Related papers: Low Complexity Regularized Phase Retrieval
The support recovery problem consists of determining a sparse subset of variables that is relevant in generating a set of observations. In this paper, we study the support recovery problem in the phase retrieval model consisting of noisy…
This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…
This paper investigates the theoretical guarantees of L1-analysis regularization when solving linear inverse problems. Most of previous works in the literature have mainly focused on the sparse synthesis prior where the sparsity is measured…
We consider the problem of exact recovery of a $k$-sparse binary vector from generalized linear measurements (such as logistic regression). We analyze the linear estimation algorithm (Plan, Vershynin, Yudovina, 2017), and also show…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…
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…
The phase retrieval problem in the presence of noise aims to recover the signal vector of interest from a set of quadratic measurements with infrequent but arbitrary corruptions, and it plays an important role in many scientific…
Recovering a signal from its Fourier magnitude is referred to as phase retrieval, which occurs in different fields of engineering and applied physics. This paper gives a new characterization of the phase retrieval problem. Particularly…
The main objective of this paper is to find algorithms accompanied by explicit error bounds for phase retrieval from noisy magnitudes of frame coefficients when the underlying frame has a low redundancy. We achieve these goals with frames…
The PhaseLift algorithm is an effective convex method for solving the phase retrieval problem from Fourier measurements with coded diffraction patterns (CDP). While exact reconstruction guarantees are well-established in the noiseless case,…
We investigate the problem of reconstructing n-by-n structured matrix signal X via convex programming, where each column xj is a vector of s-sparsity and all columns have the same l1-norm. The regularizer in use is matrix norm…
Can we recover a complex signal from its Fourier magnitudes? More generally, given a set of $m$ measurements, $y_k = |\mathbf a_k^* \mathbf x|$ for $k = 1, \dots, m$, is it possible to recover $\mathbf x \in \mathbb{C}^n$ (i.e., length-$n$…
Recovering sparse vectors and low-rank matrices from noisy linear measurements has been the focus of much recent research. Various reconstruction algorithms have been studied, including $\ell_1$ and nuclear norm minimization as well as…
During the last decade, the paradigm of compressed sensing has gained significant importance in the signal processing community. While the original idea was to utilize sparsity assumptions to design powerful recovery algorithms of vectors…
The classical phase retrieval problem arises in contexts ranging from speech recognition to x-ray crystallography and quantum state tomography. The generalization to matrix frames is natural in the sense that it corresponds to quantum…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…
Generally, phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of the linear measurements. These measurements can be, for example, the Fourier transform of the density function.…
Consider the $n$-dimensional vector $y=X\be+\e$, where $\be \in \R^p$ has only $k$ nonzero entries and $\e \in \R^n$ is a Gaussian noise. This can be viewed as a linear system with sparsity constraints, corrupted by noise. We find a…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
We propose and study a regularization method for recovering an approximate electrical conductivity solely from the magnitude of one interior current density field. Without some minimal knowledge of the boundary voltage potential, the…