Related papers: GraHTP: A Provable Newton-like Algorithm for Spars…
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…
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…
In this paper, we consider the sparse phase retrieval problem, recovering an $s$-sparse signal $\bm{x}^{\natural}\in\mathbb{R}^n$ from $m$ phaseless samples $y_i=|\langle\bm{x}^{\natural},\bm{a}_i\rangle|$ for $i=1,\ldots,m$. Existing…
Hard Thresholding Pursuit (HTP) is an iterative greedy selection procedure for finding sparse solutions of underdetermined linear systems. This method has been shown to have strong theoretical guarantee and impressive numerical performance.…
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,…
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…
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 propose and analyze a solution to the problem of recovering a block sparse signal with sparse blocks from linear measurements. Such problems naturally emerge inter alia in the context of mobile communication, in order to meet the…
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 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…
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…
A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many…
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…
Sparse phase retrieval plays an important role in many fields of applied science and thus attracts lots of attention. In this paper, we propose a \underline{sto}chastic alte\underline{r}nating \underline{m}inimizing method for…
Large-scale non-convex sparsity-constrained problems have recently gained extensive attention. Most existing deterministic optimization methods (e.g., GraSP) are not suitable for large-scale and high-dimensional problems, and thus…
We address the problem of sparse recovery using greedy compressed sensing recovery algorithms, without explicit knowledge of the sparsity. Estimating the sparsity order is a crucial problem in many practical scenarios, e.g., wireless…
We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…
In this paper we consider the problem of exact recovery of a fixed sparse vector with the measurement matrices sequentially arriving along with corresponding measurements. We propose an extension of the iterative hard thresholding (IHT)…
In the phase retrieval problem, an unknown vector is to be recovered given quadratic measurements. This problem has received considerable attention in recent times. In this paper, we present an algorithm to solve a nonconvex formulation of…
The optimization problems with a sparsity constraint is a class of important global optimization problems. A typical type of thresholding algorithms for solving such a problem adopts the traditional full steepest descent direction or…