Related papers: Prior Support Knowledge-Aided Sparse Bayesian Lear…

We consider a dictionary learning problem whose objective is to design a dictionary such that the signals admits a sparse or an approximate sparse representation over the learned dictionary. Such a problem finds a variety of applications…

Due to its self-regularizing nature and its ability to quantify uncertainty, the Bayesian approach has achieved excellent recovery performance across a wide range of sparse signal recovery applications. However, most existing methods are…

We consider the problem of recovering block-sparse signals whose structures are unknown \emph{a priori}. Block-sparse signals with nonzero coefficients occurring in clusters arise naturally in many practical scenarios. However, the…

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…

Structural damage due to excessive loading or environmental degradation typically occurs in localized areas in the absence of collapse. This prior information about the spatial sparseness of structural damage is exploited here by a…

Sparse modeling for signal processing and machine learning has been at the focus of scientific research for over two decades. Among others, supervised sparsity-aware learning comprises two major paths paved by: a) discriminative methods and…

In compressive sensing, sparse signals are recovered from underdetermined noisy linear observations. One of the interesting problems which attracted a lot of attention in recent times is the support recovery or sparsity pattern recovery…

We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed…

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,…

Sparse Bayesian learning (SBL) is a popular approach to sparse signal recovery in compressed sensing (CS). In SBL, the signal sparsity information is exploited by assuming a sparsity-inducing prior for the signal that is then estimated…

Subsampled blind deconvolution is the recovery of two unknown signals from samples of their convolution. To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in…

Identifying damage of structural systems is typically characterized as an inverse problem which might be ill-conditioned due to aleatory and epistemic uncertainties induced by measurement noise and modeling error. Sparse representation can…

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…

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…

Sparse Bayesian learning models are typically used for prediction in datasets with significantly greater number of covariates than observations. Such models often take a reproducing kernel Hilbert space (RKHS) approach to carry out the task…

Inverse problems can be described as limited-data problems in which the signal of interest cannot be observed directly. A physics-based forward model that relates the signal with the observations is typically needed. Unfortunately, unknown…

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to…

In this paper, a sparse signal recovery algorithm using Bayesian linear regression with Cauchy prior (BLRC) is proposed. Utilizing an approximate expectation maximization(AEM) scheme, a systematic hyper-parameter updating strategy is…

Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…

We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy…