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In a recent paper by A. Chambolle et al. [Geometric properties of solutions to the total variation denoising problem. Inverse Problems 33, 2017] it was proven that if the subgradient of the total variation at the noise free data is not…

Optimization and Control · Mathematics 2021-06-09 José A. Iglesias , Gwenael Mercier , Otmar Scherzer

In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…

Data Structures and Algorithms · Computer Science 2013-04-19 Rong Jin , Tianbao Yang , Shenghuo Zhu

We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. It has been shown that exact recovery is possible by…

Optimization and Control · Mathematics 2023-07-06 Stéphane Chrétien , Andrew Thompson , Bogdan Toader

We study recovery of amplitudes and nodes of a finite impulse train from noisy frequency samples. This problem is known as super-resolution under sparsity constraints and has numerous applications. An especially challenging scenario occurs…

Numerical Analysis · Mathematics 2023-03-28 Rami Katz , Nuha Diab , Dmitry Batenkov

We study the problem of super-resolution of a linear combination of Dirac distributions and their derivatives on a one-dimensional circle from noisy Fourier measurements. Following numerous recent works on the subject, we consider the…

Numerical Analysis · Mathematics 2023-03-21 Dmitry Batenkov , Nuha Diab

In compressed sensing the goal is to recover a signal from as few as possible noisy, linear measurements. The general assumption is that the signal has only a few non-zero entries. The recovery can be performed by multiple different…

Information Theory · Computer Science 2020-10-07 Hendrik Bernd Petersen , Bubacarr Bah , Peter Jung

In this paper we theoretically study exact recovery of sparse vectors from compressed measurements by minimizing a general nonconvex function that can be decomposed into the sum of single variable functions belonging to a class of smooth…

Information Theory · Computer Science 2020-10-21 Samrat Mukhopadhyay

Recent advances have demonstrated the possibility of solving the deconvolution problem without prior knowledge of the noise distribution. In this paper, we study the repeated measurements model, where information is derived from multiple…

Statistics Theory · Mathematics 2024-09-04 Jérémie Capitao-Miniconi , Elisabeth Gassiat , Luc Lehéricy

This paper is concerned with the fundamental problem of estimating chirp parameters from a mixture of linear chirp signals. Unlike most previous methods, which solve the problem by discretizing the parameter space and then estimating the…

Signal Processing · Electrical Eng. & Systems 2025-03-20 Dehui Yang , Feng Xi

This article studies the denoising performance of total variation (TV) image regularization. More precisely, we study geometrical properties of the solution to the so-called Rudin-Osher-Fatemi total variation denoising method. The first…

Optimization and Control · Mathematics 2016-12-21 Antonin Chambolle , Vincent Duval , Gabriel Peyré , Clarice Poon

The Procrustes matching (PM) problem is the problem of finding the optimal rigid motion and labeling of two point sets so that they are as close as possible. Both rigid and non-rigid shape matching problems can be formulated as PM problems.…

Optimization and Control · Mathematics 2017-11-30 Nadav Dym , Yaron Lipman

Diffusion models have established new state of the art in a multitude of computer vision tasks, including image restoration. Diffusion-based inverse problem solvers generate reconstructions of exceptional visual quality from heavily…

Image and Video Processing · Electrical Eng. & Systems 2024-08-21 Zalan Fabian , Berk Tinaz , Mahdi Soltanolkotabi

This paper considers the problem of recovering a one or two dimensional discrete signal which is approximately sparse in its discrete gradient from an incomplete subset of its discrete Fourier coefficients which have been corrupted with…

Numerical Analysis · Mathematics 2015-06-10 Clarice Poon

This paper investigates total variation minimization in one spatial dimension for the recovery of gradient-sparse signals from undersampled Gaussian measurements. Recently established bounds for the required sampling rate state that uniform…

Information Theory · Computer Science 2022-04-12 Martin Genzel , Maximilian März , Robert Seidel

This paper considers the use of total variation regularization in the recovery of approximately gradient sparse signals from their noisy discrete Fourier samples in the context of compressed sensing. It has been observed over the last…

Numerical Analysis · Mathematics 2014-07-22 Clarice Poon

Subsampled blind deconvolution is the recovery of two unknown signals from samples of their convolution. To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in…

Information Theory · Computer Science 2015-11-23 Kiryung Lee , Yanjun Li , Marius Junge , Yoram Bresler

One-bit compressed sensing (1bCS) addresses the recovery of sparse signals from highly quantized measurements, retaining only the sign of each linear measurement. In the support recovery setting, the goal is to identify $\text{supp}(x)$,…

Information Theory · Computer Science 2026-04-14 Xiaxin Li , Arya Mazumdar

Sparse signal recovery based on nonconvex and nonsmooth optimization problems has significant applications and demonstrates superior performance in signal processing and machine learning. This work deals with a scale-invariant…

Optimization and Control · Mathematics 2025-09-29 Lang Yu , Nanjing Huang

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…

Information Theory · Computer Science 2012-06-26 Galen Reeves , Michael Gastpar

The recovery of unknown signals from quadratic measurements finds extensive applications in fields such as phase retrieval, power system state estimation, and unlabeled distance geometry. This paper investigates the finite sample properties…

Statistics Theory · Mathematics 2026-04-15 Jun Fan , Jingyu Yang , Xinyu Zhang , Liqun Wang