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approximate message passing algorithm for Nonconvex Regularization

IEEE ACCESS 2019年 7卷 9080-9090页

作者： Zhang, Hui Zhang, Hai Liang, Yong Yang, Zi-Yi Ren, Yanqiong Macau Univ Sci & Technol Fac Informat Technol Macau 519020 Peoples R China Macau Univ Sci & Technol State Key Lab Qual Res Chinese Med Macau 519020 Peoples R China Northwest Univ Sch Math Xian 710127 Shaanxi Peoples R China

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 approximate message passing (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.

关键词： approximate message passing algorithm iterative thresholding algorithm nonconvex regularization sparsity variable selection

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MB-DAMPNet: a novel multi-branch denoising-based approximate message passing algorithm via deep neural network for image reconstruction

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INVERSE PROBLEMS 2021年第10期37卷 105016-105016页

作者： Yue, Huihui Guo, Jichang Yin, Xiangjun Guo, Chunle Jia, Weiguang Tianjin Univ Sch Elect & Informat Engn Tianjin Peoples R China Nankai Univ Coll Comp Sci Tianjin Peoples R China Natl Ctr Oceanog Stand & Metrol Tianjin 300112 Peoples R China

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.

关键词： image reconstruction compressive sensing deep neural network approximate message passing algorithm

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Automatic bias correction for testing in high-dimensional linear models

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STATISTICA NEERLANDICA 2023年第1期77卷 71-98页

作者： Zhou, Jing Claeskens, Gerda Katholieke Univ Leuven ORStat Naamsestr 69 B-3000 Leuven Belgium Katholieke Univ Leuven Leuven Stat Res Ctr Naamsestr 69 B-3000 Leuven Belgium

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.

关键词： l(1)-regularization approximate message passing algorithm confidence interval high-dimensional linear model hypothesis testing loss function

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Learning Image Formation and Regularization in Unrolling AMP for Lensless Image Reconstruction

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IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING 2022年 8卷 479-489页

作者： Yang, Jingyu Yin, Xiangjun Zhang, Mengxi Yue, Huihui Cui, Xingyu Yue, Huanjing Tianjin Univ Sch Elect & Informat Engn Tianjin 300072 Peoples R China

This paper proposes an unrolling learnable approximate message passing 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.

关键词： Lensless imaging approximate message passing algorithm deep unfolding method spatial-channel attention

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On Weighting/Reweighting Schemes for approximate message passing algorithms

On Weighting/Reweighting Schemes for Approximate Message Pas...

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IEEE International Conference on Communications (ICC)

作者： Zeinalkhani, Zeinab Haghighatpanah, Neda Banihashemi, Amir H. Carleton Univ Dept Syst & Comp Engn Ottawa ON Canada

ISBN: (纸本)9781479966646

In this paper, we propose a number of weighting/reweighting schemes to improve the performance of the so-called approximate message passing (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.

关键词： Block sparsity compressed sensing approximate message passing algorithm

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Near Optimal Compressed Sensing Without Priors: Parametric SURE approximate message passing

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2015年第8期63卷 2130-2141页

作者： Guo, Chunli Davies, Mike E. Univ Edinburgh Inst Digital Commun Edinburgh EH9 3JL Midlothian Scotland Univ Edinburgh Joint Res Inst Signal & Image Proc Edinburgh EH9 3JL Midlothian Scotland

Both theoretical analysis and empirical evidence confirm that the approximate message passing (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.

关键词： approximate message passing algorithm compressed sensing parametric estimator signal denoising Stein's unbiased risk estimate

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Performance Improvement of Compressed Sensing Reconstruction Using Modified-AMP algorithm

Performance Improvement of Compressed Sensing Reconstruction...

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International Conference on Artificial Intelligence and Evolutionary Computations in Engineering Systems (ICAIECES)

作者： Mathai, Nissy Sara Gandhiraj, R. Amrita Vishwa Vidyapeetham Dept Elect & Commun Coimbatore Tamil Nadu India

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.

关键词： approximate message passing algorithm Compressed sensing

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RFID Tag Acquisition via Compressed Sensing: Flexibility by Random Signature Assignment 5

RFID Tag Acquisition via Compressed Sensing: Flexibility by ...

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International EURASIP Workshop on RFID Technology (EURFID)

作者： Mayer, Martin Goertz, Norbert Vienna Univ Technol Inst Telecommun Gusshausstr 25-389 A-1040 Vienna Austria Christian Doppler Lab Wireless Technol Sustainabl Vienna Austria

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.

关键词： compressed sensing message passing radiofrequency identification signal detection telecommunication congestion control RFID tag acquisition approximate message passing algorithm random signature assignment signature pool Amplitude shift keying Compressed sensing Conferences message passing Radiofrequency identification Signal to noise ratio

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Generating Functional Analysis of Iterative algorithms for Compressed Sensing

Generating Functional Analysis of Iterative Algorithms for C...

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IEEE International Symposium on Information Theory (ISIT)

作者： Mimura, Kazushi Hiroshima City Univ Dept Informat Sci Hiroshima 7313194 Japan

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.

关键词： algorithm design and analysis Approximation algorithms Compressed sensing Correlation GFA Heuristic algorithms Iterative methods Random variables SE approximate message passing algorithm compressed sensing correlation theory functional analysis generating functional analysis iterative algorithm iterative methods one-dimensional map signal reconstruction state evolution

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