019] in, is the data matrix corresponding to the image to be restored, is the number of rows of the data matrix, is the number of columns of the data matrix, is a non-zero quantization threshold, is the noise matrix, is the matrix after the data matrix is ​​quantized by single bit, is a symbolic function.

[0020] In one implementation method, a smooth hyperbolic tangent function is used to replace the sign function in the initial image quantization model, and a low-rank matrix decomposition is performed on the image to be restored to determine the target image quantization model, including:

[0021] Using smooth hyperbolic tangent function Alternative symbol function , and the data matrix of the image to be restored Using low-rank matrix factorization , determine the target image quantization model:

[0022] ,

[0023] in, For the data matrix After the low-rank matrix decomposition, the low-dimensional submatrix that satisfies the column full rank, For the data matrix After low-rank matrix decomposition, the low-dimensional submatrix that satisfies the row full rank is obtained. For order.

[0024] In one implementation method, determining an initial optimization model according to the truncated least squares function and the target image quantization model includes:

[0025] Remember any matrix , define the truncated least squares function as:

[0026] ,

[0027] in, is a matrix Middle Rank Elements of the column, is a hyperparameter, represents the truncated least squares function;

[0028] make , determining an initial optimization model according to the truncated least squares function and the target image quantization model:

[0029] .

[0030] In one implementation method, the initial optimization model is transformed using a semi-quadratic minimization method to determine a target optimization model, including:

[0031] Let the residual , the initial optimization model is expressed as a residual-based optimization model:

[0032] ,

[0033] is the residual Middle Rank Elements of the column;

[0034] For the residual-based optimization model, the non-convex terms Constructed as a semi-quadratic form , is an auxiliary variable, is with There is a regularization term with a dual relationship, is the residual The elements in , determine the target optimization model:

[0035] ,

[0036] in, represents the Frobenius norm, A function that processes elements.

[0037] In one implementation method, a proximal block coordinate descent algorithm is used to solve the target optimization model to determine the low-dimensional sub-matrices and the noise matrix corresponding to the image to be restored, including:

[0038] The proximal block coordinate descent algorithm is used to solve the target optimization model and determine the iterative update model:

[0039] ,

[0040] ,

[0041] ,

[0042] in, is the proximal parameter, the superscript and Respectively represent Second and The updated parameters after iterations are represents a differentiable function;

[0043] A gradient descent algorithm is used to solve the iterative update model to determine each of the low-dimensional sub-matrices and the noise matrix.

[0044] In one implementation method, a gradient descent algorithm is used to solve the iterative update model to determine each of the low-dimensional sub-matrices and the noise matrix, including:

[0045] The low-dimensional sub-matrix The solution is expressed as:

[0046] ,

[0047] in, , , subscript Used to identify low-dimensional submatrices Parameters, superscript Indicates the transpose of the matrix, the subscript Indicates the total number of iterations of gradient descent. Iteration steps, 、 is a hyperparameter,

[0048] The low-dimensional sub-matrix The solution is expressed as:

[0049] ,

[0050] in, , subscript Used to identify low-dimensional submatrices Parameters,

[0051] The noise matrix The solution is expressed as:

[0052] ,

[0053] Among them, the noise matrix Processed in scalar form, for The scalar form of .

[0054] In a second aspect, an embodiment of the present invention further provides a single-bit image restoration device, wherein the single-bit image restoration device includes:

[0055] an initial image quantization model determination module, configured to obtain an image to be restored, perform single-bit quantization on the image to be restored using a non-zero quantization threshold, and determine an initial image quantization model;

[0056] a target image quantization model construction module, configured to replace the sign function in the initial image quantization model with a smooth hyperbolic tangent function, and perform low-rank matrix decomposition on the image to be restored to determine the target image quantization model;

[0057] An initial optimization model determination module, configured to determine an initial optimization model according to a truncated least squares function and the target image quantization model;

[0058] A target optimization model determination module is used to transform the initial optimization model using a semi-quadratic minimization method to determine a target optimization model;

[0059] A target optimization model solving module is used to solve the target optimization model using a proximal block coordinate descent algorithm to determine the low-dimensional sub-matrices and noise matrix corresponding to the image to be restored;

[0060] An image restoration module is used to determine a reconstructed image using each of the low-dimensional sub-matrices.

