In this paper, we study the sparse signal reconstruction with nonconvex regularization, mainly focusing on two popular nonconvex regularization methods, minimax concave penalty (MCP) and smoothly clipped absolute devi...
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In this paper, we study the sparse signal reconstruction with nonconvex regularization, mainly focusing on two popular nonconvex regularization methods, minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD). An approximatemessagepassing (AMP) algorithm is an effective method for signal reconstruction. Based on the AMP algorithm, we propose an improved MCP iterative thresholding algorithm and an improved SCAD iterative thresholding algorithm. Furthermore, we analyze the convergence of the new algorithms and provide a series of experiments to assess the performance of the new algorithms. The experiments show that the new algorithms based on AMP have stronger reconstruction capabilities, higher phase transition for sparse signal reconstruction, and better variable selection ability than the original MCP iterative thresholding algorithm and the original SCAD iterative thresholding algorithm.
Compressive sensing has gained great attention due to its effectiveness in solving linear inverse problems. However, how to further improve the accuracy of compressed image inversion while ensuring or even acceleratin...
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Compressive sensing has gained great attention due to its effectiveness in solving linear inverse problems. However, how to further improve the accuracy of compressed image inversion while ensuring or even accelerating the speed is still a major challenge. To tackle this problem, we present a novel multi-branch denoising-based approximate message passing algorithm via deep neural network, dubbed MB-DAMPNet. It mainly consists of three components, i.e. sampling subnet, initial recovery subnet, and deep recovery subnet, which are optimized jointly. The sampling subnet is constructed to obtain the compressed measurements, the initial recovery subnet is employed to generate the reconstructed image by inverse transformation, while the deep recovery subnet is designed to refine the reconstructed results obtained by the former, so as to improve the image accuracy. Moreover, the matrix multiplication in the network is all designed as matrix convolution which can be learned automatically, so that the input image of the MB-DAMPNet can be of different scales, which improves the flexibility and applicability of the network. In addition, all parameters in the network are learned end-to-end instead of fixed or hand-crafted. The numerical results validate that our method significantly outperforms other state-of-the-art methods in image reconstruction accuracy.
Hypothesis testing is challenging due to the test statistic's complicated asymptotic distribution when it is based on a regularized estimator in high dimensions. We propose a robust testing framework for l-regular...
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Hypothesis testing is challenging due to the test statistic's complicated asymptotic distribution when it is based on a regularized estimator in high dimensions. We propose a robust testing framework for l-regularized M-estimators to cope with non-Gaussian distributed regression errors, using the robust approximate message passing algorithm. The proposed framework enjoys an automatically built-in bias correction and is applicable with general convex nondifferentiable loss functions which also allows inference when the focus is a conditional quantile instead of the mean of the response. The estimator compares numerically well with the debiased and desparsified approaches while using the least squares loss function. The use of the Huber loss function demonstrates that the proposed construction provides stable confidence intervals under different regression error distributions.
This paper proposes an unrolling learnable approximatemessagepassing recurrent neural network (called ULAMP-Net) for lensless image reconstruction. By unrolling the optimization iterations, key modules and parameter...
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This paper proposes an unrolling learnable approximatemessagepassing recurrent neural network (called ULAMP-Net) for lensless image reconstruction. By unrolling the optimization iterations, key modules and parameters are made learnable to achieve high reconstruction quality. Specifically, observation matrices are rectified on the fly through network learning to suppress systematic errors in the measurement of the point spread function. We devise a domain transformation structure to achieve a more powerful representation and propose a learnable multistage threshold function to accommodate a much richer family of priors with only a small amount of parameters. Finally, we introduce a multi-layer perceptron (MLP) module to enhance the input and an attention mechanism as an output module to refine the final results. Experimental results on display captured dataset and real scene data demonstrate that, compared with the state-of-the-art methods, our method achieves the best reconstruction quality with low computational complexity and the tiny model size on the testing set. Our code will be released in https://***/Xiangjun-TJU/ULAMP-NET.
In this paper, we propose a number of weighting/reweighting schemes to improve the performance of the so-called approximatemessagepassing (AMP) algorithm of Donoho et al.. We consider the application of AMP for the ...
