Hybrid approximate message passing for generalized group sparsity

2013 ◽  
Author(s):  
Alyson K. Fletcher ◽  
Sundeep Rangan
Keyword(s):  
Message Passing ◽  
Group Sparsity ◽  
Approximate Message Passing

scholarly journals An Entropy-Based Algorithm with Nonlocal Residual Learning for Image Compressive Sensing Recovery

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 900 ◽  
Author(s):  
Zhonghua Xie ◽  
Lingjun Liu ◽  
Cui Yang
Keyword(s):  
Compressive Sensing ◽  
Latent Variables ◽  
Message Passing ◽  
Signal Reconstruction ◽  
Measurement Data ◽  
Image Recovery ◽  
Group Sparsity ◽  
Approximate Message Passing ◽  
Em Method ◽  
Laplacian Distribution

Image recovery from compressive sensing (CS) measurement data, especially noisy data has always been challenging due to its implicit ill-posed nature, thus, to seek a domain where a signal can exhibit a high degree of sparsity and to design an effective algorithm have drawn increasingly more attention. Among various sparsity-based models, structured or group sparsity often leads to more powerful signal reconstruction techniques. In this paper, we propose a novel entropy-based algorithm for CS recovery to enhance image sparsity through learning the group sparsity of residual. To reduce the residual of similar packed patches, the group sparsity of residual is described by a Laplacian scale mixture (LSM) model, therefore, each singular value of the residual of similar packed patches is modeled as a Laplacian distribution with a variable scale parameter, to exploit the benefits of high-order dependency among sparse coefficients. Due to the latent variables, the maximum a posteriori (MAP) estimation of the sparse coefficients cannot be obtained, thus, we design a loss function for expectation–maximization (EM) method based on relative entropy. In the frame of EM iteration, the sparse coefficients can be estimated with the denoising-based approximate message passing (D-AMP) algorithm. Experimental results have shown that the proposed algorithm can significantly outperform existing CS techniques for image recovery.

scholarly journals Content-Aware Compressive Sensing Recovery Using Laplacian Scale Mixture Priors and Side Information

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Zhonghua Xie ◽  
Lihong Ma ◽  
Lingjun Liu
Keyword(s):  
Compressive Sensing ◽  
Message Passing ◽  
Side Information ◽  
Group Sparsity ◽  
Scale Mixture ◽  
Self Similarity ◽  
Recovery Algorithm ◽  
Approximate Message Passing ◽  
Local Patch ◽  
Laplacian Distribution

Nonlocal methods have shown great potential in many image restoration tasks including compressive sensing (CS) reconstruction through use of image self-similarity prior. However, they are still limited in recovering fine-scale details and sharp features, when rich repetitive patterns cannot be guaranteed; moreover the CS measurements are corrupted. In this paper, we propose a novel CS recovery algorithm that combines nonlocal sparsity with local and global prior, which soften and complement the self-similarity assumption for irregular structures. First, a Laplacian scale mixture (LSM) prior is utilized to model dependencies among similar patches. For achieving group sparsity, each singular value of similar packed patches is modeled as a Laplacian distribution with a variable scale parameter. Second, a global prior and a compensation-based sparsity prior of local patch are designed in order to maintain differences between packed patches. The former refers to a prediction which integrates the information at the independent processing stage and is used as side information, while the latter enforces a small (i.e., sparse) prediction error and is also modeled with the LSM model so as to obtain local sparsity. Afterward, we derive an efficient algorithm based on the expectation-maximization (EM) and approximate message passing (AMP) frame for the maximum a posteriori (MAP) estimation of the sparse coefficients. Numerical experiments show that the proposed method outperforms many CS recovery algorithms.

Speech enhancement based on approximate message passing

2020 ◽  
Vol 17 (8) ◽  
pp. 187-198
Author(s):  
Chao Li ◽  
Ting Jiang ◽  
Sheng Wu
Keyword(s):  
Speech Enhancement ◽  
Message Passing ◽  
Approximate Message Passing

scholarly journals Bilinear Adaptive Generalized Vector Approximate Message Passing

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 4807-4815 ◽  
Author(s):  
Xiangming Meng ◽  
Jiang Zhu
Keyword(s):  
Message Passing ◽  
Approximate Message Passing

One-Bit Quantized Massive MIMO Detection Based on Variational Approximate Message Passing

2018 ◽  
Vol 66 (9) ◽  
pp. 2358-2373 ◽  
Author(s):  
Zhaoyang Zhang ◽  
Xiao Cai ◽  
Chunguang Li ◽  
Caijun Zhong ◽  
Huaiyu Dai
Keyword(s):  
Message Passing ◽  
Massive Mimo ◽  
Mimo Detection ◽  
Approximate Message Passing
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