A robust compressive sensing method based on quantization bit erasure

Abstract

A kind of robustness compressed sensing method based on quantization bit erasure, comprising the following steps: 1) sender expands image into gray vector, and obtains by Bernoulli random matrix sampling;2) quantization transmission: the quantization of sampled value y is carried out using quantizer trained by Lloyd-Max algorithm;3) quantized y and Φ are given to receiver, reed-solomon code is used in transmission to protect channel;4) generate constraint set W, and carry out dequantization;5) design iterative algorithm, estimate x using Φ and W, reconstruct original image signal by image estimation step and measurement estimation step.The present application can generate constraint set W of measurement y using the position of quantization bit erasure, then design iterative algorithm to realize image reconstruction, with higher theoretical and engineering application value.

Description

TECHNICAL FIELD

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

[0002] Compressed sensing (CS) is an efficient signal processing method that indicates that if a signal is sparse in a certain domain, i.e., the signal can be represented as a linear combination of a small number of non-zero elements, the signal can be accurately reconstructed at a sampling rate much lower than the Nyquist rate. The proposal of this theory provides a new perspective for the collection, storage and transmission of signals, and shows its unique advantages especially in 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, and has important significance for clinical diagnosis and treatment planning; in wireless communication, compressed sensing technology can reduce data transmission, efficiently complete spectrum sensing and channel estimation, and effectively prolong the life cycle of wireless networks.

[0003] Under the framework of compressed sensing, signal reconstruction algorithms play a crucial role. Since the signal needs to be recovered from the measurement value after sampling, an effective algorithm is needed to realize this process. The key of the reconstruction algorithm is 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 down-sampled measurement value and the corresponding original image. These neural networks are trained on ideal CS measurements, ignoring the influence of quantization on reconstruction. The quantization process inherently introduces quantization errors, and the erasure of quantization bits will cause a large amount of errors in the inverse quantization measurement value. When encountering missing quantization bits, these CS algorithms will reconstruct distorted images. Therefore, in the scene of quantization bit erasure, how to efficiently and accurately reconstruct the original image signal is a problem that needs to be considered. SUMMARY

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

[0005] To solve the above technical problems, the technical scheme adopted by the present application is:

[0006] A robust compressive sensing method based on quantized bit erasure, comprising the following steps:

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

[0008] 2) The measurement value y is quantized using a quantizer trained by a 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 transmission;

[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 an estimated value of the image signal x, and then reconstructs the image.

[0012] Further, in the 4), the positions of the missing bits are located, and the erased bits are replaced with 1 or 0 values to construct the constraint set of the measurement.

[0013] Further, in the 4), the measurement value y is an 8-bit quantized bit stream, and part of the data is lost during transmission. Reed-Solomon code is used to locate the missing bits, and NaN values are filled with 0 or 1. For the i-th value of the quantized measurement vector, if L i bits are erased, 0 or 1 is used to fill the set, and the final set W is formed by Cartesian product:

[0014] W = W (1) × W (2) × … × W (m) (1.1)

[0015] Where W (i) represents the set of all possible values of the i-th dimension of y, therefore, contains 2 L possible measurement values, where As the number of erased bits increases, the number increases exponentially.

[0016] Further, in the 5), the process of the data receiver obtaining the estimated value of the signal x from the measurement y and the Bernoulli random matrix Φ is:

[0017] 5.1) Initialization: set the error threshold and the maximum number of iterations, set the current iteration number 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;

[0018] 5.2) Update the reconstructed signal:

[0019]

[0020] where v k and λ k denote the parameters in the k-th iteration, Φ and Φ T denote the Bernoulli random matrix and its transpose, denote the denoiser, x k denote the estimation of x in the k-th iteration, η and η T denote the vectors subject to Gaussian distribution .

[0021] 5.3) Update the parameters:

[0022]

[0023] where λ1 and λ2 are weight parameters with values of 10 and 0.1 respectively, w k+1 denote the elements obtained from the constraint set W in the k+1-th iteration;

[0024] 5.4) Iterative update: update k, 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 the estimation of the signal x.

