Related papers: High SNR Consistent Compressive Sensing Without Si…
The problem of detecting the sparsity pattern of a k-sparse vector in R^n from m random noisy measurements is of interest in many areas such as system identification, denoising, pattern recognition, and compressed sensing. This paper…
This paper studies sequential methods for recovery of sparse signals in high dimensions. When compared to fixed sample size procedures, in the sparse setting, sequential methods can result in a large reduction in the number of samples…
With the increasing popularity of large-scale antenna arrays, the subarraying technology becomes more attractive. In this paper, we propose two effective subarraying methods right after formulating the subarray synthesis as a compressive…
Let $x\in\mathbb{C}^n$ be a spectrally sparse signal consisting of $r$ complex sinusoids with or without damping. We consider the spectral compressed sensing problem, which is about reconstructing $x$ from its partial revealed entries. By…
From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori…
Greedy approaches in general, and orthogonal matching pursuit in particular, are the most commonly used sparse recovery techniques in a wide range of applications. The complexity of these approaches is highly dependent on the size of the…
We consider parameter estimation under sparse linear regression -- an extensively studied problem in high-dimensional statistics and compressed sensing. While the minimax framework has been one of the most fundamental approaches for…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…
Given an overcomplete dictionary $A$ and a signal $b$ that is a linear combination of a few linearly independent columns of $A$, classical sparse recovery theory deals with the problem of recovering the unique sparse representation $x$ such…
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…
With the development of numbers of high resolution data acquisition systems and the global requirement to lower the energy consumption, the development of efficient sensing techniques becomes critical. Recently, Compressed Sampling (CS)…
Within the Compressive Sensing (CS) paradigm, sparse signals can be reconstructed based on a reduced set of measurements. Reliability of the solution is determined by the uniqueness condition. With its mathematically tractable and feasible…
Using a Bayesian approach, we consider the problem of recovering sparse signals under additive sparse and dense noise. Typically, sparse noise models outliers, impulse bursts or data loss. To handle sparse noise, existing methods…
Generalized orthogonal matching pursuit (gOMP) algorithm has received much attention in recent years as a natural extension of orthogonal matching pursuit. It is used to recover sparse signals in compressive sensing. In this paper, a new…
In this work, we propose a novel approach called Operational Support Estimator Networks (OSENs) for the support estimation task. Support Estimation (SE) is defined as finding the locations of non-zero elements in sparse signals. By its very…
In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…
The double sparse linear model, which has both group-wise and element-wise sparsity in regression coefficients, has attracted lots of attention recently. This paper establishes the sufficient and necessary relationship between the exact…
Sparse regression methods have been proven effective in a wide range of signal processing problems such as image compression, speech coding, channel equalization, linear regression and classification. In this paper a new convex method of…
We present a computationally-efficient method for recovering sparse signals from a series of noisy observations, known as the problem of compressed sensing (CS). CS theory requires solving a convex constrained minimization problem. We…
In this paper we present a new coherence-based performance guarantee for the Orthogonal Matching Pursuit (OMP) algorithm. An upper bound for the probability of correctly identifying the support of a sparse signal with additive white…