Related papers: Quantization and Greed are Good: One bit Phase Ret…
This paper considers the robust phase retrieval, which can be cast as a nonsmooth and nonconvex composite optimization problem. We propose two first-order algorithms with adaptive step sizes: the subgradient algorithm (AdaSubGrad) and the…
Greedy algorithms are popular in compressive sensing for their high computational efficiency. But the performance of current greedy algorithms can be degenerated seriously by noise (both multiplicative noise and additive noise). A robust…
The Compressive Sensing framework maintains relevance even when the available measurements are subject to extreme quantization, as is exemplified by the so-called one-bit compressed sensing framework which aims to recover a signal from…
We consider the problem of recovering a high-dimensional structured signal from independent Gaussian linear measurements each of which is quantized to $b$ bits. Our interest is in linear approaches to signal recovery, where "linear" means…
In this article, we discuss a novel greedy algorithm for the recovery of compressive sampled signals under noisy conditions. Most of the greedy recovery algorithms proposed in the literature require sparsity of the signal to be known or…
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…
In the undersampled phase retrieval problem, the goal is to recover an $N$-dimensional complex signal $\mathbf{x}$ from only $M<N$ noisy intensity measurements without phase information. This problem has drawn a lot of attention to reduce…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
Recent progress in robust statistical learning has mainly tackled convex problems, like mean estimation or linear regression, with non-convex challenges receiving less attention. Phase retrieval exemplifies such a non-convex problem,…
Compressed sensing (CS) is a technique which uses fewer measurements than dictated by the Nyquist sampling theorem. The traditional CS with linear measurements achieves efficient recovery performances, but it suffers from the large bit…
Many image processing applications benefited remarkably from the theory of sparsity. One model of sparsity is the cosparse analysis one. It was shown that using l_1-minimization one might stably recover a cosparse signal from a small set of…
This paper proposes a new framework to regularize the highly ill-posed and non-linear phase retrieval problem through deep generative priors using simple gradient descent algorithm. We experimentally show effectiveness of proposed algorithm…
In this paper, we study the sample complexity and develop efficient optimal algorithms for 1-bit phase retrieval: recovering a signal $\mathbf{x}\in\mathbb{R}^n$ from $m$ phaseless bits…
In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…
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 q-ary compressive sensing, an extension of 1-bit compressive sensing. We propose a novel sensing mechanism and a corresponding recovery procedure. The recovery properties of the proposed approach are analyzed both theoretically…
In this paper, we study the phase retrieval problem in the situation where the vector to be recovered has an a priori structure that can encoded into a regularization term. This regularizer is intended to promote solutions conforming to…
In this paper, we tackle the compressive phase retrieval problem in the presence of noise. The noisy compressive phase retrieval problem is to recover a $K$-sparse complex signal $s \in \mathbb{C}^n$, from a set of $m$ noisy quadratic…
Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex…
The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model targets a solution that has the least l0-norm among all signals…