Related papers: A Novel Bayesian Approach for the Two-Dimensional …

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…

In this paper, we introduce the concept of sparse bilinear logistic regression for decision problems involving explanatory variables that are two-dimensional matrices. Such problems are common in computer vision, brain-computer interfaces,…

Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as Compressed Sensing (CS). Fusion frames are very rich new signal…

Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…

Learning Bayesian networks is often cast as an optimization problem, where the computational task is to find a structure that maximizes a statistically motivated score. By and large, existing learning tools address this optimization problem…

The multiple measurement vector problem (MMV) is a generalization of the compressed sensing problem that addresses the recovery of a set of jointly sparse signal vectors. One of the important contributions of this paper is to reveal that…

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…

In this paper, we studied the problem of beam alignment for millimeter wave (mmWave) communications, in which we assume a hybrid analog and digital beamforming structure is employed at the transmitter (i.e. base station), and an…

We study the problem of exact support recovery for high-dimensional sparse linear regression under independent Gaussian design when the signals are weak, rare, and possibly heterogeneous. Under a suitable scaling of the sample size and…

A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method, referred to as nGpFBMP, performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It…

In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is…

In hyperspectral sparse unmixing, a successful approach employs spectral bundles to address the variability of the endmembers in the spatial domain. However, the regularization penalties usually employed aggregate substantial computational…

A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…

We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…

We present a strategy for the recovery of a sparse solution of a common problem in acoustic engineering, which is the reconstruction of sound source levels and locations applying microphone array measurements. The considered task bears…

Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can benefit…

We study the problem of recovering sparse signals from compressed linear measurements. This problem, often referred to as sparse recovery or sparse reconstruction, has generated a great deal of interest in recent years. To recover the…

Data-driven discovery of differential equations has been an emerging research topic. We propose a novel algorithm subsampling-based threshold sparse Bayesian regression (SubTSBR) to tackle high noise and outliers. The subsampling technique…

This paper reports an effort to consolidate numerous coherence-based sparse signal recovery results available in the literature. We present a single theory that applies to general Hilbert spaces with the sparsity of a signal defined as the…

This paper considers the problem of reconstructing sparse or compressible signals from one-bit quantized measurements. We study a new method that uses a log-sum penalty function, also referred to as the Gaussian entropy, for sparse signal…