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Related papers: Undersampled Phase Retrieval with Image Priors

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Phase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches…

In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In this paper, we provide a…

Information Theory · Computer Science 2013-09-13 Boris Alexeev , Afonso S. Bandeira , Matthew Fickus , Dustin G. Mixon

In this work we consider the problem of reconstruction of a signal from the magnitude of its Fourier transform, also known as phase retrieval. The problem arises in many areas of astronomy, crystallography, optics, and coherent diffraction…

Optics · Physics 2012-03-22 Eliyahu Osherovich

In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…

Information Theory · Computer Science 2017-03-24 Boshra Rajaei , Sylvain Gigan , Florent Krzakala , Laurent Daudet

We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements…

Optimization and Control · Mathematics 2016-11-23 Andreas M. Tillmann , Yonina C. Eldar , Julien Mairal

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…

Information Theory · Computer Science 2019-10-02 Gilles Baechler , Miranda Kreković , Juri Ranieri , Amina Chebira , Yue M. Lu , Martin Vetterli

Phase retrieval is the problem of reconstructing images from magnitude-only measurements. In many real-world applications the problem is underdetermined. When training data is available, generative models allow optimization in a…

Machine Learning · Computer Science 2023-01-20 Tobias Uelwer , Sebastian Konietzny , Stefan Harmeling

We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…

Information Theory · Computer Science 2013-11-12 Kishore Jaganathan , Samet Oymak , Babak Hassibi

We consider the problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform, or of any other linear transform. Due to the loss of the Fourier phase information, this problem is ill-posed. Therefore,…

Information Theory · Computer Science 2023-07-19 Yoav Shechtman , Amir Beck , Yonina C. Eldar

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…

Optics · Physics 2024-09-10 Zhiyuan Hu , Julián Tachella , Michael Unser , Jonathan Dong

We propose a general framework for reconstructing transform-sparse images from undersampled (squared)-magnitude data corrupted with outliers. This framework is implemented using a multi-layered approach, combining multiple initializations…

Signal recovery from nonlinear measurements involves solving an iterative optimization problem. In this paper, we present a framework to optimize the sensing parameters to improve the quality of the signal recovered by the given iterative…

Image and Video Processing · Electrical Eng. & Systems 2020-06-09 Zikui Cai , Rakib Hyder , M. Salman Asif

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…

Functional Analysis · Mathematics 2013-06-26 Afonso S. Bandeira , Yutong Chen , Dustin G. Mixon

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 considers the problem of recovering a $k$-sparse, $N$-dimensional complex signal from Fourier magnitude measurements. It proposes a Fourier optics setup such that signal recovery up to a global phase factor is possible with very…

Information Theory · Computer Science 2014-10-28 Çağkan Yapar , Volker Pohl , Holger Boche

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…

Computer Vision and Pattern Recognition · Computer Science 2018-05-10 Lokesh Boominathan , Mayug Maniparambil , Honey Gupta , Rahul Baburajan , Kaushik Mitra

A novel phase retrieval algorithm for broadband hyperspectral phase imaging from noisy intensity observations is proposed. It utilizes advantages of the Fourier Transform spectroscopy in the self-referencing optical setup and provides,…

Image and Video Processing · Electrical Eng. & Systems 2020-06-03 Igor Shevkunov , Vladimir Katkovnik , Karen Egiazarian

Phase retrieval is the inverse problem of recovering a signal from magnitude-only Fourier measurements, and underlies numerous imaging modalities, such as Coherent Diffraction Imaging (CDI). A variant of this setup, known as holography,…

Machine Learning · Computer Science 2021-04-22 Hannah Lawrence , David A. Barmherzig , Henry Li , Michael Eickenberg , Marylou Gabrié

It was recently shown that the phase retrieval imaging of a sample can be modeled as a simple convolution process. Sometimes, such a convolution depends on physical parameters of the sample which are difficult to estimate a priori. In this…

Numerical Analysis · Mathematics 2017-02-20 Eduardo X. Miqueles , Nathaly L. Archilha , Marcelo R. Dos Anjos , Harry Westfahl , Elias S. Helou

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…

Information Theory · Computer Science 2016-11-17 Emmanuel Candes , Xiaodong Li , Mahdi Soltanolkotabi