[0061] In a third aspect, an embodiment of the present invention further provides a terminal comprising a memory and one or more processors; the memory stores one or more programs; the programs include instructions for executing any of the single-bit image restoration methods described above; and the processor is used to execute the programs.

[0062] In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium on which a plurality of instructions are stored, wherein the instructions are suitable for being loaded and executed by a processor to implement any of the above-mentioned single-bit image restoration methods.

[0063] The beneficial effects of the present invention are as follows: The present invention performs single-bit quantization on the image to be restored to determine an initial image quantization model; replaces the sign function in the initial image quantization model with a smooth hyperbolic tangent function and performs low-rank matrix decomposition on the image to be restored to determine a target image quantization model; determines an initial optimization model based on the truncated least squares function and the target image quantization model; transforms the initial optimization model using a semi-quadratic minimization method to determine a target optimization model; solves the target optimization model using a proximal block coordinate descent algorithm to obtain low-dimensional submatrices and a noise matrix; and determines a reconstructed image based on the low-dimensional submatrices. This effectively solves the problem that existing technologies cannot effectively suppress quantization noise, thereby affecting image restoration accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0065] Figure 1 It is a flowchart of a single-bit image restoration method provided by an embodiment of the present invention.

[0066] Figure 2 These are images restored using different algorithms provided by the embodiments of the present invention.

[0067] Figure 3 These are four grayscale images used for testing provided by an embodiment of the present invention.

[0068] Figure 4 Schematic diagram of the internal modules of the single-bit image restoration device provided by an embodiment of the present invention.

[0069] Figure 5 This is a principle block diagram of a terminal provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0070] The present invention discloses a single-bit image restoration method, apparatus, terminal, and medium. To clarify the objectives, technical solutions, and effects of the present invention, the present invention is further described below with reference to the accompanying drawings and examples. It should be understood that the specific examples described herein are intended only to illustrate the present invention and are not intended to limit the present invention.

[0071] It will be understood by those skilled in the art that, unless expressly stated otherwise, the singular forms "a", "an", "said" and "the" used herein may also include the plural forms. It should be further understood that the term "comprising" used in the description of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof. It should be understood that when we refer to an element as being "connected" or "coupled" to another element, it may be directly connected or coupled to the other element, or there may be intermediate elements. In addition, "connected" or "coupled" as used herein may include wireless connections or wireless couplings. The term "and / or" used herein includes all or any units and all combinations of one or more associated listed items.

[0072] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0073] Existing image restoration methods based on single-bit low-rank matrices primarily rely on maximum likelihood estimation based on the Gaussian assumption or equivalent loss functions. However, in practical applications, since single-bit quantization preserves sign information but loses amplitude information, the fitting error often deviates from the Gaussian assumption, thus affecting the accuracy of image restoration.

[0074] To address the above-mentioned shortcomings of the prior art, the present invention provides a single-bit image restoration method. The method determines an initial image quantization model by performing single-bit quantization on the image to be restored; replaces the sign function in the initial image quantization model with a smooth hyperbolic tangent function, and performs low-rank matrix decomposition on the image to be restored to determine a target image quantization model; determines an initial optimization model based on the truncated least squares function and the target image quantization model; transforms the initial optimization model using a semi-quadratic minimization method to determine a target optimization model; solves the target optimization model using a proximal block coordinate descent algorithm to obtain low-dimensional submatrices and a noise matrix; and determines a reconstructed image based on the low-dimensional submatrices. This method effectively addresses the problem that the prior art cannot effectively suppress quantization noise, thereby affecting image restoration accuracy.

[0075] Exemplary methods:

[0076] like Figure 1 As shown, the method includes:

[0077] Step S100: obtaining an image to be restored, performing single-bit quantization on the image to be restored using a non-zero quantization threshold, and determining an initial image quantization model;

[0078] Single-bit quantization of the image to be restored refers to mapping the original image (8-bit grayscale) represented in floating point format into a binary image. In this embodiment, the image to be restored is quantized using a pre-built single-bit quantization model to obtain an initial image quantization model corresponding to the image to be restored.