[0025] The present application has the beneficial effect that it can effectively reconstruct the image signal in the scene of quantization bit erasure, and avoid the image distortion. BRIEF DESCRIPTION OF DRAWINGS

[0026] Fig. 1 is the framework diagram of the present application for reconstructing the original image signal x from the received measurement y. After the original image is compressed and quantized, the phenomenon of loss of quantization bits will occur in the transmission process. We reconstruct the original image by constructing the constraint set W through the iterative algorithm.

[0027] Fig. 2 is the framework diagram of the present application for compressing and quantizing the original image signal x.

[0028] Fig. 3 is the framework diagram of the present application for constructing the constraint set W. Since the measurement y will have some bits lost after transmission, i.e. NaN values, it is necessary to randomly fill in 0 or 1 values to generate the constraint set W containing all the possibilities of the measurement. DETAILED DESCRIPTION

[0029] In order to make the purposes, technical solutions and advantages of the present application clearer, the specific implementation method of the present application is further deduced and described below in combination with specific embodiments and drawings:

[0030] Referring to Figs. 1-3 , a robust compressive sensing method based on quantized bit erasure includes the following steps:

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

[0032] 2) The measurement value y is quantized using a quantizer trained by a 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 transmission;

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

[0035] In the transmission process of the present embodiment, the compressive sensing (CS) measurement value is susceptible to the bit erasure problem, especially under poor channel conditions, which will bring uncertainty to the measurement value. In the scheme proposed in the present application, as shown in Fig. 2 , the quantized CS value is directly transmitted without channel coding, and the bits in the quantized measurement bit stream will be randomly discarded. The discarded bits will appear as NaN (non-numeric) values at the receiving end. The existence of NaN values in the measurement bit stream leads to multiple decoding possibilities.

[0036] The present application defines a set to contain all potential 8-bit measurement values, taking into account the bit erasure in each measurement coordinate. Assuming that the i-th value of the m-th dimensional measurement vector after quantization has L i erased bits, the present application constructs the set by replacing the erased bits with 1 or 0 values. Then these sets are combined by Cartesian product operation to form the set:

[0037] W=W (1) ×W (2) ×…×W (m) .(1.1)

[0038] Therefore, the set W contains 2 L possible measurement values, where The number of erased bits increases exponentially with the number of erased bits. To illustrate this construction process, Fig. 2 An example of constructing the 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 estimate of the image signal x, and then reconstructs the image; the process of the data receiver obtaining the estimate of the signal x from the measurement y and the Bernoulli random matrix Φ is as follows:

[0040] 5.1) Initialization: set the error threshold and the 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, and obtain the constraint set W of the measurement y;

[0041] 5.2) Update the reconstructed signal:

[0042]

[0043] where v k and λ k represent the parameters in the kth iteration, Φ and Φ T represent the Bernoulli random matrix and its transpose, denotes the denoiser, x k represents the estimate of x in the kth iteration, η and η T represent vectors subject to Gaussian distribution .

[0044] 5.3) Update the parameters:

[0045]

[0046] where λ1 and λ2 are weight parameters, and the values are 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, 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 the estimate of the signal x.

[0048] In this embodiment, since the true measurement value belongs to the constraint set W, the compressed sensing problem can be re-expressed as follows:

[0049]

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

[0051]

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

[0053]

[0054] It corresponds to a hard-min distance. However, compared to the hard-min distance, the soft-min distance, which 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 equation (1.10) into equation (1.8), the entire compressed sensing objective function can be succinctly represented as:

[0057]

[0058] Here, λ1, λ2, and λ3 represent 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] The present invention then uses the ADMM method to iteratively update the three parameters. Equation (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 used 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 includes two main sub-steps: first, a momentum gradient step is taken towards 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 represented as follows:

[0063]

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

[0065]

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

[0067]

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

[0069]

[0070] Here, denotes a Gaussian distributed random vector matching the size of the reconstructed image. In the experimental section, various image denoisers are tested in the CS scheme of the present invention. The results show that using an effective image denoiser can significantly improve the quality of the reconstructed image.

