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

Abstract

The invention discloses a single-bit image recovery method and device, a terminal and a medium, and relates to the field of image processing. The method comprises the following steps: performing single-bit quantization on a to-be-recovered image by adopting a non-zero quantization threshold, and determining an initial image quantization model; replacing a sign function in the initial image quantization model with a smooth hyperbolic tangent function, performing low-rank matrix decomposition on the to-be-recovered image, and determining a target image quantization model; determining an initial optimization model according to the truncated least square function and the target image quantization model; a semi-quadratic minimization method is adopted to convert the initial optimization model, and a target optimization model is determined; solving the target optimization model by adopting a near-end block coordinate descent algorithm to obtain each low-dimension sub-matrix and a noise matrix; and determining a reconstructed image by using each low-dimensional sub-matrix. The problem that in the prior art, quantization noise cannot be effectively restrained, and therefore image restoration precision is affected is effectively solved.

Description

Technical Field

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

[0002] Images are often affected by noise interference during wireless transmission or have reduced quality due to bit data loss during the signal acquisition phase. The low-rank matrix recovery technology can utilize the low-rank structure contained in the observed matrix after being interfered by noise to effectively reconstruct the original low-dimensional information and is widely used in image processing.

[0003] The 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, only retains the data symbol information, and performs low-rank data matrix recovery based on the data symbol information, which can improve the use efficiency of system resources while ensuring the accuracy of image data recovery.

[0004] Existing image restoration methods based on single-bit low-rank matrix recovery mainly rely on maximum likelihood estimation based on Gaussian assumptions or equivalent loss functions. However, since single-bit quantization retains symbol information while losing amplitude information, the fitting error usually deviates from the Gaussian assumption and cannot 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, apparatus, terminal, and medium for the above-mentioned defects of the existing technology, aiming to solve the problem that the existing technology cannot effectively suppress quantization noise and thus affects the accuracy of image restoration.

[0007] The technical solution adopted by the present invention to solve the problem is as follows: In a first aspect, an embodiment of the present invention provides a single-bit image restoration method, where the method includes: 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; 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 a target image quantization model; Determine an initial optimization model according to the truncated least squares function and the target image quantization model; Use the semi-quadratic minimization method to transform the initial optimization model to determine a target optimization model; Solve the target optimization model by using the proximal block coordinate descent algorithm, and determine each low-dimensional submatrix and noise matrix corresponding to the image to be restored; Determine the reconstructed image by using each of the low-dimensional submatrices.

[0008] In an implementation method, perform single-bit quantization on the image to be restored by using a non-zero quantization threshold to determine an initial image quantization model, including: Perform single-bit quantization on the image to be restored by using a single-bit low-rank matrix recovery model based on the non-zero quantization threshold to determine the image quantization model; Extract the noise matrix in the image quantization model to the outside of the sign function to determine the initial image quantization model: , where, 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 the non-zero quantization threshold, is the noise matrix, is the matrix after single-bit quantization of the data matrix, is the sign function.

[0009] In an implementation method, 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, including: Use the smooth hyperbolic tangent function to replace the sign function , and perform low-rank matrix decomposition on the data matrix of the image to be restored to determine the target image quantization model: , where, is the low-dimensional submatrix that satisfies full column rank after low-rank matrix decomposition of the data matrix , is the low-dimensional submatrix that satisfies full row rank after low-rank matrix decomposition of the data matrix , is the rank.

[0010] In an implementation method, determine the initial optimization model according to the truncated least squares function and the target image quantization model, including: Denote any matrix , and define the truncated least squares function as: , Among them, is a matrix in the th row and th column of the element, is a hyperparameter, indicating a truncated least squares function; Let , and determine an initial optimization model according to the truncated least squares function and the target image quantization model: .

[0011] In an implementation method, a semi - quadratic minimization method is used to transform the initial optimization model to determine a target optimization model, including: Let the residual , and represent the initial optimization model as an optimization model based on the residual: , is the th row and th column element in the residual ; For the optimization model based on the residual, construct the non - convex term into a semi - quadratic form , is an auxiliary variable, is a regularization term with a dual relationship with , is the element in the residual , and determine the target optimization model: , Among them, represents the Frobenius norm, is an element - wise processing function.

