Robustness compressed sensing method based on quantization bit erasure

Abstract

A robustness compressed sensing method based on quantization bit erasure comprises the following steps: 1) a sender unfolds an image into a gray vector, and the gray vector is obtained by sampling through a Bernoulli random matrix; 2) quantized transmission: quantizing the sampling value y by using a quantizer trained by a Lloyd-Max algorithm; 3) the quantized y and phi are transmitted to a receiver, and a Reed-Solomon code is adopted to protect a channel during transmission; 4) generating a constraint set W, and performing inverse quantization; and 5) designing an iterative algorithm, estimating x by using phi and W, and reconstructing an original image signal through an image estimation step and a measurement estimation step. According to the method, the constraint set W for measuring y can be generated by using the position of quantized bit erasure, and then the iterative algorithm is designed to realize image reconstruction, so that the method has relatively high theoretical and engineering application values.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence and image feature extraction and image reconstruction under computer graphics, and specifically belongs to the field of compressed sensing technology, and relates to an image compressed sensing reconstruction technology, in particular to a compressed sensing reconstruction algorithm D-AMP using a denoiser. Background Art

[0002] Compressed Sensing (CS) is an efficient signal processing method that states that if a signal is sparse in a certain domain, that is, the signal can be represented as a linear combination of a small number of non-zero elements, then the signal can be accurately reconstructed at a sampling rate much lower than the Nyquist rate. The introduction of this theory provides a new perspective for signal acquisition, storage and transmission, especially showing its unique advantages when processing high-dimensional data. At present, compressed sensing technology has shown great application potential in many fields: in the field of medical imaging, especially in magnetic resonance imaging (MRI), compressed sensing technology can shorten the scanning time while maintaining image quality, improve image resolution and signal-to-noise ratio, which is of great significance for clinical diagnosis and treatment planning; in wireless communications, compressed sensing technology can reduce the amount of data transmission, efficiently complete spectrum sensing and channel estimation, and effectively extend the life cycle of wireless networks.

[0003] In the framework of compressed sensing, signal reconstruction algorithms play a vital role. Since the signal needs to be recovered from the measurement value after sampling, an effective algorithm is needed to implement this process. The key to the reconstruction algorithm is to be able to accurately recover the original signal from the linear measurement of the sparse signal. Most of the existing state-of-the-art (SOTA) CS reconstruction algorithms use deep neural networks to learn the complex mapping relationship between the downsampled measurement value and its corresponding original image. These neural networks are trained on ideal CS measurements and ignore the impact of quantization on reconstruction. The quantization process inherently introduces quantization errors, and the erasure of quantization bits can cause large errors in the inverse quantization measurement value. When encountering missing quantization bits, these CS algorithms will reconstruct distorted images. Therefore, in the scenario of quantization bit erasure, how to efficiently and accurately reconstruct the original image signal is a problem that needs to be considered. Summary of the invention

[0004] In order to overcome the shortcomings of the prior art, the present invention provides a robust compressed sensing method based on quantization bit erasure, which can still effectively reconstruct the original image in the scenario of quantization bit loss.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0006] A robust compressed sensing method based on quantized bit erasure comprises the following steps:

[0007] 1) The data sender expands the pixel value matrix of the image data to obtain the gray value vector as the original image signal x, and uses the Bernoulli random matrix Φ to compress and sample the image signal x to obtain the measurement value y;

[0008] 2) quantize the measured value y using the quantizer trained by the Lloyd-Max quantization algorithm;

[0009] 3) The data sender transmits the quantized measurement value y and the Bernoulli random matrix Φ to the data receiver, and uses Reed-Solomon code for channel protection during the transmission process;

[0010] 4) The data receiver identifies the missing bits from the quantized measurement value y and creates a constraint set W containing all possible values;

[0011] 5) Image reconstruction step: The data receiver uses the Bernoulli random matrix Φ and the measurement set W to obtain the estimated value of the image signal x and then reconstruct the image.

[0012] Furthermore, in 4), the position of the lost bits is located, and the erased bits are replaced with 1 or 0 values ​​to construct a constraint set for measurement.