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

[0072]

[0073] This equation provides a direct method to update the variable y. To minimize the objective function in equation (1.14), the present invention tries to find a point with zero gradient. Given the tight approximation of w to y, the present invention has the following approximation:

[0074]

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

[0076]

[0077] Then, let The present invention has the update of w as follows:

[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 the embodiment verifies the performance of the algorithm by image reconstruction. The data set adopts Set11 and BSD68. The data set is widely used in the field of image processing. The data set image is a gray picture.

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

[0082] In the simulation of the application, the quantized measurement data is transmitted through a binary erasure channel (BEC). The transmission bits are randomly removed with a probability of P BEC . The simulation result is calculated by averaging the results of 10 experiments for a specific P BEC value. The erasure ratio is calculated as the ratio of the number of erased bits N e to the total number of transmission bits N t , that is, ER = N e / N t .

[0083] The application compares and analyzes four most advanced CS algorithms, namely AMPNet, ISTANet+, OPINENet and CSformer. The application uses Reed-Solomon encoding to protect the measurements of the comparison methods. 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 as the ER increases, the algorithm of the application still maintains good reconstruction effect.

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

[0085]

[0086] Table 1

[0087] By observing the image reconstruction result of SR = 25% and ER = 12%, the application effectively avoids the problem of reconstruction image distortion caused by quantization bit erasure.

[0088] Finally, it should be noted that the above-described embodiments are merely specific embodiments of the present application, which are used to illustrate the technical solutions of the present application, but not to limit the same. The protection scope of the present application is not limited thereto. Although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that any person skilled in the art can still modify or easily think of changes to the technical solutions recorded in the foregoing embodiments, or make equivalent replacements to some of the technical features, within the technical scope disclosed by the present application. The modifications, changes or replacements do not cause the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A robust compressed sensing method based on quantization bit erasure, characterized in that, Includes the following steps: 1) The data sender expands the pixel value matrix of the image data to obtain a grayscale value vector as the original image signal. Using Bernoulli random matrix For image signals Compressed sampling is performed to obtain the measurement value. ; 2) Use the quantizer trained by the Lloyd-Max quantization algorithm to measure the values. Quantify; 3) The data sender will send the quantified measurement values. and Bernoulli random matrix The data is transmitted to the receiver, and Reed-Solomon codes are used for channel protection during transmission. 4) The data receiver receives the quantized measurement values. Identify missing bits and create a constraint set containing all possible values. ; 5) Image reconstruction steps: The data receiver uses a Bernoulli random matrix... and constraint set To obtain the image signal The estimated value is then used to reconstruct the image; In step 4), the location of the missing bit is located, and the erased bit is replaced with a 1 or 0 value to construct a set of constraints for measurement; In the above 4), the measured value It is an 8-bit quantized bitstream. Some data is lost during transmission. Reed-Solomon codes are used to locate the missing bits, and NaN values ​​are filled with 0s or 1s. For the quantized measurement vector... A value, if erased If there are 1 bit, fill the set with 0 or 1, and form the final constraint set through Cartesian product. : (1.1)； in, express The The set of all possible values ​​for each dimension, containing 10 possible measurement values, of which As the number of erased bits increases, its quantity grows exponentially; In step 5), the data receiver receives the quantized measurement value. and Bernoulli random matrix Signal obtained The process of estimating the value is as follows: 5.1) Initialization: Set the error threshold and maximum number of iterations, set the current iteration number k=0, and set the initial value. Obtain the quantized measurement value constraint set ; 5.2) Update the reconstructed signal: (1.2)； (1.3)； (1.4)； in, and Indicates the first Parameters in the next iteration and Represent the Bernoulli random matrix and its transpose. Indicates a noise denoiser. Indicates the first In the next iteration, The estimate, and Indicates that it follows a Gaussian distribution ; 5.3) Update parameters: (1.5)； (1.6)； in, and These are weight parameters, with values ​​of 10 and 0.1 respectively. Indicates the first In the next iteration, from the constraint set The element retrieved; 5.4) Iterative Update: Update Repeat steps 5.2)-5.3) until the error limit is met or the maximum number of iterations is reached, then output the result. As a signal The estimated value.

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