Related papers: Phase retrieval for imaging problems
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…
This review article provides a contemporary overview of phase retrieval in optical imaging, linking the relevant optical physics to the information processing methods and algorithms. Its purpose is to describe the current state of the art…
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…
We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x of C^n about which we have phaseless samples of the form y_r = |< a_r,x >|^2, r = 1,2,...,m (knowledge…
Phase retrieval algorithms have become an important component in many modern computational imaging systems. For instance, in the context of ptychography and speckle correlation imaging, they enable imaging past the diffraction limit and…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [27]. The improved algorithm admits deterministic measurement constructions together with a robust, fast recovery…
We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal…
Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this…
In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the…
Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…
This paper concerns the problem of recovering an unknown but structured signal $x \in R^n$ from $m$ quadratic measurements of the form $y_r=|<a_r,x>|^2$ for $r=1,2,...,m$. We focus on the under-determined setting where the number of…
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…
Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…
Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that are currently used to solve this reconstruction…
We propose a flexible yet interpretable model for high-dimensional data with time-varying second order statistics, motivated and applied to functional neuroimaging data. Motivated by the neuroscience literature, we factorize the covariances…
The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…
The problem of estimating the delays and amplitudes of a positive stream of pulses appears in many applications, such as single-molecule microscopy. This paper suggests estimating the delays and amplitudes using a convex program, which is…
Phase retrieval is an important problem with significant physical and industrial applications. In this paper, we consider the case where the magnitude of the measurement of an underlying signal is corrupted by Gaussian noise. We introduce a…
In this paper, we consider compressive/sparse affine phase retrieval proposed in [B. Gao B, Q. Sun, Y. Wang and Z. Xu, Adv. in Appl. Math., 93(2018), 121-141]. By the lift technique, and heuristic nuclear norm for convex relaxation of rank…