[0012] In an implementation method, a proximal block - coordinate descent algorithm is used to solve the target optimization model to determine each low - dimensional sub - matrix and noise matrix corresponding to the image to be restored, including: Use the proximal block - coordinate descent algorithm to solve the target optimization model to determine an iterative update model: , , , Among them, is a proximal parameter, the superscript and respectively represent the th and the The parameters after the next iteration update represent differentiable functions; The gradient descent algorithm is used to solve the iterative update model to determine each of the low-dimensional submatrices and the noise matrix.

[0013] In one implementation method, using the gradient descent algorithm to solve the iterative update model to determine each of the low-dimensional submatrices and the noise matrix includes: The solution of the low-dimensional submatrix is expressed as: , where , , the subscript is used to identify the parameters of the low-dimensional submatrix , the superscript represents the transpose of the matrix, and the subscript represents the th iteration step in the total number of iterations of gradient descent, , are hyperparameters, The solution of the low-dimensional submatrix is expressed as: , where , the subscript is used to identify the parameters of the low-dimensional submatrix , The solution of the noise matrix is expressed as: , where the noise matrix is processed in scalar form, is the scalar form of, .

[0014] In a second aspect, an embodiment of the present invention further provides a single-bit image restoration device, where the single-bit image restoration device includes: 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 a 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, configured to transform the initial optimization model by using a semi - quadratic minimization method to determine a target optimization model; A target optimization model solving module, configured to solve the target optimization model by using a proximal block coordinate descent algorithm to determine each low - dimensional sub - matrix and noise matrix corresponding to the image to be restored; An image restoration module, configured to determine a reconstructed image by using each of the low - dimensional sub - matrices.

[0015] In a third aspect, an embodiment of the present invention further provides a terminal, where the terminal includes a memory and more than one processor; the memory stores more than one program; the program includes instructions for executing the single - bit image restoration method as described in any one of the above; the processor is configured to execute the program.

[0016] In a fourth aspect, an embodiment of the present invention further provides a computer - readable storage medium, on which multiple instructions are stored, where the instructions are suitable for being loaded and executed by a processor to implement the single - bit image restoration method as described in any one of the above.

[0017] Advantages of the present invention: In the embodiment of the present invention, by performing single - bit quantization on the image to be restored, an initial image quantization model is determined; a smooth hyperbolic tangent function is used to replace the sign function in the initial image quantization model, and low - rank matrix decomposition is performed on the image to be restored to determine a target image quantization model; an initial optimization model is determined according to a truncated least squares function and the target image quantization model; the initial optimization model is transformed by 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 obtain each low - dimensional sub - matrix and noise matrix; a reconstructed image is determined according to each low - dimensional sub - matrix. It effectively solves the problem that the prior art cannot effectively suppress quantization noise, thus affecting the accuracy of image restoration. Description of the Drawings

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following - described drawings are only some embodiments recorded in the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained according to these drawings.

[0019] Figure 1 It is a schematic flowchart of the single - bit image restoration method provided by the embodiment of the present invention.

[0020] Figure 2It is the image restored by different algorithms provided by the embodiments of the present invention.

[0021] Figure 3 They are four grayscale images for testing provided by the embodiments of the present invention.

[0022] Figure 4 It is a schematic diagram of the internal module of the single-bit image restoration device provided by the embodiments of the present invention.

[0023] Figure 5 It is a schematic block diagram of the terminal provided by the embodiments of the present invention. Detailed implementation manners

[0024] The present invention discloses a single-bit image restoration method, device, terminal and medium. To make the purpose, technical solution and effect of the present invention clearer and more definite, the following further describes the present invention in detail with reference to the accompanying drawings and by way of examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0025] Those skilled in the art of the present technology can understand that unless specifically stated, the singular forms "a", "an", "the" and "said" used herein may also include the plural forms. It should be further understood that the term "comprising" used in the specification of the present invention means the presence of the described 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 their groups. It should be understood that when we say that an element is "connected" or "coupled" to another element, it can be directly connected or coupled to other elements, or there may also be intermediate elements. In addition, the "connection" or "coupling" used herein may include wireless connection or wireless coupling. The phrase "and / or" used herein includes all or any unit and all combinations of one or more related listed items.

[0026] Those skilled in the art of the present technology can understand that unless otherwise defined, all terms (including technical terms and scientific terms) used herein have the same meaning as the general understanding of those of ordinary skill in the art to which the present invention belongs. It should also be understood that terms such as those defined in a general dictionary should be understood to have a meaning consistent with the meaning in the context of the prior art, and will not be interpreted with an idealized or overly formal meaning unless specifically defined as here.

