English
Related papers

Related papers: Adapted variable density subsampling for compresse…

200 papers

Reducing acquisition time is a crucial challenge for many imaging techniques. Compressed Sensing (CS) theory offers an appealing framework to address this issue since it provides theoretical guarantees on the reconstruction of sparse…

Applications · Statistics 2014-07-17 Nicolas Chauffert , Philippe Ciuciu , Jonas Kahn , Pierre Weiss

We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm…

Statistics Theory · Mathematics 2020-09-04 Benjamin Aubin , Bruno Loureiro , Antoine Baker , Florent Krzakala , Lenka Zdeborová

Computational capability often falls short when confronted with massive data, posing a common challenge in establishing a statistical model or statistical inference method dealing with big data. While subsampling techniques have been…

Methodology · Statistics 2024-10-31 Yixiao Ruan , Zan Li , Zhaohui Li , Dennis K. J. Lin , Qingpei Hu , Dan Yu

We discuss a novel sparsity prior for compressive imaging in the context of the theory of compressed sensing with coherent redundant dictionaries, based on the observation that natural images exhibit strong average sparsity over multiple…

Information Theory · Computer Science 2013-05-03 Rafael E. Carrillo , Jason D. McEwen , Dimitri Van De Ville , Jean-Philippe Thiran , Yves Wiaux

This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized…

Statistics Theory · Mathematics 2020-07-07 Xiaowei Yang , Huiming Zhang , Haoyu Wei , Shouzheng Zhang

A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a…

Machine Learning · Statistics 2010-02-08 Michael B. Wakin

This paper exploits recent developments in compressive sensing (CS) to efficiently perform the direction finding via amplitude comprarison. The new method is proposed based on unimodal characteristic of antenna pattern and sparse property…

Information Theory · Computer Science 2010-06-25 Ruiming Yang , Yipeng Liu , Qun Wan , Wanlin Yang

In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…

Information Theory · Computer Science 2016-08-24 Susanne Sparrer , Robert F. H. Fischer

Radio channels are typically sparse in the delay domain, and ideal for compressed sensing. A new compressed sensing algorithm called eX-OMP is developed that yields performance similar to that of the optimal MMSE estimator. The new…

Information Theory · Computer Science 2016-12-23 Jonathan Ling , Dmitry Chizhik , A. Tulino , Inaki Esnaola

We consider the problem of deciding on sampling strategy, in particular sampling design. We propose a risk measure, whose minimizing value guides the choice. The method makes use of a superpopulation model and takes into account uncertainty…

Methodology · Statistics 2020-07-06 Edgar Bueno , Dan Hedlin

In this paper, we exploit the theory of compressive sensing to perform detection of a random source in a dense sensor network. When the sensors are densely deployed, observations at adjacent sensors are highly correlated while those…

Information Theory · Computer Science 2017-07-27 Thakshila Wimalajeewa , Pramod K. Varshney

In this work, we formulate the fixed-length distribution matching as a Bayesian inference problem. Our proposed solution is inspired from the compressed sensing paradigm and the sparse superposition (SS) codes. First, we introduce sparsity…

Information Theory · Computer Science 2018-11-27 Mohamad Dia , Vahid Aref , Laurent Schmalen

The problem of minimization of the number of measurements needed for digital image acquisition and reconstruction with a given accuracy is addressed. Basics of the sampling theory are outlined to show that the lower bound of signal sampling…

Computer Vision and Pattern Recognition · Computer Science 2018-03-01 Leonid P. Yaroslavsky

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

The weak-$\ell^p$ norm can be used to define a measure $s$ of sparsity. When we compute $s$ for the discrete cosine transform coefficients of a signal, the value of $s$ is related to the information content of said signal. We use this value…

Information Theory · Computer Science 2020-02-25 Alfredo Nava-Tudela

In the problem of adaptive compressed sensing, one wants to estimate an approximately $k$-sparse vector $x\in\mathbb{R}^n$ from $m$ linear measurements $A_1 x, A_2 x,\ldots, A_m x$, where $A_i$ can be chosen based on the outcomes $A_1…

Data Structures and Algorithms · Computer Science 2018-04-26 Vasileios Nakos , Xiaofei Shi , David P. Woodruff , Hongyang Zhang

It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…

Methodology · Statistics 2007-11-13 Emmanuel J. Candes , Michael B. Wakin , Stephen P. Boyd

The linear inverse source and scattering problems are studied from the perspective of compressed sensing, in particular the idea that sufficient incoherence and sparsity guarantee uniqueness of the solution. By introducing the sensor as…

Data Analysis, Statistics and Probability · Physics 2009-05-19 Albert Fannjiang , Pengchong Yan , Thomas Strohmer

Consider the problem of recovering an unknown signal from undersampled measurements, given the knowledge that the signal has a sparse representation in a specified dictionary $D$. This problem is now understood to be well-posed and…

Information Theory · Computer Science 2015-06-09 Felix Krahmer , Deanna Needell , Rachel Ward

Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a…

Information Theory · Computer Science 2014-07-08 Felix Krahmer , Holger Rauhut