Related papers: Sparse Bayesian Learning Using Approximate Message…

For certain sensing matrices, the Approximate Message Passing (AMP) algorithm efficiently reconstructs undersampled signals. However, in Magnetic Resonance Imaging (MRI), where Fourier coefficients of a natural image are sampled with…

Sparse Group LASSO (SGL) is a regularized model for high-dimensional linear regression problems with grouped covariates. SGL applies $l_1$ and $l_2$ penalties on the individual predictors and group predictors, respectively, to guarantee…

We present a novel compressed sensing recovery algorithm - termed Bayesian Optimal Structured Signal Approximate Message Passing (BOSSAMP) - that jointly exploits the prior distribution and the structured sparsity of a signal that shall be…

This paper revisits the CHAMPAGNE algorithm within the Sparse Bayesian Learning (SBL) framework and establishes its connection to reweighted sparse coding. We demonstrate that the SBL objective can be reformulated as a reweighted…

Sparse learning has been widely studied to capture critical information from enormous data sources in the filed of system identification. Often, it is essential to understand internal working mechanisms of unknown systems (e.g. biological…

This paper introduces a new sparse Bayesian learning (SBL) algorithm that jointly recovers a temporal sequence of edge maps from noisy and under-sampled Fourier data. The new method is cast in a Bayesian framework and uses a prior that…

We give a fast, spectral procedure for implementing approximate-message passing (AMP) algorithms robustly. For any quadratic optimization problem over symmetric matrices $X$ with independent subgaussian entries, and any separable AMP…

Approximate message passing algorithm enjoyed considerable attention in the last decade. In this paper we introduce a variant of the AMP algorithm that takes into account glassy nature of the system under consideration. We coin this…

Deep learning has gained great popularity due to its widespread success on many inference problems. We consider the application of deep learning to the sparse linear inverse problem, where one seeks to recover a sparse signal from a few…

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…

This paper considers the massive connectivity problem in an asynchronous grant-free random access system, where a huge number of devices sporadically transmit data to a base station (BS) with imperfect synchronization. The goal is to design…

High-dimensional signal recovery of standard linear regression is a key challenge in many engineering fields, such as, communications, compressed sensing, and image processing. The approximate message passing (AMP) algorithm proposed by…

This paper begins with considering the identification of sparse linear time-invariant networks described by multivariable ARX models. Such models possess relatively simple structure thus used as a benchmark to promote further research. With…

The recovery of block-sparse signals with unknown structural patterns remains a fundamental challenge in structured sparse signal reconstruction. By proposing a variance transformation framework, this paper unifies existing pattern-based…

We consider the problem of recovering clustered sparse signals with no prior knowledge of the sparsity pattern. Beyond simple sparsity, signals of interest often exhibits an underlying sparsity pattern which, if leveraged, can improve the…

The generalized approximate message passing (GAMP) algorithm under the Bayesian setting shows advantage in recovering under-sampled sparse signals from corrupted observations. Compared to conventional convex optimization methods, it has a…

Approximate message passing (AMP) is a low-cost iterative signal recovery algorithm for linear system models. When the system transform matrix has independent identically distributed (IID) Gaussian entries, the performance of AMP can be…

In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP,…

This work is a re-examination of the sparse Bayesian learning (SBL) of linear regression models of Tipping (2001) in a high-dimensional setting. We propose a hard-thresholded version of the SBL estimator that achieves, for orthogonal design…

Sparse Bayesian learning (SBL) associates to each weight in the underlying linear model a hyperparameter by assuming that each weight is Gaussian distributed with zero mean and precision (inverse variance) equal to its associated…