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Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representations. When such a signal is acquired according to the principles of CS, the measurements still…

Information Theory · Computer Science 2019-11-19 Arman Arian , Ozgur Yilmaz

Recovering sparse signals from linear measurements has demonstrated outstanding utility in a vast variety of real-world applications. Compressive sensing is the topic that studies the associated raised questions for the possibility of a…

Optimization and Control · Mathematics 2020-07-24 Ahmad Mousavi , Mehdi Rezaee , Ramin Ayanzadeh

A recently designed hyperspectral imaging device enables multiplexed acquisition of an entire data volume in a single snapshot thanks to monolithically-integrated spectral filters. Such an agile imaging technique comes at the cost of a…

Computer Vision and Pattern Recognition · Computer Science 2015-02-09 K. Degraux , V. Cambareri , L. Jacques , B. Geelen , C. Blanch , G. Lafruit

The best practical techniques for exact solution of instances of the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a branch-and-bound framework, working with a…

Optimization and Control · Mathematics 2024-02-19 Zhongzhu Chen , Marcia Fampa , Jon Lee

We study the problem of reconstructing a signal from its projection on a subspace. The proposed signal reconstruction algorithms utilize a guiding subspace that represents desired properties of reconstructed signals. We show that optimal…

Information Theory · Computer Science 2016-06-13 Akshay Gadde , Andrew Knyazev , Dong Tian , Hassan Mansour

Compressed sensing (CS) exploits the sparsity of a signal in order to integrate acquisition and compression. CS theory enables exact reconstruction of a sparse signal from relatively few linear measurements via a suitable nonlinear…

Information Theory · Computer Science 2014-09-04 Shmuel Friedland , Qun Li , Dan Schonfeld , Edgar A. Bernal

Quantized compressive sensing (QCS) deals with the problem of representing compressive signal measurements with finite precision representation, i.e., a mandatory process in any practical sensor design. To characterize the signal…

Information Theory · Computer Science 2018-05-14 Chunlei Xu , Vincent Schellekens , Laurent Jacques

Compressed sensing (CS) provides an elegant framework for recovering sparse signals from compressed measurements. For example, CS can exploit the structure of natural images and recover an image from only a few random measurements. CS is…

Machine Learning · Computer Science 2019-05-21 Yan Wu , Mihaela Rosca , Timothy Lillicrap

This paper provides an extension of compressed sensing which bridges a substantial gap between existing theory and its current use in real-world applications. It introduces a mathematical framework that generalizes the three standard…

Information Theory · Computer Science 2014-06-24 Ben Adcock , Anders C. Hansen , Clarice Poon , Bogdan Roman

Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…

Information Theory · Computer Science 2013-04-04 Jean Barbier , Florent Krzakala , Marc Mézard , Lenka Zdeborová

Linear inverse problems are ubiquitous in various science and engineering disciplines. Of particular importance in the past few decades, is the incorporation of sparsity based priors, in particular $\ell_1$ priors, into linear inverse…

Statistics Theory · Mathematics 2025-03-04 Ryan O'Dowd , Raghu G. Raj , Hrushikesh N. Mhaskar

We address the problem of image reconstruction from incomplete measurements, encompassing both upsampling and inpainting, within a learning-based framework. Conventional supervised approaches require fully sampled ground truth data, while…

Computer Vision and Pattern Recognition · Computer Science 2026-03-23 Benjamin Walder , Daniel Toader , Robert Nuster , Günther Paltauf , Peter Burgholzer , Gregor Langer , Lukas Krainer , Markus Haltmeier

We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal…

Computer Vision and Pattern Recognition · Computer Science 2015-06-11 Virginia Estellers , Jean-Philippe Thiran , Xavier Bresson

We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…

Information Theory · Computer Science 2015-03-19 David L. Donoho , Adel Javanmard , Andrea Montanari

Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. The difficulty of a reconstruction problem depends on multiple factors, such as the ground…

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

We introduce the broad subclass of algebraic compressed sensing problems, where structured signals are modeled either explicitly or implicitly via polynomials. This includes, for instance, low-rank matrix and tensor recovery. We employ…

Numerical Analysis · Mathematics 2024-07-02 Paul Breiding , Fulvio Gesmundo , Mateusz Michałek , Nick Vannieuwenhoven

This paper deals with numerical methods for reconstruction of inhomogeneous conductivities. We use the concept of Generalized Polarization Tensors, which were introduced in [3], to do reconstruction. Basic resolution and stability analysis…

Analysis of PDEs · Mathematics 2015-10-28 Xiaoping Fang , Youjun Deng

This paper considers the problem of optimum reconstruction in generalized sampling-reconstruction processes (GSRPs). We propose constrained GSRP, a novel framework that minimizes the reconstruction error for inputs in a subspace, subject to…

Signal Processing · Electrical Eng. & Systems 2019-10-23 Bashir Sadeghi , Runyi Yu , Vishnu Naresh Boddeti

We use compressed sensing to demonstrate theoretically the reconstruction of sub-wavelength features from measured far-field, and provide experimental proof-of-concept. The methods can be applied to non-optical microscopes, provided the…

Optics · Physics 2015-05-14 Snir Gazit , Alexander Szameit , Yonina C. Eldar , Mordechai Segev

Deep generative models have become a standard for modeling priors for inverse problems, going beyond classical sparsity-based methods. However, existing theoretical guarantees are mostly confined to finite-dimensional vector spaces,…

Numerical Analysis · Mathematics 2026-03-04 Paolo Angella , Vito Paolo Pastore , Matteo Santacesaria