Related papers: Sparse recovery by reduced variance stochastic app…
This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise…
Orthogonal matching pursuit (OMP) is a greedy algorithm popularly being used for the recovery of sparse signals. In this paper, we study the performance of OMP for support recovery of sparse signal under noise. Our analysis shows that under…
This article aims to provide a comprehensive overview of sparse optimization, with a focus on both sparse signal recovery and sparse regularization techniques. We will begin by exploring the foundations of sparse optimization, delving into…
This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…
Recently, many practical algorithms have been proposed to recover the sparse signal from fewer measurements. Orthogonal matching pursuit (OMP) is one of the most effective algorithm. In this paper, we use the restricted isometry property to…
In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In several applications the…
We introduce a dynamic sparse training algorithm based on linearized Bregman iterations / mirror descent that exploits the naturally incurred sparsity by alternating between periods of static and dynamic sparsity pattern updates. The key…
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…
In this report, a novel efficient algorithm for recovery of jointly sparse signals (sparse matrix) from multiple incomplete measurements has been presented, in particular, the NESTA-based MMV optimization method. In a nutshell, the jointly…
We analyze continuous-time mirror descent applied to sparse phase retrieval, which is the problem of recovering sparse signals from a set of magnitude-only measurements. We apply mirror descent to the unconstrained empirical risk…
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…
We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
We propose a Multi-step Screening Procedure (MSP) for the recovery of sparse linear models in high-dimensional data. This method is based on a repeated small penalty strategy that quickly converges to an estimate within a few iterations.…
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…
We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…
The SparseStep algorithm is presented for the estimation of a sparse parameter vector in the linear regression problem. The algorithm works by adding an approximation of the exact counting norm as a constraint on the model parameters and…
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…
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…
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…