Related papers: Dictionary Learning Phase Retrieval from Noisy Dif…
Phase-retrieval from coded diffraction patterns (CDP) is important to X-ray crystallography, diffraction tomography and astronomical imaging, yet remains a hard, non-convex inverse problem. We show that CDP recovery can be reformulated…
We investigate the recovery of signals exhibiting a sparse representation in a general (i.e., possibly redundant or incomplete) dictionary that are corrupted by additive noise admitting a sparse representation in another general dictionary.…
Exploring the idea of phase retrieval has been intriguing researchers for decades, due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phaseless…
The problem of phase retrieval (PR) involves recovering an unknown image from limited amplitude measurement data and is a challenge nonlinear inverse problem in computational imaging and image processing. However, many of the PR methods are…
Various algorithms have been proposed for dictionary learning. Among those for image processing, many use image patches to form dictionaries. This paper focuses on whole-image recovery from corrupted linear measurements. We address the open…
The problem of signal recovery from its Fourier transform magnitude is of paramount importance in various fields of engineering and has been around for over 100 years. Due to the absence of phase information, some form of additional…
Applying standard algorithms to sparse data problems in photoacoustic tomography (PAT) yields low-quality images containing severe under-sampling artifacts. To some extent, these artifacts can be reduced by iterative image reconstruction…
X-ray phase contrast tomography (XPCT) is widely used for 3D imaging of objects with weak contrast in X-ray absorption index but strong contrast in refractive index decrement. To reconstruct an object imaged using XPCT, phase retrieval…
Dictionary learning and sparse representation (DLSR) is a recent and successful mathematical model for data representation that achieves state-of-the-art performance in various fields such as pattern recognition, machine learning, computer…
We derive a set of ptychography phase-retrieval iterative engines based on proximal algorithms originally developed in convex optimization theory, and discuss their connections with existing ones. The use of proximal operator creates a…
In diffraction imaging, one is tasked with reconstructing a signal from its power spectrum. To resolve the ambiguity in this inverse problem, one might invoke prior knowledge about the signal, but phase retrieval algorithms in this vein…
Learned sparse retrieval (LSR) is a family of neural methods that encode queries and documents into sparse lexical vectors that can be indexed and retrieved efficiently with an inverted index. We explore the application of LSR to the…
The problem of phase retrieval, or the algorithmic recovery of lost phase information from measured intensity alone, underlies various imaging methods from astronomy to nanoscale imaging. Traditional methods of phase retrieval are iterative…
We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…
We develop two iterative algorithms for solving the low rank phase retrieval (LRPR) problem. LRPR refers to recovering a low-rank matrix $\X$ from magnitude-only (phaseless) measurements of random linear projections of its columns. Both…
In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…
The problem of reconstructing a sparse signal vector from magnitude-only measurements (a.k.a., compressive phase retrieval), emerges naturally in diverse applications, but it is NP-hard in general. Building on recent advances in nonconvex…
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…
We propose and demonstrate a new phase retrieval method for imaging through random media. Although methods to recover the Fourier amplitude through random distortions are well established, recovery of the Fourier phase has been a more…
In this paper, we develop a novel phase retrieval approach to reconstruct x-ray differential phase shift induced by an object. A primary advantage of our approach is a higher-order accuracy over that with the conventional linear…