Related papers: Phase Retrieval Under a Generative Prior
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit…
Phase retrieval with prior information can be cast as a nonsmooth and nonconvex optimization problem. We solve the problem by graph projection splitting (GPS), where the two proximity subproblems and the graph projection step can be solved…
This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…
Phase retrieval aims at reconstructing unknown signals from magnitude measurements of linear mixtures. In this paper, we consider the phase retrieval with dictionary learning problem, which includes an additional prior information that the…
Using a low-dimensional parametrization of signals is a generic and powerful way to enhance performance in signal processing and statistical inference. A very popular and widely explored type of dimensionality reduction is sparsity; another…
The sparsity in levels model recently inspired a new generation of effective acquisition and reconstruction modalities for compressive imaging. Moreover, it naturally arises in various areas of signal processing such as parallel…
Phase retrieval with pre-defined optical masks can provide extra constraint and thus achieve improved performance. The recent progress in optimization theory demonstrates the superiority of random masks in phase retrieval algorithms.…
Fourier Ptychography is a recently proposed imaging technique that yields high-resolution images by computationally transcending the diffraction blur of an optical system. At the crux of this method is the phase retrieval algorithm, which…
Proximal algorithms have gained popularity in recent years in large-scale and distributed optimization problems. One such problem is the phase retrieval problem, for which proximal operators have been proposed recently. The phase retrieval…
Trained generative models have shown remarkable performance as priors for inverse problems in imaging -- for example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements than sparsity priors.…
Classical results in sparse recovery guarantee the exact reconstruction of $s$-sparse signals under assumptions on the dictionary that are either too strong or NP-hard to check. Moreover, such results may be pessimistic in practice since…
Recovering a signal from its Fourier intensity underlies many important applications, including lensless imaging and imaging through scattering media. Conventional algorithms for retrieving the phase suffer when noise is present but display…
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…
Phase retrieval (PR) aims to recover a signal from the magnitudes of a set of inner products. This problem arises in many audio signal processing applications which operate on a short-time Fourier transform magnitude or power spectrogram,…
The aim of this paper is to study the stability of the $\ell_1$ minimization for the compressive phase retrieval and to extend the instance-optimality in compressed sensing to the real phase retrieval setting. We first show that the…
The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases. We consider the closely-related problem of recovering a signal from its phaseless…
Zernike's phase contrast microscopy (PCM) is among the most widely used techniques for observing phase objects, but it lacks quantitative nature, as it cannot directly provide phase information. Current methods for computationally…
Phase retrieval (PR) is an important component in modern computational imaging systems. Many algorithms have been developed over the past half-century. Recent advances in deep learning have introduced new possibilities for a robust and fast…
In many signal processing problems arising in practical applications, we wish to reconstruct an unknown signal from its phaseless measurements with respect to a frame. This inverse problem is known as the phase retrieval problem. For each…