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ISBN:
(纸本)9781479966646
In this paper, we propose a number of weighting/reweighting schemes to improve the performance of the so-called approximatemessagepassing (AMP) algorithm of Donoho et al.. We consider the application of AMP for the recovery of sparse signals from an under-determined system of linear equations, and variants of AMP for the recovery of block sparse signals. The proposed schemes for block sparse signals cover both cases of known and unknown block borders. Simulation results, both in noiseless and noisy scenarios, show significant performance improvement over the standard AMP algorithm and a considerably better performance/complexity trade-off compared to other state-of-the-art recovery algorithms.
Both theoretical analysis and empirical evidence confirm that the approximatemessagepassing (AMP) algorithm can be interpreted as recursively solving a signal denoising problem: at each AMP iteration, one observes a...
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Both theoretical analysis and empirical evidence confirm that the approximatemessagepassing (AMP) algorithm can be interpreted as recursively solving a signal denoising problem: at each AMP iteration, one observes a Gaussian noise perturbed original signal. Retrieving the signal amounts to a successive noise cancellation until the noise variance decreases to a satisfactory level. In this paper, we incorporate the Stein's unbiased risk estimate (SURE) based parametric denoiser with the AMP framework and propose the novel parametric SURE-AMP algorithm. At each parametric SURE-AMP iteration, the denoiser is adaptively optimized within the parametric class by minimizing SURE, which depends purely on the noisy observation. In this manner, the parametric SURE-AMP is guaranteed with the best-in-class recovery and convergence rate. If the parametric family includes the families of the mimimum mean squared error (MMSE) estimators, we are able to achieve the Bayesian optimal AMP performance without knowing the signal prior. In the paper, we resort to the linear parameterization of the SURE based denoiser and propose three different kernel families as the base functions. Numerical simulations with the Bernoulli-Gaussian, k-dense and Student's-t signals demonstrate that the parametric SURE-AMP does not only achieve the state-of-the-art recovery but also runs more than 20 times faster than the EM-GM-GAMP algorithm. Natural image simulations confirm the advantages of the parametric SURE-AMP for signals without prior information.
Compressed sensing (CS) is an emerging field which enables the undersampling of sparse signals rather than at the Nyquist rate. But the main computational challenge involved is in the reconstruction process as it is n...
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ISBN:
(纸本)9788132226567;9788132226543
Compressed sensing (CS) is an emerging field which enables the undersampling of sparse signals rather than at the Nyquist rate. But the main computational challenge involved is in the reconstruction process as it is nonlinear in nature and the solution is obtained by solving a set of under determined linear equations. Greedy algorithms offer the solution to these kinds of problems with less computational complexity than the convex relaxations or linear programming methods. The approximate message passing algorithm offers accurate reconstruction of even the approximately sparse signals with reasonable computational intensity. In this paper, we have implemented a modified version of AMP algorithm and obtained a 50 % reduction in mean squared error and an improvement in signal-to-noise ratio.
Classical Radio Frequency IDentification (RFID) schemes such as Frame Slotted ALOHA (FSA) try to avoid colliding tag responses in the acquisition phase. We propose a scheme that exploits collisions in the acquisition ...
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ISBN:
(纸本)9783200037359
Classical Radio Frequency IDentification (RFID) schemes such as Frame Slotted ALOHA (FSA) try to avoid colliding tag responses in the acquisition phase. We propose a scheme that exploits collisions in the acquisition phase, which is enabled by compressed sensing techniques. As an extension to previous work, it allows a more flexible usage of the compressed sensing-based approach for RFID. All activated tags randomly select a signature from a huge signature pool and simultaneously transmit it as a response to a query from the reader. The number of superposed signatures at the reader is significantly smaller than the total signature count, which introduces sparsity to the problem. Utilizing compressed sensing recovery, we determine the set of activated tags, which can then be read out and identified. Our formulation allows to use a computationally efficient approximate message passing algorithm for recovery. The tag identification proves to be quicker and more robust to noise compared to FSA, which we show by simulation.
It has been shown that approximate message passing algorithm is effective in reconstruction problems for compressed sensing. To evaluate dynamics of such an algorithm, the state evolution (SE) has been proposed. If an...
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ISBN:
(纸本)9781457705953
It has been shown that approximate message passing algorithm is effective in reconstruction problems for compressed sensing. To evaluate dynamics of such an algorithm, the state evolution (SE) has been proposed. If an algorithm can cancel the correlation between the present messages and their past values, SE can accurately tract its dynamics via a simple one-dimensional map. In this paper, we focus on dynamics of algorithms which cannot cancel the correlation and evaluate it by the generating functional analysis (GFA), which allows us to study the dynamics by an exact way in the large system limit.
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