Related papers: Improved Recovery Guarantees for Phase Retrieval f…
This paper is concerned with the inverse source problem of reconstructing an unknown acoustic excitation from phaseless measurements of the radiated fields away at multiple frequencies. It is well known that the non-uniqueness issue is a…
Phase retrieval is a well known ill-posed inverse problem where one tries to recover images given only the magnitude values of their Fourier transform as input. In recent years, new algorithms based on deep learning have been proposed,…
We introduce a method to recover a continuous domain representation of a piecewise constant two-dimensional image from few low-pass Fourier samples. Assuming the edge set of the image is localized to the zero set of a trigonometric…
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…
We address the problem of phase retrieval (PR) from quantized measurements. The goal is to reconstruct a signal from quadratic measurements encoded with a finite precision, which is indeed the case in many practical applications. We develop…
We study the problem of recovering a structured signal from independently and identically drawn linear measurements. A convex penalty function $f(\cdot)$ is considered which penalizes deviations from the desired structure, and signal…
This note formulates a deterministic recovery result for vectors $x$ from quadratic measurements of the form $(Ax)_i \overline{(Ax)_j}$ for some left-invertible $A$. Recovery is exact, or stable in the noisy case, when the couples $(i,j)$…
This paper investigates noise-robust phase retrieval by enhancing the prDeep architecture with difference of convex functions (DC) and DnCNN-based denoising regularization. This research introduces two novel algorithms, prDeep-DC and…
We propose a new problem of missing data reconstruction in the time-frequency plane. This problem called phase inpainting, consists in reconstructing a signal from time-frequency observations where all amplitudes and some phases are known…
In this paper, we present a new algorithm, called MagnitudeCut, for recovering a signal from the phase of its Fourier transform. We casted our recovering problem into a new convex optimization problem, and then solved it by the block…
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…
The phase retrieval problem has a long history and is an important problem in many areas of optics. Theoretical understanding of phase retrieval is still limited and fundamental questions such as uniqueness and stability of the recovered…
A cascaded iterative Fourier transform (CIFT) algorithm is presented for optical security applications. Two phase-masks are designed and located in the input and the Fourier domains of a 4-f correlator respectively, in order to implement…
In this paper we present an algorithm for optical phase evaluation based on the wavelet transform technique. The main advantage of this method is that it requires only one fringe pattern. This algorithm is based on the use of a second…
We present a new method for real- and complex-valued image reconstruction from two intensity measurements made in the Fourier plane: the Fourier magnitude of the unknown image, and the intensity of the interference pattern arising from…
Phase retrieval is concerned with recovering a function $f$ from the absolute value of its Fourier transform $|\widehat{f}|$. We study the stability properties of this problem in Lebesgue spaces. Our main results shows that $$ \|…
We introduce a framework for the reconstruction of the amplitude, phase and polarisation of an optical vector-field using calibration measurements acquired by an imaging device with an unknown linear transformation. By incorporating…
Fourier phase retrieval, which seeks to reconstruct a signal from its Fourier magnitude, is of fundamental importance in fields of engineering and science. In this paper, we give a theoretical understanding of algorithms for Fourier phase…
Coherent X-ray diffraction imaging (CXDI) experiments are intrinsically limited by shot noise, a lack of prior knowledge about the sample's support, and missing measurements due to the experimental geometry. We propose a flexible, iterative…
Phase retrieval aims to recover a signal from intensity-only measurements, a fundamental problem in many fields such as imaging, holography, optical computing, crystallography, and microscopy. Although there are several well-known phase…