Related papers: Phase Retrieval via Sparse Wirtinger Flow
Iterative phase retrieval methods based on the Gerchberg-Saxton (GS) or Fienup algorithm require a large number of iterations to converge to a meaningful solution. For complex-valued or phase objects, these approaches also suffer from…
We study the sparse phase retrieval problem, recovering an $s$-sparse length-$n$ signal from $m$ magnitude-only measurements. Two-stage non-convex approaches have drawn much attention in recent studies for this problem. Despite…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
Compressed sensing investigates the recovery of sparse signals from linear measurements. But often, in a wide range of applications, one is given only the absolute values (squared) of the linear measurements. Recovering such signals (not…
We describe a new algorithm to solve a particular phase retrieval problem, that has wide applications in audio processing: the reconstruction of a function from its scalogram, that is from the modulus of its wavelet transform. It is a…
In this paper we propose a new fast Fourier transform to recover a real nonnegative signal ${\bf x}$ from its discrete Fourier transform. If the signal ${\mathbf x}$ appears to have a short support, i.e., vanishes outside a support interval…
We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements…
For audio source separation applications, it is common to estimate the magnitude of the short-time Fourier transform (STFT) of each source. In order to further synthesizing time-domain signals, it is necessary to recover the phase of the…
Traditional phase-shifting interferometry technique cannot be used to measure time-varying phase distributions. But single shot techniques could resolve the problem. Many efforts have been made on the phase retrieval methods from a single…
Solving quadratic systems of equations in n variables and m measurements of the form $y_i = |a^T_i x|^2$ , $i = 1, ..., m$ and $x \in R^n$ , which is also known as phase retrieval, is a hard nonconvex problem. In the case of standard…
This paper investigates the effects of setting the sampling frequency significantly higher than conventional guidelines in system identification. Although continuous-time identification methods resolve the numerical difficulties encountered…
We consider the problem of conjugate phase retrieval in Paley-Wiener space $PW_{\pi}$. The goal of conjugate phase retrieval is to recover a signal $f$ from the magnitudes of linear measurements up to unknown phase factor and unknown…
We present the first phase retrieval algorithm guaranteed to solve the multidimensional phase retrieval problem in polynomial arithmetic complexity without prior information. The method successfully terminates in O(N log(N)) operations for…
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…
Affine phase retrieval is the problem of recovering signals from the magnitude-only measurements with a priori information. In this paper, we use the $\ell_1$ minimization to exploit the sparsity of signals for affine phase retrieval,…
Diffusion models have demonstrated their utility as learned priors for solving various inverse problems. However, most existing approaches are limited to linear inverse problems. This paper exploits the efficient and unsupervised posterior…
Phase retrieval (PR), a long-established challenge for recovering a complex-valued signal from its Fourier intensity-only measurements, has attracted considerable attention due to its widespread applications in digital imaging. Recently,…
This work introduces a novel Fourier phase retrieval model, called polarimetric phase retrieval that enables a systematic use of polarization information in Fourier phase retrieval problems. We provide a complete characterization of…
This paper considers the phase retrieval problem in which measurements consist of only the magnitude of several linear measurements of the unknown, e.g., spectral components of a time sequence. We develop low-complexity algorithms with…
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…