[0027] Existing image restoration methods based on single-bit low-rank matrices mainly rely on maximum likelihood estimation based on Gaussian assumptions or loss functions equivalent thereto. However, in practical applications, since single-bit quantization retains sign information while losing amplitude information, the fitting error usually deviates from the Gaussian assumption, thus affecting the accuracy of image restoration.

[0028] In view of the above defects 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 according to the truncated least squares function and the target image quantization model; uses the semi-quadratic minimization method to transform the initial optimization model to determine a target optimization model; uses the proximal block coordinate descent algorithm to solve the target optimization model to obtain each low-dimensional sub-matrix and the noise matrix; determines the reconstructed image according to each low-dimensional sub-matrix. It effectively solves the problem that the prior art cannot effectively suppress quantization noise, thereby affecting the image restoration accuracy.

[0029] Exemplary method: As Figure 1 shown, the method includes: Step S100, obtain the 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; Performing single-bit quantization on the image to be restored means mapping the original image represented by floating-point (8-bit grayscale) to a binary image. In this embodiment, the image to be restored is quantized through a pre-constructed single-bit quantization model to obtain the initial image quantization model corresponding to the image to be restored.

[0030] In one implementation, performing single-bit quantization on the image to be restored using a non-zero quantization threshold and determining 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, 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 has a rank of , is the number of rows of the data matrix, is the number of columns of the data matrix. When , the matrix can be considered low-rank. The additive noise matrix is . Given a known non-zero quantization threshold , is the matrix obtained after single-bit quantization of the data matrix. The image quantization model can be expressed as: , where is the element-wise sign function, which is defined as: , , , , are, in sequence, the elements in the , , , th row and th column of the matrix.

[0031] Since the property of single-bit quantization that only preserves the sign information masks the noise distribution, it is difficult to find a suitable loss function. To solve this problem, this embodiment considers the influence of noise on the single-bit quantization of data, extracts the noise matrix in the image quantization model outside the sign function, and determines the initial image quantization model: , wherein, is the data matrix corresponding to the image to be restored, is the non-zero quantization threshold, is the noise matrix, is the matrix after single-bit quantization of the data matrix, is the element-wise sign function.

[0032] The element in the matrix indicates that the structure of is independent of the distribution of . It should be noted that the non-zero elements in take values of -2 or 2, and the distribution and amplitude change of only affect the number of non-zero elements in . Therefore, it can be considered that

[0033] has sparsity, and thus this prior knowledge can be used to design a model to improve the performance of single-bit low-rank matrix recovery.

[0034] Step S200: 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. Specifically, considering that the property of the sign function being neither continuous nor semi-continuous makes it very difficult to handle the optimization problem, a smooth hyperbolic tangent function is further used to replace the sign function : wherein, the smooth hyperbolic tangent function is also an element-wise processing function and is defined as: , Hyperparameter , used to amplify the value by times. When , the smooth hyperbolic tangent function can gradually approximate the sign function.

[0035] To satisfy the low-rank structure, and then perform low-rank matrix decomposition on the data matrix of the image to be restored, 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: , where is the low-dimensional submatrix that satisfies full column rank after the low-rank matrix decomposition of the data matrix , is the low-dimensional submatrix that satisfies full row rank after the low-rank matrix decomposition of the data matrix , is the rank.

[0036] Step S300, determine the initial optimization model according to the truncated least squares function and the target image quantization model.

[0037] Specifically, in the construction of the optimization problem, use the truncated least squares function to eliminate the influence of additive sparse noise . Denote any matrix , and define the truncated least squares function as: , where is the element in the th row and th column of the matrix , is the hyperparameter, used as a threshold to suppress outliers. Set an appropriate so that the truncated least squares function can suppress the outliers to this threshold value without affecting the normal values, represents the truncated least squares function. In addition, when , the truncated least squares function is equivalent to the Frobenius norm: .

[0038] Let , to mitigate the influence of noise on the restoration result, determine the initial optimization model according to the truncated least squares function and the target image quantization model: .

[0039] Compared with the Frobenius norm, the truncated least squares function can effectively suppress the influence of outliers when the data signs are flipped. In the case where the signs are not flipped, its model is equivalent to using the Frobenius norm for processing. Compared with the L-p norm (a type of norm) method, the truncated least squares function can eliminate the influence brought by sign flipping without disturbing the normal data input. Therefore, the least squares function exhibits better robustness than the L-p norm in the sign-flipping scenario and maintains performance comparable to the Frobenius norm in the case of no sign flipping.

