Sparse Signal Reconstruction With Statistical Prior Information: A Data-Driven Method

Zhi Liao,Jun Zhang,Yuanqing Li,Cheng Li,Dandan Hu,Lin Zhu

doi:10.1109/access.2019.2950003

Abstract

Weighted $\ell _{1}$ minimization (WL1M) is a general and powerful framework for reconstructing sparse signals from underdetermined measurements. The performance improvement of WL1M owes to the incorporation of additional structural priors of signals by means of its weights. However, the selection of weights relies on hand-crafted designs in existing works, so that high-order structural priors of signals are hard to be captured. This paper proposes a data-driven method, namely RBM-WL1M, to alleviate this situation. In the RBM-WL1M, restricted Boltzmann machines (RBMs) are employed to learn the prior distribution of the signals from training data; furthermore, utilizing the RBM, high frequency support set and non-zero probabilities for each of the entries in signals can be estimated effectively, which are used to appropriately select the weights. In our experiments, the proposed framework demonstrates superior performance over several state-of-the-art CS methods on the Physikalisch-Technische Bundesanstalt(PTB) Diagnostic ECG Data set.

Highlights

Reconstructing a signal from significantly fewer linear measurements than their ambient dimension is an important step for a wide range of signal processing applications [1]–[5]
The expectations can be approximated by samples drawn from the corresponding distributions based on Markov chain Monte Carlo (MCMC) techniques [22], such as Contrastive Divergence (CD) [23] and Gibbs Sampling [24]
Zigel et al [28] has classified the different values of percentage root-mean-square difference (PRD) based on the signal quality perceived by specialists

Summary

INTRODUCTION

Reconstructing a signal from significantly fewer linear measurements than their ambient dimension is an important step for a wide range of signal processing applications [1]–[5]. Z. Liao et al.: Sparse Signal Reconstruction With Statistical Prior Information: Data-Driven Method the following weighted 1 minimization (WL1M) problem h. Some other deep learning based methods, such as autoencoder (AE) [17], [18], have been used for reconstructing sparse signals from underdetermined measurements These methods treat the problem as a black-box so that large volumes of data are often required for the training of the models. Owing to the representational power of RBMs, the RBM-WL1M can obtain a significant performance gain, compared with the other weighting strategies It is different with Polanía’s works [15], [16] that we used the RBM to determine the crucial parameters W of the WL1M, rather than identify the support of x∗ on line for a given y via an MAP estimator.

RESTRICTED BOLTZMANN MACHINE

ESTIMATE OF HIGH FREQUENCY SUPPORT SET

DETERMINING W IN THE WL1M

EXPERIMENTAL RESULTS

EXPERIMENTAL SETUP

CONCLUSION