[0079] In one implementation, single-bit quantization is performed on the image to be restored using a non-zero quantization threshold to determine an initial image quantization model, including:

[0080] The image to be restored is single-bit quantized using a single-bit low-rank matrix restoration model based on a non-zero quantization threshold to determine the image quantization model, including: In this embodiment, the image to be restored is input into a traditional single-bit low-rank matrix restoration model based on a non-zero quantization threshold to obtain an initial image quantization model. Assume that the data matrix corresponding to the image to be restored is The rank of , is the number of rows in the data matrix, is the number of columns of the data matrix, when When the matrix can be considered as low rank. The additive noise matrix is , given a known non-zero quantization threshold , is the matrix obtained by single-bit quantization of the data matrix. The image quantization model can be expressed as:

[0081] ,

[0082] in, is an element-wise symbolic function defined as:

[0083] ,

[0084] 、 、 、 The matrix 、 、 、 Middle Rank Elements of a column.

[0085] Since the single-bit quantization only retains the sign information, it masks the noise distribution, making it difficult to find a suitable loss function. To solve this problem, this embodiment considers the noise The impact on single-bit quantization of data is extracted by extracting the noise matrix in the image quantization model outside the sign function to determine the initial image quantization model:

[0086] ,

[0087] in, is the data matrix corresponding to the image to be restored, is a non-zero quantization threshold, is the noise matrix, is the matrix after the data matrix is ​​quantized by single bit, is an element-wise symbolic function.

[0088] Elements in a matrix , which shows that The structure and It is worth noting that The non-zero elements in are either -2 or 2, and The distribution and amplitude changes only affect Therefore, it can be considered that There is sparsity, so this prior knowledge can be used to design a model to improve the single-bit low-rank matrix recovery performance.

[0089] Step S200: using a smooth hyperbolic tangent function to replace the sign function in the initial image quantization model, and performing low-rank matrix decomposition on the image to be restored to determine a target image quantization model.

[0090] Specifically, considering that the sign function is neither continuous nor semi-continuous, which makes it very difficult to deal with the optimization problem, we further adopt the smooth hyperbolic tangent function Alternative symbol function :

[0091] ,

[0092] Among them, the smooth hyperbolic tangent function is also an element-wise processing function and is defined as:

[0093] ,

[0094] Hyperparameters , used to The value of times. When , the smooth hyperbolic tangent function can gradually approach the sign function.

[0095] In order to satisfy the low-rank structure, the data matrix of the restored image is treated as Using low-rank matrix factorization , determine the target image quantization model to avoid using singular value decomposition, thereby reducing the computational complexity to a certain extent. The target image quantization model is expressed as:

[0096] ,

[0097] in, For the data matrix After the low-rank matrix decomposition, the low-dimensional submatrix that satisfies the column full rank, For the data matrix After low-rank matrix decomposition, the low-dimensional submatrix that satisfies the row full rank is obtained. For order.

[0098] Step S300: determining an initial optimization model according to the truncated least squares function and the target image quantization model.

[0099] Specifically, in the construction of the optimization problem, the truncated least squares function is used to eliminate the additive sparse noise. The influence of . Note that any matrix , define the truncated least squares function as:

[0100] ,

[0101] in, is a matrix Middle Rank Elements of the column, As a hyperparameter, it is used as a threshold to suppress outliers. The truncated least squares function can suppress the outliers to the threshold value without affecting the normal values. represents the truncated least squares function. In addition, when When , the truncated least squares function is equivalent to the Frobenius norm:

[0102] .

[0103] make In order to alleviate the influence of noise on the restoration result, the initial optimization model is determined according to the truncated least squares function and the target image quantization model:

[0104] .

[0105] Compared to the Frobenius norm, the truncated least squares function effectively suppresses the impact of outliers when the data sign flips. When the sign does not flip, its model is equivalent to using the Frobenius norm. Compared to the Lp norm (a type of norm), the truncated least squares function eliminates the impact of sign flips without interfering with normal data input. Therefore, the least squares function demonstrates superior robustness to the Lp norm in sign flip scenarios, while maintaining comparable performance to the Frobenius norm in the absence of sign flips.

