相关论文: Optimal Spectral Initialization for Signal Recover…
Group synchronization asks to recover group elements from their pairwise measurements. It has found numerous applications across various scientific disciplines. In this work, we focus on orthogonal and permutation group synchronization…
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…
In this work we consider the problem of reconstruction of a signal from the magnitude of its Fourier transform, also known as phase retrieval. The problem arises in many areas of astronomy, crystallography, optics, and coherent diffraction…
We study nonconvex optimization for phase retrieval and the more general problem of semidefinite low-rank matrix sensing; in particular, we focus on the global nonconvex landscape of overparametrized versions of the nonsmooth amplitude…
In this work, we study the robust phase retrieval problem where the task is to recover an unknown signal $\theta^* \in \mathbb{R}^d$ in the presence of potentially arbitrarily corrupted magnitude-only linear measurements. We propose an…
We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy…
We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…
We propose an inverse-design approach for computational spectrometers in which the scattering media are topology-optimized to achieve better performance in inference of unknown spectra. Unlike traditional end-to-end approaches, our inverse…
Phase retrieval refers to the problem of recovering real- or complex-valued vectors from magnitude measurements. The best-known algorithms for this problem are iterative in nature and rely on so-called spectral initializers that provide…
Currently, the engineering of miniature spectrometers mainly faces three problems: the mismatch between the number of filters at the front end of the detector and the spectral reconstruction accuracy; the lack of a stable spectral…
This paper studies the problem of reconstructing spectrally sparse signals from a small random subset of time domain samples via low-rank Hankel matrix completion with the aid of prior information. By leveraging the low-rank structure of…
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…
Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization we…
Suppose we wish to recover a signal x in C^n from m intensity measurements of the form |<x,z_i>|^2, i = 1, 2,..., m; that is, from data in which phase information is missing. We prove that if the vectors z_i are sampled independently and…
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…
The problem of phase retrieval is a classic one in optics and arises when one is interested in recovering an unknown signal from the magnitude (intensity) of its Fourier transform. While there have existed quite a few approaches to phase…
In phase retrieval we want to recover an unknown signal $\boldsymbol x\in\mathbb C^d$ from $n$ quadratic measurements of the form $y_i = |\langle{\boldsymbol a}_i,{\boldsymbol x}\rangle|^2+w_i$ where $\boldsymbol a_i\in \mathbb C^d$ are…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
We introduce a generalized version of phase retrieval called multiplexed phase retrieval. We want to recover the phase of amplitude-only measurements from linear combinations of them. This corresponds to the case in which multiple…
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…