[0040] Step S400: Transform the initial optimization model using the semi-quadratic minimization method to determine the target optimization model.

[0041] For the initial optimization model, let the residual , for each element of the residual, represent the initial optimization model as an optimization model based on the residual: , is the element in the -th row and -th column of the residual The semi-quadratic minimization method can transform a non-smooth or complex cost function into a problem of alternating optimization of two variables. Its core is to introduce auxiliary variables to decouple non-linear or non-convex terms. For the above optimization model based on the residual, construct the non-convex term into its equivalent semi-quadratic form , is the auxiliary variable, is a certain regularization term to be proved, which has a dual relationship with , is the element in the matrix , and construct the target optimization model:

[0042] where, represents the Frobenius norm, is an element-wise function, which is derived and proved using the convex conjugate transform (Legendre-Fenchel Transform) and is defined as: .

[0043] Step S500: Solve the target optimization model using the proximal block coordinate descent algorithm to determine the respective low-dimensional sub-matrices corresponding to the image to be restored and the noise matrix.

[0044] Specifically, the proximal block coordinate descent algorithm is adopted to solve the target optimization model, and an iterative update model is determined: , , , where is the proximal parameter, and the superscripts and represent the parameters after the -th and -th iterative updates respectively, represents a differentiable function. Based on the above iterative update model, in each iteration of the proximal block coordinate descent algorithm, each variable is gradually updated, and other variables are fixed during the process of updating the current variable.

[0045] The gradient descent algorithm is adopted to solve the iterative update model, and each of the low-dimensional submatrices and the noise matrix is determined, specifically including: Updating the low-dimensional submatrix : For simplicity of expression, the iterative update model in is expanded, and let , then we get:

[0046] Although the loss function is non-convex with respect to , it is smooth and differentiable. Using the gradient descent algorithm to solve, the solution of the low-dimensional submatrix is expressed as: , where , , the subscript is used to identify the parameters of the low-dimensional submatrix , the superscript represents the transpose of the matrix, and the subscript represents the -th iteration step in the total number of iterations of the gradient descent . In the -th iteration process of the proximal block coordinate descent algorithm, set and .

[0047] Updating the low-dimensional submatrix : Use the same method as updating the parameter to update the parameter , so as to obtain the low-dimensional submatrix using the gradient descent method The solution is expressed as:

[0048] where , and the subscript is used to identify the parameter of the low-dimensional submatrix .

[0049] Update the noise matrix : For the noise matrix , rewrite the expression of the problem: , where , because each element of only depends on and and , so the iterative update of the model can be processed in scalar form. To simplify the expression, the element position subscript is ignored, , assuming that the parameter after iterative updates is the optimal solution, the optimal solution of the above formula is: , When is extremely small, for example , the above equation is satisfied:

[0050] Under this condition, the optimal solution can be simplified to:

[0051] Obtain the optimal solution of the noise matrix , expressed as:

[0052] where is the scalar form of . According to the optimal solution of the above formula, it should be noted that is affected by the parameter in the truncated least squares function. This embodiment analyzes the appropriate range of the parameter . Given , and the elements in satisfy: , where the smaller indicates that and the corresponding elements in have the same sign. Conversely, if is close to its upper bound 2, it indicates that a sign flip may have occurred due to noise interference. Therefore the appropriate range of is between . In addition, this parameter can also distinguish between correct and incorrect measurement data based on the fitting error. In practice, considering the noise conditions is usually set to 2.

[0053] S600. Determine the reconstructed image using each of the low-dimensional submatrices.

[0054] In this embodiment, through the low-dimensional submatrix and the low-dimensional submatrix product, that is , the reconstructed image is obtained.

[0055] In the single-bit image restoration method of this embodiment, its objective function is bounded and has the Kurdyka–Lojasiewicz (KL) property. In addition, the complexity of updating the parameter and the complexity of updating the parameter is , the complexity of updating the parameter is , so the complexity of the single-bit image restoration method is .