[0013] Furthermore, in 4), the measurement value y is an 8-bit quantized bit stream, and part of the data is lost during transmission. The lost bits are located using Reed-Solomon code, and NaN values ​​are filled with 0 or 1; for the i-th value of the quantized measurement vector, if L is erased i bits, fill the constructed set with 0 or 1, and form the final set W through Cartesian product:

[0014] W=W (1) ×W (2) ×…×W (m) (1.1)

[0015] Among them, W (i) represents the set of all possible values ​​of the i-th dimension of y, so it contains 2 L possible measurements, where Its number grows exponentially as the number of erased bits increases.

[0016] Furthermore, in 5), the process by which the data receiver obtains the estimated value of the signal x from the measured y and the Bernoulli random matrix Φ is:

[0017] 5.1) Initialization: Set the error threshold and maximum number of iterations, set the current number of iterations k = 0, set the initial value v 0=0,x 0 =0,λ 0 =0,y 0 = 0. Get the constraint set W for measuring y;

[0018] 5.2) Update the reconstruction signal:

[0019]

[0020] Among them, v k and λ k denotes the parameters in the kth iteration, Φ and Φ T represents the Bernoulli random matrix and its transpose, represents the denoiser, x k represents the estimate of x in the kth iteration, η and η T Indicates that it follows a Gaussian distribution A vector of

[0021] 5.3) Update parameters:

[0022]

[0023] Among them, λ 1 and λ 2 is the weight parameter, with values ​​of 10 and 0.1, respectively, w k+1 represents the element obtained from the constraint set W in the k+1th iteration;

[0024] 5.4) Iterative update: Update k and repeat steps 5.2)-5.3) until the error limit is met or the maximum number of iterations is reached, and output x K+1 as an estimate of the signal x.

[0025] The beneficial effect of the present invention is that it can effectively reconstruct image signals in a scenario where quantization bits are erased, thereby avoiding image distortion. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is a framework diagram of the invention for reconstructing the original image signal x from the received measurement y. After the original image is quantized by compressed sampling, quantization bits will be lost during the transmission process. We construct a constraint set W and reconstruct the original image through an iterative algorithm.

[0027] Figure 2 It is a framework diagram of the present invention for compressing and sampling the original image signal x and quantizing it.

[0028] Figure 3 This is a framework diagram of the present invention for constructing a constraint set W. Since some bits of the measurement y are lost after transmission, that is, NaN values ​​appear, it is necessary to randomly fill in 0 or 1 values ​​to generate a constraint set W containing all possibilities of the measurement. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical solution and advantages of the present invention more clear, the specific implementation method of the present invention is further derived and described below in combination with specific implementation and drawings:

[0030] Reference Figure 1 to Figure 3 , a robust compressed sensing method based on quantized bit erasure, comprising the following steps:

[0031] 1) The data sender expands the pixel value matrix of the image data to obtain the gray value vector as the original image signal x, and uses the Bernoulli random matrix Φ to compress and sample the image signal x to obtain the measurement value y;

[0032] 2) quantize the measured value y using the quantizer trained by the Lloyd-Max quantization algorithm;

[0033] 3) The data sender transmits the quantized measurement value y and the Bernoulli random matrix Φ to the data receiver, and uses Reed-Solomon code for channel protection during the transmission process;

[0034] 4) The data receiver identifies the missing bits from the quantized measurement y, creates a constraint set W containing all possible values, and performs inverse quantization.

[0035] In the transmission process of this embodiment, the compressed sensing (CS) measurement value is easily affected by the bit erasure problem, especially under poor channel conditions, which will bring uncertainty to the measurement value. Figure 2 As shown in FIG. 1 , the quantized CS value is directly transmitted without channel coding, and bits in the quantized measurement bit stream are randomly discarded. The discarded bits appear as NaN (not a number) values ​​at the receiving end. The presence of NaN values ​​in the measurement bit stream leads to multiple decoding possibilities.

[0036] The present invention defines a set to include all potential 8-bit measurement values, taking into account the bit erasure in each measurement coordinate. Assume that the i-th value of the m-th dimension measurement vector after quantization erases L i bits, the present invention constructs a set by replacing the erased bits with 1 or 0 values. These sets are then combined by a Cartesian product operation to form a set:

[0037] W=W (1) ×W (2) ×…×W (m) .(1.1)

[0038] Therefore, including 2 L possible measurements, where As the number of erased bits increases, its number grows exponentially. To illustrate this construction process, Figure 2 An example of constructing a restricted set W is given.

