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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…

Machine Learning · Computer Science 2018-08-20 Fahad Shamshad , Ali Ahmed

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…

Image and Video Processing · Electrical Eng. & Systems 2025-01-07 Mehmet Onurcan Kaya , Figen S. Oktem

This study presents a noise-robust framework for 1-bit diffraction tomography, a novel imaging approach that relies on intensity-only binary measurements obtained through coded apertures. The proposed reconstruction scheme leverages random…

Information Theory · Computer Science 2025-05-27 Pengwen Chen , Albert Fannjiang

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

Generally, phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of the linear measurements. These measurements can be, for example, the Fourier transform of the density function.…

Optimization and Control · Mathematics 2019-11-21 Bing Gao , Haixia Liu , Yang Wang

The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a…

Information Theory · Computer Science 2014-07-21 Volker Pohl , Fanny Yang , Holger Boche

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

The high performance of denoising diffusion models for image generation has paved the way for their application in unsupervised medical anomaly detection. As diffusion-based methods require a lot of GPU memory and have long sampling times,…

Computer Vision and Pattern Recognition · Computer Science 2024-03-19 Julia Wolleb , Florentin Bieder , Paul Friedrich , Peter Zhang , Alicia Durrer , Philippe C. Cattin

Non-regular sampling can reduce aliasing at the expense of noise. Recently, it has been shown that non-regular sampling can be carried out using a conventional regular imaging sensor when the surface of its individual pixels is partially…

Image and Video Processing · Electrical Eng. & Systems 2022-03-02 Simon Grosche , Jürgen Seiler , André Kaup

In coherent X-ray diffraction microscopy the diffraction pattern generated by a sample illuminated with coherent x-rays is recorded, and a computer algorithm recovers the unmeasured phases to synthesize an image. By avoiding the use of a…

This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations…

Information Theory · Computer Science 2011-09-21 Emmanuel J. Candes , Yonina Eldar , Thomas Strohmer , Vlad Voroninski

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…

Biological Physics · Physics 2017-03-03 Liang Shi , Gordon Wetzstein , Thomas J. Lane

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…

Numerical Analysis · Mathematics 2016-12-07 Mark A. Iwen , Brian Preskitt , Rayan Saab , Aditya Viswanathan

Phase retrieval is a problem encountered not only in speech and audio processing, but in many other fields such as optics. Iterative algorithms based on non-convex set projections are effective and frequently used for retrieving the phase…

Audio and Speech Processing · Electrical Eng. & Systems 2022-11-10 Tal Peer , Simon Welker , Timo Gerkmann

Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to…

Optics · Physics 2015-06-12 Albert Fannjiang , Wenjing Liao

In this work we develop an algorithm for signal reconstruction from the magnitude of its Fourier transform in a situation where some (non-zero) parts of the sought signal are known. Although our method does not assume that the known part…

Optics · Physics 2012-03-06 Eliyahu Osherovich , Michael Zibulevsky , Irad Yavneh

Diffusion probabilistic models have been recently used in a variety of tasks, including speech enhancement and synthesis. As a generative approach, diffusion models have been shown to be especially suitable for imputation problems, where…

Audio and Speech Processing · Electrical Eng. & Systems 2023-06-05 Tal Peer , Simon Welker , Timo Gerkmann

We consider the problem of finding a low rank symmetric matrix satisfying a system of linear equations, as appears in phase retrieval. In particular, we solve the gauge dual formulation, but use a fast approximation of the spectral…

Optimization and Control · Mathematics 2020-06-02 Ron Estrin , Yifan Sun , Halyun Jeong , Michael Friedlander

Traditional halftoning usually drops colors when dithering images with binary dots, which makes it difficult to recover the original color information. We proposed a novel halftoning technique that converts a color image into a binary…

Computer Vision and Pattern Recognition · Computer Science 2024-02-08 Cheuk-Kit Lau , Menghan Xia , Tien-Tsin Wong

In the last five decades, iterative phase retrieval methods draw large amount of interest across the research community as a non-interferometric approach to recover quantitative phase distributions from one (or more) intensity measurement.…

Optics · Physics 2020-07-21 Nathaniel Hai , Joseph Rosen