[0056] To better demonstrate the superiority of the method proposed in the present invention, two existing comparison algorithms are selected, namely the One-bit Singular Value Thresholding (OBSVT) and the Majorization Minimization Gauss-Newton (MMGN) algorithm. It should be noted that both the method proposed in the present invention and the one-bit singular value thresholding algorithm 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 realizes the low-rank structure through the nuclear norm constraint, so a hyperparameter needs to be adjusted to control the rank of the matrix. In addition, both the method proposed in the present invention and the one-bit singular value thresholding algorithm assume that the rank of the matrix is a known condition.

[0057] As Figure 2As shown, a window image with a resolution of 512×512 was tested. In the experiment, two scenarios were considered: without noise and with noise interference. In the case of noise interference, Gaussian noise with zero mean was added to the image, and then single-bit quantization was performed. In the noiseless scenario, both the method proposed in the present invention and the single-bit singular value threshold algorithm can achieve the recovery of high-resolution images from single-bit observations. However, in terms of two key evaluation metrics, peak signal-to-noise ratio (PSNR) and structural similarity (SSIM), the method proposed in the present invention is superior to the single-bit singular value threshold algorithm, showing better image reconstruction quality. The method proposed in the present invention was compared with the majorization-minimization Gaussian-Newton algorithm with a zero quantization threshold. The experimental results show that multiple all-zero rows appeared at the bottom of the image in the majorization-minimization Gaussian-Newton algorithm, resulting in serious distortion of the recovery result. The main reason is that using a zero threshold for quantization causes some pixel regions to completely lose information, thus posing a great challenge to local reconstruction. In the scenario with Gaussian noise, the method proposed in the present invention still shows strong robustness, and its reconstruction performance is better than that of existing benchmark methods. The image results show that the single-bit singular value threshold algorithm is sensitive to noise and the reconstruction quality drops significantly; while the majorization-minimization Gaussian-Newton algorithm, although it recovers some details under noisy conditions, still fails to effectively suppress noise interference.

[0058] In addition, four images shown in Image 1, Image 2, Image 3, and Image 4 in Figure 3 were also 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 for both the noisy and noiseless scenarios. From the data in the table, it can be seen that compared with the single-bit singular value threshold algorithm and the majorization-minimization Gaussian-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 has better performance than existing algorithms in the single-bit image recovery task, with stronger recovery ability and higher image fidelity.

[0059] Table 1 Performance comparison between different algorithms

[0060] Based on the above embodiments, the present invention also provides a single-bit image recovery device, as shown in Figure 4 The device includes: An initial image quantization model determination module 01, configured to obtain an image to be recovered, perform single-bit quantization on the image to be recovered using a non-zero quantization threshold, and determine an initial image quantization model; 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; The initial optimization model determination module 03 is used to determine the initial optimization model according to the truncated least squares function and the target image quantization model; The target optimization model determination module 04 is used to transform the initial optimization model by using the semi-quadratic minimization method to determine the target optimization model; The target optimization model solving module 05 is used to solve the target optimization model by using the proximal block coordinate descent algorithm to determine each low-dimensional submatrix and the noise matrix corresponding to the image to be restored; The image restoration module 06 is used to determine the reconstructed image by using each of the low-dimensional submatrices.

[0061] Based on the above embodiments, the present invention also provides a terminal, and its principle block diagram can be as Figure 5 shown. The terminal includes a processor, a memory, a network interface, and a display screen connected through a system bus. Among them, 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 through a network connection. When the computer program is executed by the processor, it realizes the single-bit image restoration method. The display screen of the terminal can be a liquid crystal display screen or an electronic ink display screen.

[0062] Those skilled in the art can understand that Figure 5 the principle block diagram shown in

[0063] merely shows the block diagram of some structures 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 those shown in the figure, or combine some components, or have different component arrangements.

[0064] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium used in the various embodiments provided by the present invention can include non-volatile and / or volatile memories. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM), etc.

[0065] In summary, the present invention discloses a single-bit image restoration method, apparatus, terminal, and medium. 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 according to the truncated least squares function and the target image quantization model; uses the semi-quadratic minimization method to transform the initial optimization model to determine a target optimization model; uses the proximal block coordinate descent algorithm to solve the target optimization model to obtain each low-dimensional sub-matrix and the noise matrix; determines the reconstructed image according to each low-dimensional sub-matrix. It effectively solves the problem that the prior art cannot effectively suppress quantization noise, thereby affecting the image restoration accuracy.