[0039] 5) Image reconstruction step: The data receiver uses the Bernoulli random matrix Φ and the measurement set W to obtain the estimated value of the image signal x, and then reconstructs the image; the process by which the data receiver obtains the estimated value of the signal x from the measurement y and the Bernoulli random matrix Φ is:

[0040] 5.1) Initialization: Set the error threshold and maximum number of iterations, set the current number of iterations k = 0, and set the initial value v 0 =0,x 0 =0,λ 0 =0,y 0 = 0, obtain the constraint set W of measurement y;

[0041] 5.2) Update the reconstruction signal:

[0042]

[0043] Among them, v k and λ k denotes the parameters in the kth iteration, Φ and Φ T represents the Bernoulli random matrix and its transpose, represents the denoiser, x k represents the estimate of x in the kth iteration, η and η T Indicates that it follows a Gaussian distribution The vector of;

[0044] 5.3) Update parameters:

[0045]

[0046] Among them, λ 1 and λ 2 is the weight parameter, with values ​​of 10 and 0.1, respectively, w k+1 represents the element obtained from the constraint set W in the k+1th iteration;

[0047] 5.4) Iterative update: Update k and repeat steps 5.2)-5.3) until the error limit is met or the maximum number of iterations is reached, and output x K+1 as an estimate of the signal x.

[0048] In this embodiment, considering that the true measurement value belongs to the constraint set W, the compressed sensing problem can be restated as follows:

[0049]

[0050] Then, the Lagrange multiplier method is used to transform formula (1.7) into an unconstrained optimization problem:

[0051]

[0052] where functions R and D quantify the distance between variables x and y with respect to sets C and W, respectively. Specifically, R is used as an image noise level estimator, and D aims to find the closest element from W to y, expressed as:

[0053]

[0054] It corresponds to the hard-min distance. However, compared with the hard-min distance, the soft-min distance that takes into account the distances to multiple neighboring points tends to be more stable and less sensitive to noise. Therefore, the present invention considers the soft-min distance between y and the set W, defined as:

[0055]

[0056] Introducing formula (1.10) into formula (1.8), the entire compressed sensing objective function can be concisely expressed as:

[0057]

[0058] Here, λ 1 , 2 and λ 3 represents the Lagrange multipliers that balance the various terms. The optimization problem outlined above requires the determination of three optimization parameters: x, y, and w.

[0059] Then, the present invention uses the ADMM method to iteratively update the three parameters. Formula (1.11) is decomposed into three independent sub-optimization problems, namely:

[0060]

[0061] Therefore, the reconstruction process of the present invention includes an image update step and a measurement update step. The image update step corresponds to the first super-optimization problem (1.12), while the measurement update step corresponds to the last two sub-optimization problems (1.13) and (1.14)).

[0062] Image update step: The first sub-optimization is for image estimation, which is very similar to the formulation of the traditional CS problem. In this regard, the present invention utilizes the established approximate message passing algorithm to update x. This update process consists of two main sub-steps: first, a momentum gradient step is taken to the affine subspace of {x|y=Φx}, and second, an image denoiser is applied to map the result to the set of natural images. The calculation of the momentum gradient term is expressed as follows:

[0063]

[0064] The subsequent steps require an image denoiser to map the intermediate results to a set of natural images:

[0065]

[0066] In equation (1.15), λ k-1 v k-1 is the Onsager correction term, ensuring that x k +v k The effective noise follows the AWGN model, λ k The value of is In x k +v k Divergence of a point:

[0067]

[0068] The present invention uses a fast Monte Carlo approximation method to estimate λ k :

[0069]

[0070] here, represents a Gaussian distributed random vector that matches the size of the reconstructed image. In the experimental part, various image denoisers are tested in the CS scheme of the present invention. The results show that the quality of the reconstructed image can be significantly improved by using an effective image denoiser.

[0071] Measurement update step: The estimation of the metric requires the sequential update of y and w. The objective of formula (1.13) has a strictly quadratic function and a linear closed solution:

[0072]

[0073] This equation provides a direct way to update the variable y. In order to minimize the objective function in formula (1.14), the present invention attempts to find a point where the gradient is zero. Given the close proximity of w to y, the present invention has the following approximation:

[0074]

[0075] Substituting this approximation into (1.14), the gradient of formula (1.14) is calculated as follows:

[0076]

[0077] Then, let The present invention has the following updates:

[0078]

[0079] These updates of x, y, and w are iteratively applied to reconstruct the image from the quantized measurements with bit erasures.

