Related papers: Approximate methods for phase retrieval via gauge …

In this work we propose a nonconvex two-stage \underline{s}tochastic \underline{a}lternating \underline{m}inimizing (SAM) method for sparse phase retrieval. The proposed algorithm is guaranteed to have an exact recovery from $O(s\log n)$…

High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…

We consider the phase retrieval problem, in which the observer wishes to recover a $n$-dimensional real or complex signal $\mathbf{X}^\star$ from the (possibly noisy) observation of $|\mathbf{\Phi} \mathbf{X}^\star|$, in which…

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…

Phase retrieval aims at recovering a complex-valued signal from magnitude-only measurements, which attracts much attention since it has numerous applications in many disciplines. However, phase recovery involves solving a system of…

This paper explores the problem of generalized phase retrieval, which involves reconstructing a length-$n$ signal $\bm{x}$ from its $m$ phaseless samples $y_k = \left|\langle \bm{a}_k,\bm{x}\rangle\right|^2$, where $k = 1,2,...,m$, and…

We consider a recently proposed convex formulation, known as the PhaseMax method, for solving the phase retrieval problem. Using the replica method from statistical mechanics, we analyze the performance of PhaseMax in the high-dimensional…

Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…

We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and…

We consider the recovery of a (real- or complex-valued) signal from magnitude-only measurements, known as phase retrieval. We formulate phase retrieval as a convex optimization problem, which we call PhaseMax. Unlike other convex methods…

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…

This paper concerns with a noisy structured low-rank matrix recovery problem which can be modeled as a structured rank minimization problem. We reformulate this problem as a mathematical program with a generalized complementarity constraint…

Many problems in data science can be treated as estimating a low-rank matrix from highly incomplete, sometimes even corrupted, observations. One popular approach is to resort to matrix factorization, where the low-rank matrix factors are…

Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…

Low-rank matrix recovery problems arise naturally as mathematical formulations of various inverse problems, such as matrix completion, blind deconvolution, and phase retrieval. Over the last two decades, a number of works have rigorously…

The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of…

We propose a novel formulation for phase synchronization -- the statistical problem of jointly estimating alignment angles from noisy pairwise comparisons -- as a nonconvex optimization problem that enforces consistency among the pairwise…

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

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…

It was recently shown that the phase retrieval imaging of a sample can be modeled as a simple convolution process. Sometimes, such a convolution depends on physical parameters of the sample which are difficult to estimate a priori. In this…