[0066] It should be understood that the application of the present invention is not limited to the above examples. For those of ordinary skill in the art, improvements or transformations can be made according to the above description. All such improvements and transformations should fall within the protection scope of the appended claims of the present invention.

Claims

1. A single-bit image restoration method, characterized in that, The method includes: Obtain the 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; 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 a target image quantization model; Determine an initial optimization model according to the truncated least squares function and the target image quantization model; Transform the initial optimization model using the semi-quadratic minimization method to determine a target optimization model; Solve the target optimization model using the proximal block coordinate descent algorithm to determine each low-dimensional submatrix and noise matrix corresponding to the image to be restored; Determine a reconstructed image using each of the low-dimensional submatrices.

2. The single-bit image restoration method according to claim 1, wherein Performing single-bit quantization on the image to be restored using a non-zero quantization threshold to determine an initial image quantization model includes: Perform single-bit quantization on the image to be restored using a single-bit low-rank matrix recovery model based on a non-zero quantization threshold to determine an image quantization model; Extract the noise matrix in the image quantization model outside the sign function to determine the initial image quantization model: ， Among them, 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 the non-zero quantization threshold, is the noise matrix, is the matrix after single-bit quantization of the data matrix, is the sign function.

3. The single-bit image restoration method according to claim 2, wherein Replacing the sign function in the initial image quantization model with a smooth hyperbolic tangent function and performing low-rank matrix decomposition on the image to be restored to determine a target image quantization model includes: Adopt a smooth hyperbolic tangent function to replace the sign function , and use low-rank matrix decomposition for the data matrix of the image to be restored to determine the target image quantization model: ​ ， Among them, is the data matrix a low-dimensional submatrix that satisfies full column rank after low-rank matrix decomposition, is the data matrix a low-dimensional submatrix that satisfies full row rank after low-rank matrix decomposition, is the rank.

4. The single-bit image restoration method according to claim 3, wherein Determining an initial optimization model according to the truncated least squares function and the target image quantization model includes: Denote an arbitrary matrix , and define the truncated least squares function as: ， wherein, is a matrix in the th row and the th column of the element, is a hyperparameter, represents a truncated least squares function; Let , determine an initial optimization model according to the truncated least squares function and the target image quantization model: 。 5. The single-bit image restoration method according to claim 4, wherein Transforming the initial optimization model using the semi-quadratic minimization method to determine a target optimization model includes: Let the residual , and represent the initial optimization model as an optimization model based on the residual: ， For the residual in the row and column elements; For the residual-based optimization model, the non-convex term is constructed in a semi-quadratic form , is an auxiliary variable, is a regularization term having a dual relationship with , is the residual element, to determine the target optimization model: ， Among them, represents the Frobenius norm, is an element-wise function.

6. The single-bit image restoration method according to claim 5, wherein Solving the target optimization model using the proximal block coordinate descent algorithm to determine each low-dimensional submatrix and noise matrix corresponding to the image to be restored includes: Solve the target optimization model using the proximal block coordinate descent algorithm to determine an iterative update model: ， ， ， Among them, is the proximal parameter, and the superscripts and represent the parameters after the -th and -th iterative updates respectively, and represents a differentiable function. Solve the iterative update model using the gradient descent algorithm to determine each of the low-dimensional submatrices and the noise matrix.

7. The single-bit image restoration method according to claim 6, wherein Solving the iterative update model using the gradient descent algorithm to determine each of the low-dimensional submatrices and the noise matrix includes: The low-dimensional submatrix is represented as: ， Among them, , , the subscript is used to identify the parameter of the low-dimensional submatrix , the superscript represents the transpose of the matrix, and the subscript represents the th iteration step in the total number of iterations of gradient descent, , are hyperparameters. The low-dimensional sub-matrix is represented as: ， Among them, , the subscript is used to identify the parameters of the low-dimensional submatrix . The noise matrix is represented as: ， Among them, the noise matrix is processed in scalar form, which is the scalar form of .

8. A single-bit image restoration device, characterized in that, The apparatus includes: 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 a target image quantization model; An initial optimization model determination module, configured to determine an initial optimization model according to the truncated least squares function and the target image quantization model; A target optimization model determination module, configured to transform the initial optimization model using the semi-quadratic minimization method to determine a target optimization model; A target optimization model solving module, configured to solve the target optimization model using the proximal block coordinate descent algorithm to determine each low-dimensional submatrix 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 submatrices.

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

10. 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 as described in any one of claims 1-7 above.

Images