[0106] Step S400: transform the initial optimization model using a semi-quadratic minimization method to determine a target optimization model.

[0107] For the initial optimization model, let the residual , for each element of the residual , the initial optimization model is expressed as a residual-based optimization model:

[0108] ,

[0109] is the residual Middle Rank Elements of the column;

[0110] The semi-quadratic minimization method can transform a non-smooth or complex cost function into a two-variable alternating optimization problem. Its core is to introduce auxiliary variables to decouple nonlinear or non-convex terms. For the above residual-based optimization model, the non-convex terms Construct its equivalent semiquadratic form , is an auxiliary variable, is some kind of regularization term to be proved, which is related to There is a dual relationship, is a matrix Elements in , build the target optimization model:

[0111]

[0112] in, represents the Frobenius norm, is an element-wise function, which is derived and proved using the convex conjugate transformation (Legendre-Fenchel Transform) and is defined as:

[0113] .

[0114] Step S500: using a proximal block coordinate descent algorithm to solve the target optimization model, and determining the low-dimensional sub-matrices corresponding to the image to be restored and the noise matrix.

[0115] Specifically, the proximal block coordinate descent algorithm is used to solve the target optimization model and determine the iterative update model:

[0116] ,

[0117] ,

[0118] ,

[0119] in, is the proximal parameter, the superscript and Respectively represent Second and The updated parameters after iterations are Represents a differentiable function. Based on the above iterative update model, the proximal block coordinate descent algorithm gradually updates each variable in each iteration and fixes other variables in the process of updating the current variable.

[0120] Solving the iterative update model using a gradient descent algorithm to determine each of the low-dimensional sub-matrices and the noise matrix specifically includes:

[0121] Update the low-dimensional sub-matrix :

[0122] To simplify the expression, the model will be updated iteratively in Expand and make , then we get:

[0123]

[0124] Although the loss function is about It is non-convex, but it is smooth and differentiable. Use the gradient descent algorithm to solve it and get the low-dimensional submatrix The solution is expressed as:

[0125] ,

[0126] in, , , subscript Used to identify low-dimensional submatrices Parameters, superscript Indicates the transpose of the matrix, the subscript Represents the total number of iterations in gradient descent Middle Iteration step. During the iteration, set and .

[0127] Update the low-dimensional sub-matrix :

[0128] Using and updating parameters The same method is used to update the parameters , and then use the gradient descent method to obtain the low-dimensional sub-matrix The solution is expressed as:

[0129]

[0130] in, , subscript Used to identify low-dimensional submatrices Parameters.

[0131] Update the noise matrix :

[0132] For the noise matrix , rewrite the problem expression:

[0133] ,

[0134] in, ,because Each element of Depends only on and , so the model is updated iteratively Can be processed in scalar form. To simplify the expression, the element subscript is ignored. ,

[0135] ,

[0136] Assumptions The parameters updated after the iteration are the optimal solution. for:

[0137] ,

[0138] when In very small amounts, e.g. , the above equation satisfies:

[0139]

[0140] Under this condition, the optimal solution can be simplified to:

[0141]

[0142] Get the noise matrix The optimal solution is expressed as:

[0143]

[0144] in, for scalar form. According to the optimal solution of the above formula, it should be noted that Parameters in the truncated least squares function This example analyzes the parameters Suitable range of. ,and Elements in satisfy:

[0145] ,

[0146] Among them, the smaller show and have the same sign. Conversely, if Close to its upper bound 2, indicating The sign may have flipped due to noise. The appropriate range is In addition, this parameter can also distinguish correct and incorrect measurement data based on the fitting error. In practice, considering the noise condition, Typically set to 2.

[0147] S600: Determine a reconstructed image using each of the low-dimensional sub-matrices.

[0148] In this embodiment, a low-dimensional sub-matrix is ​​used and the low-dimensional submatrix The product of , and obtain the reconstructed image.

[0149] In the single-bit image restoration method of this embodiment, the objective function is bounded and has the Kurdyka–Lojasiewicz (KL) property. In addition, the update parameter and update parameters The complexity is , update the parameters The complexity is , so the complexity of the single-bit image restoration method is .

