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This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…

Machine Learning · Statistics 2025-04-15 The Tien Mai

A new phase-coherent technique for the calibration of polarimetric data is presented. Similar to the one-dimensional form of convolution, data are multiplied by the response function in the frequency domain. Therefore, the system response…

Astrophysics · Physics 2009-11-07 W. van Straten

Ptychography has risen as a reference X-ray imaging technique: it achieves resolutions of one billionth of a meter, macroscopic field of view, or the capability to retrieve chemical or magnetic contrast, among other features. A…

Optimization and Control · Mathematics 2019-06-10 Huibin Chang , Pable Enfedaque , Stefano Marchesini

High-throughput computational imaging requires efficient processing algorithms to retrieve multi-dimensional and multi-scale information. In computational phase imaging, phase retrieval (PR) is required to reconstruct both amplitude and…

Image and Video Processing · Electrical Eng. & Systems 2021-09-15 Xuyang Chang , Liheng Bian , Jun Zhang

Phase retrieval seeks to recover a complex signal from amplitude-only measurements, a challenging nonlinear inverse problem. Current theory and algorithms often ignore signal priors. By contrast, we evaluate here a variety of image priors…

Image and Video Processing · Electrical Eng. & Systems 2025-09-19 Stanislas Ducotterd , Zhiyuan Hu , Michael Unser , Jonathan Dong

In this paper, we introduce an iterative speckle filtering method for polarimetric SAR (PolSAR) images based on the bilateral filter. To locally adapt to the spatial structure of images, this filter relies on pixel similarities in both…

Computer Vision and Pattern Recognition · Computer Science 2013-11-04 Olivier D'Hondt , Stéphane Guillaso , Olaf Hellwich

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…

Information Theory · Computer Science 2013-10-10 Henrik Ohlsson , Yonina C. Eldar

Polarimetric imaging captures surface polarization characteristics, such as the Degree of Linear Polarization (DoLP) and the Angle of Polarization (AoP). In mainstream Division of-Focal-Plane (DoFP) color polarization imaging, recovering…

Computer Vision and Pattern Recognition · Computer Science 2026-05-12 Chenggong Li , Yidong Luo , Junchao Zhang , Boxin Shi , Degui Yang

We present a technique to automatically classify the wave type of seismic phases that are recorded on a single six-component recording station (measuring both three components of translational and rotational ground motion) at the earth's…

Geophysics · Physics 2023-03-01 David Sollberger , Nicholas Bradley , Pascal Edme , Johan O. A. Robertsson

This paper proposes a novel algorithm for image phase retrieval, i.e., for recovering complex-valued images from the amplitudes of noisy linear combinations (often the Fourier transform) of the sought complex images. The algorithm is…

Signal Processing · Electrical Eng. & Systems 2018-10-19 Joshin P. Krishnan , José M. Bioucas-Dias , Vladimir Katkovnik

The phase retrieval problem asks to recover a natural signal $y_0 \in \mathbb{R}^n$ from $m$ quadratic observations, where $m$ is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to…

Information Theory · Computer Science 2018-07-12 Paul Hand , Oscar Leong , Vladislav Voroninski

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,…

Image and Video Processing · Electrical Eng. & Systems 2022-04-21 Leon Gugel , Shai Dekel

This paper considers the question of recovering the phase of an object from intensity-only measurements, a problem which naturally appears in X-ray crystallography and related disciplines. We study a physically realistic setup where one can…

Information Theory · Computer Science 2013-11-08 Emmanuel Candes , Xiaodong Li , Mahdi Soltanolkotabi

Phase reconstruction is important in transmission electron microscopy for structural studies. We describe electron Fourier ptychography and its application to phase reconstruction of both radiation-resistant and beam-sensitive materials. We…

Phase retrieval(PR) problem is a kind of ill-condition inverse problem which can be found in various of applications. Utilizing the sparse priority, an algorithm called SWF(Sparse Wirtinger Flow) is proposed in this paper to deal with…

Information Theory · Computer Science 2017-04-12 Ziyang Yuan , Qi Wang , Hongxia Wang

A general mathematical framework and recovery algorithm is presented for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a "reference" portion of the signal to be recovered…

Information Theory · Computer Science 2024-12-20 David A. Barmherzig , Ju Sun , T. J. Lane , Po-Nan Li , Emmanuel J. Candès

This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…

Machine Learning · Statistics 2015-09-08 Ömer Deniz Akyıldız

We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…

Information Theory · Computer Science 2015-10-28 Sohail Bahmani , Justin Romberg

This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…

Information Theory · Computer Science 2014-02-25 Fabien Lauer , Henrik Ohlsson

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.…

Numerical Analysis · Mathematics 2025-10-20 Veit Elser