[0080] The simulation experiment of this embodiment verifies the performance of the algorithm by reconstructing the image. The data set uses Set11 and BSD68. This data set is widely used in the field of image processing. The data set image is a grayscale picture.

[0081] The sampling ratio (SR) is calculated as the ratio of the measurement size to the overall image size, ie, SR = m / n. All measurements are uniformly quantized to 8-bit values.

[0082] In the simulation of the present invention, the present invention transmits the quantized measurement data through the binary erase channel (BEC). The transmission bit is P BEC The simulation results are obtained by BEC The erasure ratio is calculated by averaging the results of 10 tests of the value. The erasure ratio is calculated as the number of erased bits N e The total number of transmitted bits N t The ratio of ER = N e / N t .

[0083] The present invention compares and analyzes four state-of-the-art CS algorithms, namely AMPNet, ISTANet+, OPINENet and CSformer. And the present invention uses Reed-Solomon coding to protect the measurement of the comparison method. The results of calculating the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) of the reconstructed image are shown in Table 1. It can be seen that with the increase of ER, the algorithm of the present invention still maintains a good reconstruction effect.

[0084] Table 1 shows the results of calculating the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) for the reconstructed image;

[0085]

[0086] Table 1

[0087] By observing the image reconstruction results with SR of 25% and ER of 12%, the present invention effectively avoids the problem of reconstructed image distortion caused by quantization bit erasure.

[0088] Finally, it should be noted that the above-described embodiments are only specific implementations of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The protection scope of the present invention is not limited thereto. Although the present invention is described in detail with reference to the above-described embodiments, ordinary technicians in the field should understand that any technician familiar with the technical field can still modify the technical solutions recorded in the above-described embodiments within the technical scope disclosed by the present invention, or can easily think of changes, or make equivalent replacements for some of the technical features therein; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A robust compressed sensing method based on quantization bit erasure, characterized in that: The method comprises the following steps: 1) The sender expands the image into a grayscale vector x and samples it using the Bernoulli random matrix Φ to obtain y; 2) Quantize the sample value y using the quantizer trained by the Lloyd-Max algorithm; 3) The sender transmits the quantized y and Φ to the receiver and protects the channel with Reed-Solomon code; 4) The receiver determines the missing bit position in the measured value y, generates a constraint set W containing all possible values, and performs dequantization; 5) Use Φ and W to estimate x and reconstruct the image.

2. The robust compressed sensing method based on quantization bit erasure according to claim 1, characterized in that: In 4), the positions of the missing bits are located, and the erased bits are replaced with 1 or 0 values ​​to construct a constraint set for measurement.

3. The robust compressed sensing method based on quantization bit erasure according to claim 2, characterized in that: In 4), the measurement value y is an 8-bit quantized bit stream. Some data is lost during transmission. The lost bits are located using Reed-Solomon code, and NaN values ​​are filled with 0 or 1. For the i-th value of the quantized measurement vector, if L is erased, i bits, fill the constructed set with 0 or 1, and form the final set W through Cartesian product: W=W (1) ×W (2) ×…×W (m) (1.1) Among them, W (i) represents the set of all possible values ​​of the i-th dimension of y, so it contains 2 L possible measurements, where Its number grows exponentially as the number of erased bits increases.

4. A robust compressed sensing method based on quantization bit erasure according to any one of claims 1 to 3, characterized in that: In 5), the process by which the data receiver obtains the estimated value of the signal x from the measured y and the Bernoulli random matrix Φ is: 5.1) Initialization: Set the error threshold and maximum number of iterations, set the current number of iterations k = 0, and set the initial value v 0 =0,x 0 =0,λ 0 =0,y 0 = 0, obtain the constraint set W of measurement y; 5.2) Update the reconstruction signal: Among them, v k and λ k denotes the parameters in the kth iteration, Φ and Φ T represents the Bernoulli random matrix and its transpose, represents the denoiser, x k represents the estimate of x in the kth iteration, η and η T Indicates that it follows a Gaussian distribution A vector of 5.3) Update parameters: Among them, λ1 and λ2 are weight parameters, with values ​​of 10 and 0.1 respectively, and w k+1 represents the element obtained from the constraint set W in the k+1th iteration; 5.4) Iterative update: Update k and repeat steps 5.2)-5.3) until the error limit is met or the maximum number of iterations is reached, and output x K+1 as an estimate of the signal x.

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