[0150] In order to better reflect the superiority of the method proposed in the present invention, two existing comparison algorithms are selected, namely the one-bit singular value thresholding algorithm (OBSVT) and the majorization minimization Gauss-Newton algorithm (MMGN). It should be pointed out that the method proposed in the present invention and the one-bit singular value thresholding algorithm both use non-zero threshold quantization, while the majorization minimization Gauss-Newton algorithm uses zero threshold quantization. It is worth noting that the one-bit singular value thresholding algorithm achieves a low-rank structure through nuclear norm constraints, so it is necessary to adjust a hyperparameter to control the rank of the matrix. In addition, the method proposed in the present invention and the one-bit singular value thresholding algorithm both assume that the rank of the matrix is ​​a known condition.

[0151] like Figure 2 As shown, a test was conducted on a 512×512 resolution window image. The experiments considered both noise-free and noise-involved scenarios. In the noise-involved scenario, zero-mean Gaussian noise was added to the image, followed by single-bit quantization. In the noise-free scenario, both the proposed method and the single-bit singular value thresholding algorithm were able to recover a high-resolution image from a single-bit observation. However, in terms of two key evaluation metrics, peak signal-to-noise ratio (PSNR) and structural similarity, the proposed method outperformed the single-bit singular value thresholding algorithm, demonstrating superior image reconstruction quality. The proposed method was compared with a zero-thresholded Gauss-Newton algorithm. Experimental results show that the zero-thresholded Gauss-Newton algorithm produces multiple all-zero rows at the bottom of the image, resulting in severe distortion in the restored image. This is primarily due to the use of a zero-threshold for quantization, which completely loses information in certain pixel regions, posing significant challenges to local reconstruction. In the presence of Gaussian noise, the proposed method still demonstrates strong robustness, outperforming existing baseline methods in reconstruction performance. The image results show that the single-bit singular value threshold algorithm method is more sensitive to noise and the reconstruction quality is significantly reduced; while the principalization minimization Gauss-Newton algorithm method, although it can restore certain details under noisy conditions, still fails to effectively suppress noise interference.

[0152] In addition, the Figure 3The four images shown in Figure 1, Image 2, Image 3, and Image 4 are used for evaluation. The numerical results of the relevant peak signal-to-noise ratio and structural similarity are listed in Table 1, which includes the evaluation results of two scenarios with and without noise interference. It can be seen from the data in the table that compared with the single-bit singular value threshold algorithm and the principalized minimization Gauss-Newton algorithm, the method proposed in the present invention shows higher peak signal-to-noise ratio and structural similarity in all evaluation scenarios. In summary, the method proposed in the present invention performs better than the existing algorithms in the single-bit image restoration task, and has stronger restoration ability and higher image fidelity.

[0153] Table 1 Performance comparison between different algorithms

[0154]

[0155] Based on the above embodiment, the present invention also provides a single-bit image restoration device, such as Figure 4 As shown, the device includes:

[0156] The initial image quantization model determination module 01 is used to obtain an image to be restored, perform single-bit quantization on the image to be restored using a non-zero quantization threshold, and determine an initial image quantization model;

[0157] The target image quantization model construction module 02 is used to replace the sign function in the initial image quantization model with a smooth hyperbolic tangent function, and perform low-rank matrix decomposition on the image to be restored to determine the target image quantization model;

[0158] An initial optimization model determination module 03 is used to determine an initial optimization model according to a truncated least squares function and the target image quantization model;

[0159] The target optimization model determination module 04 is used to transform the initial optimization model using a semi-quadratic minimization method to determine the target optimization model;

[0160] The target optimization model solving module 05 is used to solve the target optimization model using a proximal block coordinate descent algorithm to determine the low-dimensional sub-matrices and noise matrix corresponding to the image to be restored;

[0161] The image restoration module 06 is configured to determine a reconstructed image using each of the low-dimensional sub-matrices.

[0162] Based on the above embodiment, the present invention further provides a terminal, whose principle block diagram can be shown as follows: Figure 5As shown. The terminal includes a processor, a memory, a network interface, and a display screen connected via a system bus. The processor of the terminal is used to provide computing and control capabilities. The memory of the terminal includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the terminal is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, a single-bit image recovery method is implemented. The display screen of the terminal can be a liquid crystal display or an electronic ink display.

