Related papers: Undersampled Phase Retrieval with Outliers

This paper introduces Laplace techniques for designing a neural network, with the goal of estimating simplex-constraint sparse vectors from compressed measurements. To this end, we recast the problem of MMSE estimation (w.r.t. a pre-defined…

We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…

Reconstruction of magnetic resonance imaging (MRI) data has been positively affected by deep learning. A key challenge remains: to improve generalisation to distribution shifts between the training and testing data. Most approaches aim to…

Undersampling the k-space during MR acquisitions saves time, however results in an ill-posed inversion problem, leading to an infinite set of images as possible solutions. Traditionally, this is tackled as a reconstruction problem by…

In this paper, we tackle the compressive phase retrieval problem in the presence of noise. The noisy compressive phase retrieval problem is to recover a $K$-sparse complex signal $s \in \mathbb{C}^n$, from a set of $m$ noisy quadratic…

Sparse channel estimation for massive multiple-input multiple-output systems has drawn much attention in recent years. The required pilots are substantially reduced when the sparse channel state vectors can be reconstructed from a few…

So-called sparse estimators arise in the context of model fitting, when one a priori assumes that only a few (unknown) model parameters deviate from zero. Sparsity constraints can be useful when the estimation problem is under-determined,…

We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…

In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of…

Anomalies and outliers are common in real-world data, and they can arise from many sources, such as sensor faults. Accordingly, anomaly detection is important both for analyzing the anomalies themselves and for cleaning the data for further…

Multiplicative noise (also known as speckle noise) models are central to the study of coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. These models introduce two additional layers of…

The 2D phase unwrapping problem seeks to recover a phase image from its observation modulo 2$\pi$, and is a crucial step in a variety of imaging applications. In particular, it is one of the most time-consuming steps in the interferometric…

This paper considers phase retrieval from the magnitude of 1D over-sampled Fourier measurements, a classical problem that has challenged researchers in various fields of science and engineering. We show that an optimal vector in a…

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

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…

This paper fortifies the recently introduced hierarchical-optimization recursive least squares (HO-RLS) against outliers which contaminate infrequently linear-regression models. Outliers are modeled as nuisance variables and are estimated…

We estimate $n$ phases (angles) from noisy pairwise relative phase measurements. The task is modeled as a nonconvex least-squares optimization problem. It was recently shown that this problem can be solved in polynomial time via convex…

This work addresses the recovery and demixing problem of signals that are sparse in some general dictionary. Involved applications include source separation, image inpainting, super-resolution, and restoration of signals corrupted by…

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…

In this paper, we present an algorithm for effectively reconstructing an object from a set of its tomographic projections without any knowledge of the viewing directions or any prior structural information, in the presence of pathological…