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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

A simple coherent-imaging method due to Paganin et al. is widely employed for phase-amplitude reconstruction of samples using a single paraxial x-ray propagation-based phase-contrast image. The method assumes that the sample-to-detector…

Optical imaging plays a critical role in advancing our understanding of three dimensional dynamics of biological systems. Coherent imaging (CI) methods exploit spatial phase information, encoded through propagation of coherent signal light…

Optics · Physics 2015-07-24 Jeffrey J. Field , David G. Winters , Randy A. Bartels

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

Extracting as much information as possible about an object when probing with a limited number of photons is an important goal with applications from biology and security to metrology. Imaging with a few photons is a challenging task as the…

We demonstrate high-resolution non-iterative holographic coherent diffraction imaging with hard X-rays using a novel phase-shifting reference, fabricated by atomic layer deposition to produce nanosharp 3D structure. The method surpasses the…

Mesoscale and Nanoscale Physics · Physics 2016-10-17 Mirna Saliba , Jeroen Bosgra , Christoph Rau , Christian David , Aaron D. Parsons , Ulrich H. Wagner , Pierre Thibault

Based on phase retrieval, lensless coherent imaging and in particular holography offers quantitative phase and amplitude images. This is of particular importance for spectral ranges where suitable lenses are challenging, such as for hard…

Image and Video Processing · Electrical Eng. & Systems 2022-09-01 Simon Huhn , Leon Merten Lohse , Jens Lucht , Tim Salditt

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…

We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known…

Computational Physics · Physics 2019-02-06 T. Ramos , Bastian E. Grønager , Martin Skovgaard Andersen , J. W. Andreasen

Coherent Diffraction Imaging (CDI), a technique where an object is reconstructed from a single (2D or 3D) diffraction pattern, recovers the lost diffraction phases without a priori knowledge of the extent (support) of the object, which…

Materials Science · Physics 2020-08-27 Vincent Favre-Nicolin , Steven Leake , Yuriy Chushkin

Phase retrieval, a long-established challenge for recovering a complex-valued signal from its Fourier intensity measurements, has attracted significant interest because of its far-flung applications in optical imaging. To enhance accuracy,…

Signal Processing · Electrical Eng. & Systems 2023-05-16 Qiuliang Ye , Bingo Wing-Kuen Ling , Li-Wen Wang , Daniel Pak-Kong Lun

Low-light image enhancement is a classical computer vision problem aiming to recover normal-exposure images from low-light images. However, convolutional neural networks commonly used in this field are good at sampling low-frequency local…

Computer Vision and Pattern Recognition · Computer Science 2022-09-19 Yunliang Zhuang , Zhuoran Zheng , Chen Lyu

Fourier imaging is an indirect imaging method which records the diffraction pattern of the object scene coherently in the focal plane of the imaging system and reconstructs the image using computational resources. The spatial resolution,…

Optics · Physics 2023-06-05 Hui Yuan , Alvydas Lisauskas , Mark D. Thomson , Hartmut G. Roskos

In this paper, a new phase-retrieval algorithm from an X-ray schlieren image is proposed. The schlieren method allows phase-contrast imaging with an objective lens and a knife-edge filter placed at the back focal plane of the objective.…

In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex…

Information Theory · Computer Science 2017-01-10 David Gross , Felix Krahmer , Richard Kueng

The one-dimensional phase retrieval problem consists in the recovery of a complex-valued signal from its Fourier intensity. Due to the well-known ambiguousness of this problem, the determination of the original signal within the extensive…

Numerical Analysis · Mathematics 2021-03-19 Robert Beinert

Quantitative phase imaging (QPI) is important in many applications such as microscopy and crystallography. To quantitatively reveal phase information, people could either employ interference to map phase distribution into intensity fringes,…

Optics · Physics 2020-11-11 Xianye Li , Yafei sun , Yikang He , Xun Li , Baoqing Sun

We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…

Numerical Analysis · Mathematics 2024-07-11 Robert Beinert , Michael Quellmalz

We demonstrate a novel imaging approach and associated reconstruction algorithm for far-field coherent diffractive imaging, based on the measurement of a pair of laterally sheared diffraction patterns. The differential phase profile…

Optics · Physics 2018-05-23 G. S. M. Jansen , A. C. C. de Beurs , X. Liu , K. S. E. Eikema , S. Witte

Coherent X-ray photons with energies higher than 50 keV offer new possibilities for imaging nanoscale lattice distortions in bulk crystalline materials using Bragg peak phase retrieval methods. However, the compression of reciprocal space…

Signal Processing · Electrical Eng. & Systems 2018-08-14 Siddharth Maddali , Irene Calvo-Almazan , Jonathan Almer , Peter Kenesei , Jun-Sang Park , Ross Harder , Youssef Nashed , Stephan Hruszkewycz