[0163] Those skilled in the art will understand that Figure 5 The principle block diagram shown in the figure is only a block diagram of a partial structure related to the solution of the present invention, and does not constitute a limitation on the terminal to which the solution of the present invention is applied. The specific terminal may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0164] In one implementation, the terminal has one or more programs stored in its memory, and is configured to be executed by one or more processors, wherein the one or more programs include instructions for performing a single-bit image restoration method.

[0165] Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing the relevant hardware using a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the above-described method embodiments. Any reference to memory, storage, database, or other media used in the various embodiments provided herein may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct RAMbus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM).

[0166] In summary, the present invention discloses a single-bit image restoration method, device, terminal, and medium. The method determines an initial image quantization model by single-bit quantizing the image to be restored; replaces the sign function in the initial image quantization model with a smooth hyperbolic tangent function and performs low-rank matrix decomposition on the image to be restored to determine a target image quantization model; determines an initial optimization model based on the truncated least squares function and the target image quantization model; transforms the initial optimization model using a semi-quadratic minimization method to determine a target optimization model; solves the target optimization model using a proximal block coordinate descent algorithm to obtain low-dimensional submatrices and a noise matrix; and determines a reconstructed image based on the low-dimensional submatrices. This method effectively solves the problem that existing technologies cannot effectively suppress quantization noise, thereby affecting image restoration accuracy.

[0167] It should be understood that the application of the present invention is not limited to the above examples. For those skilled in the art, improvements or changes can be made based on the above description. All these improvements and changes should fall within the scope of protection of the claims attached to the present invention.

Claims

1. A single-bit image restoration method, characterized in that: The method comprises: Acquire an image to be restored, perform single-bit quantization on the image to be restored using a non-zero quantization threshold, and determine an initial image quantization model; A smooth hyperbolic tangent function is used to replace the sign function in the initial image quantization model, and a low-rank matrix decomposition is performed on the image to be restored to determine a target image quantization model; determining an initial optimization model according to a truncated least squares function and the target image quantization model; The initial optimization model is transformed using a semi-quadratic minimization method to determine a target optimization model; A proximal block coordinate descent algorithm is used to solve the target optimization model to determine the low-dimensional sub-matrices and the noise matrix corresponding to the image to be restored; Determine a reconstructed image using each of the low-dimensional sub-matrices; Performing single-bit quantization on the image to be restored using a non-zero quantization threshold to determine an initial image quantization model includes: Performing single-bit quantization on the image to be restored using a single-bit low-rank matrix restoration model based on a non-zero quantization threshold to determine an image quantization model; The noise matrix in the image quantization model is extracted outside the sign function to determine the initial image quantization model: ， in, is the data matrix corresponding to the image to be restored, is the number of rows of the data matrix, is the number of columns of the data matrix, is a non-zero quantization threshold, is the noise matrix, is the matrix after the data matrix is ​​quantized by single bit, is a symbolic function; The method comprises the following steps: replacing the sign function in the initial image quantization model with a smooth hyperbolic tangent function, performing low-rank matrix decomposition on the image to be restored, and determining a target image quantization model. The method comprises the following steps: Using smooth hyperbolic tangent function Alternative symbol function , and the data matrix of the image to be restored Using low-rank matrix factorization , determine the target image quantization model: ， in, For the data matrix After the low-rank matrix decomposition, the low-dimensional submatrix that satisfies the column full rank, For the data matrix After low-rank matrix decomposition, the low-dimensional submatrix that satisfies the row full rank is obtained. For order.

2. The single-bit image restoration method according to claim 1, wherein: Determining an initial optimization model according to the truncated least squares function and the target image quantization model includes: Remember any matrix , define the truncated least squares function as: ， in, is a matrix Middle Rank Elements of the column, is a hyperparameter, represents the truncated least squares function; make , determining an initial optimization model according to the truncated least squares function and the target image quantization model: 。 3. The single-bit image restoration method according to claim 2, wherein: The initial optimization model is transformed using a semi-quadratic minimization method to determine a target optimization model, including: Let the residual , the initial optimization model is expressed as a residual-based optimization model: ， is the residual Middle Rank Elements of the column; For the residual-based optimization model, the non-convex terms Constructed as a semi-quadratic form , is an auxiliary variable, is with There is a regularization term with a dual relationship, is the residual The elements in , determine the target optimization model: ， in, represents the Frobenius norm, A function that processes elements.

