Related papers: Structured Random Model for Fast and Robust Phase …
Fourier phase retrieval is a classical problem of restoring a signal only from the measured magnitude of its Fourier transform. Although Fienup-type algorithms, which use prior knowledge in both spatial and Fourier domains, have been widely…
Phase retrieval, the problem of recovering lost phase information from measured intensity alone, is an inverse problem that is widely faced in various imaging modalities ranging from astronomy to nanoscale imaging. The current process of…
Fourier domain structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation and wavelet regularization. These priors specify that a convolutional structured matrix,…
Image stacks provide invaluable 3D information in various biological and pathological imaging applications. Fourier ptychographic microscopy (FPM) enables reconstructing high-resolution, wide field-of-view image stacks without z-stack…
In this short note, we consider the worst case noise robustness of any phase retrieval algorithm which aims to reconstruct all nonvanishing vectors $\mathbf{x} \in \mathbb{C}^d$ (up to a single global phase multiple) from the magnitudes of…
The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science. Fourier phase retrieval poses fundamental theoretical and…
Measurements achieved with ptychographic imaging are a special case of diffraction measurements. They are generated by illuminating small parts of a sample with, e.g., a focused X-ray beam. By shifting the sample, a set of far-field…
Phase retrieval (PR) concerns the recovery of complex phases from complex magnitudes. We identify the connection between the difficulty level and the number and variety of symmetries in PR problems. We focus on the most difficult far-field…
The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, speech recognition, quantum mechanics and,…
We introduce an adaptive structured low rank algorithm to recover MR images from their undersampled Fourier coefficients. The image is modeled as a combination of a piecewise constant component and a piecewise linear component. The Fourier…
Diffusion Probabilistic Models (DPMs) have been recently utilized to deal with various blind image restoration (IR) tasks, where they have demonstrated outstanding performance in terms of perceptual quality. However, the task-specific…
We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…
In this paper we tackle the problem of recovering the phase of complex linear measurements when only magnitude information is available and we control the input. We are motivated by the recent development of dedicated optics-based hardware…
Photoacoustic tomography is a hybrid imaging technique that combines high optical tissue contrast with high ultrasound resolution. Direct reconstruction methods such as filtered backprojection, time reversal and least squares suffer from…
Phase recovery from intensity-only measurements forms the heart of coherent imaging techniques and holography. Here we demonstrate that a neural network can learn to perform phase recovery and holographic image reconstruction after…
We propose neural network layers that explicitly combine frequency and image feature representations and show that they can be used as a versatile building block for reconstruction from frequency space data. Our work is motivated by the…
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…
Fourier ptychographic microscopy (FPM) is a pivotal computational imaging technique that achieves phase and amplitude reconstruction with high resolution and wide field of view, using low numerical aperture objectives and LED array…
We present the first phase retrieval algorithm guaranteed to solve the multidimensional phase retrieval problem in polynomial arithmetic complexity without prior information. The method successfully terminates in O(N log(N)) operations for…
Classical phase retrieval problem is the recovery of a constrained image from the magnitude of its Fourier transform. Although there are several well-known phase retrieval algorithms including the hybrid input-output (HIO) method, the…