An improved sparse reconstruction algorithm for speech compressive sensing using structured priors

Jiang, Xiaobo; Ying, Rendong; Wen, Fei; Jiang, Sumxin; Liu, Peilin

doi:10.1109/icme.2016.7552972

Cited by 7 publications

(11 citation statements)

References 18 publications

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“…, the algorithm updated via (31) and ( 32) is a descent algorithm and the generated sequence {(X k 1 , X k 2 )} converges to a critical point of the problem (28).…”

Section: A Bcd Algorithm For Multitaskmentioning

confidence: 99%

Nonconvex Regularization-Based Sparse Recovery and Demixing With Application to Color Image Inpainting

et al. 2017

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This work addresses the recovery and demixing problem of signals that are sparse in some general dictionary. Involved applications include source separation, image inpainting, super-resolution, and restoration of signals corrupted by clipping, saturation, impulsive noise, or narrowband interference. We employ the q -norm (0 ≤ q < 1) for sparsity inducing and propose a constrained q -minimization formulation for the recovery and demixing problem. This nonconvex formulation is approximately solved by two efficient first-order algorithms based on proximal coordinate descent and alternative direction method of multipliers (ADMM), respectively. The new algorithms are convergent in the nonconvex case under some mild conditions and scale well for high-dimensional problems. A convergence condition of the new ADMM algorithm has been derived. Furthermore, extension of the two algorithms for multi-channels joint recovery has been presented, which can further exploit the joint sparsity pattern among multi-channel signals. Various numerical experiments showed that the new algorithms can achieve considerable performance gain over the 1-regularized algorithms.Index Terms-Alternative direction method of multipliers, proximal coordinate descent, q -norm minimization, sparse recovery, signal separation, inpainting.

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“…, the algorithm updated via (31) and ( 32) is a descent algorithm and the generated sequence {(X k 1 , X k 2 )} converges to a critical point of the problem (28).…”

Section: A Bcd Algorithm For Multitaskmentioning

confidence: 99%

Nonconvex Regularization-Based Sparse Recovery and Demixing With Application to Color Image Inpainting

et al. 2017

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“…We adopted this concept in this paper. Jiang et al [ 16 ] modeled the persistency of supports in each frame of speech signal as a Markov chain. They showed that the exploitation of the dependence between neighboring frequency components has improved the reconstruction quality.…”

Section: Related Workmentioning

confidence: 99%

Speech Compressive Sampling Using Approximate Message Passing and a Markov Chain Prior

Jia

Liu

Jiang

2020

Sensors

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By means of compressive sampling (CS), a sparse signal can be efficiently recovered from its far fewer samples than that required by the Nyquist–Shannon sampling theorem. However, recovering a speech signal from its CS samples is a challenging problem, as it is not sparse enough on any existing canonical basis. To solve this problem, we propose a method which combines the approximate message passing (AMP) and Markov chain that exploits the dependence between the modified discrete cosine transform (MDCT) coefficients of a speech signal. To reconstruct the speech signal from CS samples, a turbo framework, which alternately iterates AMP and belief propagation along the Markov chain, is utilized. In addtion, a constrain is set to the turbo iteration to prevent the new method from divergence. Extensive experiments show that, compared to other traditional CS methods, the new method achieves a higher signal-to-noise ratio, and a higher perceptual evaluation of speech quality (PESQ) score. At the same time, it maintaines a better similarity of the energy distribution to the original speech spectrogram. The new method also achieves a comparable speech enhancement effect to the state-of-the-art method.

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“…In the past decade, compressive sensing has attracted extensive studies [14]- [17] and has found wide applications in radar [18], [19], communications [20], medical imaging [21], image processing [22], and speech signal processing [23]. In the CS framework, sparse signals (or signals can be sparsely represented in some basis) can be acquired at a significantly lower rate than the classical Nyquist sampling, and signals only need to be sampled at a rate proportional to their information content.…”

Section: A Compressive Sensingmentioning

confidence: 99%

A Survey on Nonconvex Regularization-Based Sparse and Low-Rank Recovery in Signal Processing, Statistics, and Machine Learning

et al. 2018

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In the past decade, sparse and low-rank recovery have drawn much attention in many areas such as signal/image processing, statistics, bioinformatics and machine learning. To achieve sparsity and/or low-rankness inducing, the 1 norm and nuclear norm are of the most popular regularization penalties due to their convexity. While the 1 and nuclear norm are convenient as the related convex optimization problems are usually tractable, it has been shown in many applications that a nonconvex penalty can yield significantly better performance. In recent, nonconvex regularization based sparse and low-rank recovery is of considerable interest and it in fact is a main driver of the recent progress in nonconvex and nonsmooth optimization. This paper gives an overview of this topic in various fields in signal processing, statistics and machine learning, including compressive sensing (CS), sparse regression and variable selection, sparse signals separation, sparse principal component analysis (PCA), large covariance and inverse covariance matrices estimation, matrix completion, and robust PCA. We present recent developments of nonconvex regularization based sparse and low-rank recovery in these fields, addressing the issues of penalty selection, applications and the convergence of nonconvex algorithms. Code is available at https://github.com/FWen/ncreg.git.

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An improved sparse reconstruction algorithm for speech compressive sensing using structured priors

Cited by 7 publications

References 18 publications

Nonconvex Regularization-Based Sparse Recovery and Demixing With Application to Color Image Inpainting

Nonconvex Regularization-Based Sparse Recovery and Demixing With Application to Color Image Inpainting

Speech Compressive Sampling Using Approximate Message Passing and a Markov Chain Prior

A Survey on Nonconvex Regularization-Based Sparse and Low-Rank Recovery in Signal Processing, Statistics, and Machine Learning

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