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We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…

Spike and Slab priors have been of much recent interest in signal processing as a means of inducing sparsity in Bayesian inference. Applications domains that benefit from the use of these priors include sparse recovery, regression and…

Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of…

Recently, a number of mostly $\ell_1$-norm regularized least squares type deterministic algorithms have been proposed to address the problem of \emph{sparse} adaptive signal estimation and system identification. From a Bayesian perspective,…

This work proposes a decentralized, iterative, Bayesian algorithm called CB-DSBL for in-network estimation of multiple jointly sparse vectors by a network of nodes, using noisy and underdetermined linear measurements. The proposed algorithm…

The sparse Beyesian learning (also referred to as Bayesian compressed sensing) algorithm is one of the most popular approaches for sparse signal recovery, and has demonstrated superior performance in a series of experiments. Nevertheless,…

This paper introduces a novel approach for recovering sparse signals using sorted L1/L2 minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively…

Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…

Sparse signal recovery algorithms like sparse Bayesian learning work well but the complexity quickly grows when tackling higher dimensional parametric dictionaries. In this work we propose a novel Bayesian strategy to address the two…

Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…

Matrix completion and robust principal component analysis have been widely used for the recovery of data suffering from missing entries or outliers. In many real-world applications however, the data is also time-varying, and the naive…

This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…

The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…

Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…

Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as…

Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…

Spike and slab priors play a key role in inducing sparsity for sparse signal recovery. The use of such priors results in hard non-convex and mixed integer programming problems. Most of the existing algorithms to solve the optimization…

We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we…

A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…

Sparse Bayesian learning (SBL) can be implemented with low complexity based on the approximate message passing (AMP) algorithm. However, it is vulnerable to `difficult' measurement matrices as AMP can easily diverge. Damped AMP has been…