Related papers: Newton-Direction-Based ReLU-Thresholding Methods f…

Sparse signal recovery or compressed sensing can be formulated as certain sparse optimization problems. The classic optimization theory indicates that the Newton-like method often has a numerical advantage over the gradient method for…

Sparse signals can be possibly reconstructed by an algorithm which merges a traditional nonlinear optimization method and a certain thresholding technique. Different from existing thresholding methods, a novel thresholding technique…

Thresholding algorithms for sparse optimization problems involve two key components: search directions and thresholding strategies. In this paper, we use the compressed Newton direction as a search direction, derived by confining the…

This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit…

We prove the first guarantees of sparse recovery for ReLU neural networks, where the sparse network weights constitute the signal to be recovered. Specifically, we study structural properties of the sparse network weights for two-layer,…

This paper introduces recovery thresholding hyperinterpolations, a novel class of methods for sparse signal reconstruction in the presence of noise. We develop a framework that integrates thresholding operators--including hard thresholding,…

Recovering a sparse signal from outlier-contaminated measurements is a fundamental challenge in many applications. While existing algorithms predominantly address scenarios with bounded noise or assume known signal sparsity, few methods…

We consider multichannel sparse recovery problem where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known…

Algorithms based on the hard thresholding principle have been well studied with sounding theoretical guarantees in the compressed sensing and more general sparsity-constrained optimization. It is widely observed in existing empirical…

Sparse signal recovery is one of the most fundamental problems in various applications, including medical imaging and remote sensing. Many greedy algorithms based on the family of hard thresholding operators have been developed to solve the…

We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…

It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…

In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…

The hard thresholding technique plays a vital role in the development of algorithms for sparse signal recovery. By merging this technique and heavy-ball acceleration method which is a multi-step extension of the traditional gradient descent…

Hard-thresholding-based algorithms have seen various advantages for sparse optimization in controlling the sparsity and allowing for fast computation. Recent research shows that when techniques of the Newton-type methods are integrated,…

We demonstrate a simple greedy algorithm that can reliably recover a d-dimensional vector v from incomplete and inaccurate measurements x. Here our measurement matrix is an N by d matrix with N much smaller than d. Our algorithm,…

The algorithms based on the technique of optimal $k$-thresholding (OT) were recently proposed for signal recovery, and they are very different from the traditional family of hard thresholding methods. However, the computational cost for…

Orthogonal matching pursuit (OMP) is a widely used algorithm for recovering sparse high dimensional vectors in linear regression models. The optimal performance of OMP requires \textit{a priori} knowledge of either the sparsity of…

We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…

We propose a new iterative greedy algorithm for reconstructions of sparse signals with or without noisy perturbations in compressed sensing. The proposed algorithm, called \emph{subspace thresholding pursuit} (STP) in this paper, is a…