4. The single-bit image restoration method according to claim 3, wherein: The target optimization model is solved by using a proximal block coordinate descent algorithm to determine the low-dimensional sub-matrices and the noise matrix corresponding to the image to be restored, including: The proximal block coordinate descent algorithm is used to solve the target optimization model and determine the iterative update model: ， ， ， in, is the proximal parameter, the superscript and Respectively represent Second and The updated parameters after iterations are represents a differentiable function; A gradient descent algorithm is used to solve the iterative update model to determine each of the low-dimensional sub-matrices and the noise matrix.

5. The single-bit image restoration method according to claim 4, characterized in that: Solving the iterative update model using a gradient descent algorithm to determine each of the low-dimensional sub-matrices and the noise matrix includes: The low-dimensional sub-matrix The solution is expressed as: ， in, , , subscript Used to identify low-dimensional submatrices Parameters, superscript Indicates the transpose of the matrix, the subscript Indicates the total number of iterations of gradient descent. The low-dimensional sub-matrix of the iteration step, 、 is a hyperparameter, The low-dimensional sub-matrix The solution is expressed as: ， in, , subscript Used to identify low-dimensional submatrices Parameters, The noise matrix The solution is expressed as: ， Among them, the noise matrix Processed in scalar form, for The scalar form of 。 6. A single-bit image restoration device, characterized in that: The device comprises: an initial image quantization model determination module, configured to obtain an image to be restored, perform single-bit quantization on the image to be restored using a non-zero quantization threshold, and determine an initial image quantization model; a target image quantization model construction module, configured to replace the sign function in the initial image quantization model with a smooth hyperbolic tangent function, and perform low-rank matrix decomposition on the image to be restored to determine the target image quantization model; An initial optimization model determination module, configured to determine an initial optimization model according to a truncated least squares function and the target image quantization model; A target optimization model determination module is used to transform the initial optimization model using a semi-quadratic minimization method to determine a target optimization model; A target optimization model solving module is used to solve the target optimization model using a proximal block coordinate descent algorithm to determine the low-dimensional sub-matrices and noise matrix corresponding to the image to be restored; An image restoration module, configured to determine a reconstructed image using each of the low-dimensional sub-matrices; Performing single-bit quantization on the image to be restored using a non-zero quantization threshold to determine an initial image quantization model includes: Performing single-bit quantization on the image to be restored using a single-bit low-rank matrix restoration model based on a non-zero quantization threshold to determine an image quantization model; The noise matrix in the image quantization model is extracted outside the sign function to determine the initial image quantization model: ， in, is the data matrix corresponding to the image to be restored, is the number of rows of the data matrix, is the number of columns of the data matrix, is a non-zero quantization threshold, is the noise matrix, is the matrix after the data matrix is ​​quantized by single bit, is a symbolic function; The method comprises the following steps: replacing the sign function in the initial image quantization model with a smooth hyperbolic tangent function, performing low-rank matrix decomposition on the image to be restored, and determining a target image quantization model. The method comprises the following steps: Using smooth hyperbolic tangent function Alternative symbol function , and the data matrix of the image to be restored Using low-rank matrix factorization , determine the target image quantization model: ， in, For the data matrix After the low-rank matrix decomposition, the low-dimensional submatrix that satisfies the column full rank, For the data matrix After low-rank matrix decomposition, the low-dimensional submatrix that satisfies the row full rank is obtained. For order.

7. A terminal, characterized in that: The terminal includes a memory and one or more processors; the memory stores one or more programs; the programs include instructions for executing the single-bit image restoration method as described in any one of claims 1-5; and the processor is used to execute the programs.

8. A computer-readable storage medium having a plurality of instructions stored thereon, characterized in that: The instructions are loaded and executed by the processor to implement the steps of the single-bit image restoration method described in any one of claims 1 to 5.

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