Journal ArticleDOI
Bayesian Compressive Sensing Using Laplace Priors
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TLDR
This paper model the components of the compressive sensing (CS) problem, i.e., the signal acquisition process, the unknown signal coefficients and the model parameters for the signal and noise using the Bayesian framework and develops a constructive (greedy) algorithm designed for fast reconstruction useful in practical settings.Abstract:
In this paper, we model the components of the compressive sensing (CS) problem, i.e., the signal acquisition process, the unknown signal coefficients and the model parameters for the signal and noise using the Bayesian framework. We utilize a hierarchical form of the Laplace prior to model the sparsity of the unknown signal. We describe the relationship among a number of sparsity priors proposed in the literature, and show the advantages of the proposed model including its high degree of sparsity. Moreover, we show that some of the existing models are special cases of the proposed model. Using our model, we develop a constructive (greedy) algorithm designed for fast reconstruction useful in practical settings. Unlike most existing CS reconstruction methods, the proposed algorithm is fully automated, i.e., the unknown signal coefficients and all necessary parameters are estimated solely from the observation, and, therefore, no user-intervention is needed. Additionally, the proposed algorithm provides estimates of the uncertainty of the reconstructions. We provide experimental results with synthetic 1-D signals and images, and compare with the state-of-the-art CS reconstruction algorithms demonstrating the superior performance of the proposed approach.read more
Citations
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Journal ArticleDOI
Off-Grid Direction of Arrival Estimation Using Sparse Bayesian Inference
Zai Yang,Lihua Xie,Cishen Zhang +2 more
TL;DR: An iterative algorithm is developed based on the off-grid model from a Bayesian perspective while joint sparsity among different snapshots is exploited by assuming a Laplace prior for signals at all snapshots.
Journal ArticleDOI
Compressive Sensing in Electromagnetics - A Review
TL;DR: A review of the state-of-the-art and most recent advances of compressive sensing and related methods as applied to electromagnetics can be found in this article, where a wide set of applicative scenarios comprising the diagnosis and synthesis of antenna arrays, the estimation of directions of arrival, and the solution of inverse scattering and radar imaging problems are reviewed.
Journal ArticleDOI
Chaotic Time Series Prediction Based on a Novel Robust Echo State Network
TL;DR: A robust recurrent neural network is presented in a Bayesian framework based on echo state mechanisms that is robust in the presence of outliers and is superior to existing methods.
Journal ArticleDOI
Sparse Bayesian Classification of EEG for Brain–Computer Interface
TL;DR: A sparse Bayesian method is introduced by exploiting Laplace priors, namely, SBLaplace, for EEG classification by learning a sparse discriminant vector with a Laplace prior in a hierarchical fashion under a Bayesian evidence framework.
Journal ArticleDOI
Bayesian compressive sensing for cluster structured sparse signals
TL;DR: The experimental results show that the proposed algorithm outperforms many state-of-the-art algorithms, and solves the inverse problem automatically-prior information on the number of clusters and the size of each cluster is unknown.
References
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