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Compressed sensing is an imaging paradigm that allows one to invert an underdetermined linear system by imposing the a priori knowledge that the sought after solution is sparse (i.e., mostly zeros). Previous works have shown that if one…

Image and Video Processing · Electrical Eng. & Systems 2023-12-05 Nicholas Dwork , Erin K. Englund

Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…

Numerical Analysis · Mathematics 2018-01-08 Lenny Fukshansky , Deanna Needell , Benny Sudakov

Federated learning is a privacy-preserving approach to train a global model at a central server by collaborating with wireless devices, each with its own local training data set. In this paper, we present a compressive sensing approach for…

Signal Processing · Electrical Eng. & Systems 2020-08-06 Yo-Seb Jeon , Mohammad Mohammadi Amiri , Jun Li , H. Vincent Poor

Compressed sensing is a scheme that allows for sparse signals to be acquired, transmitted and stored using far fewer measurements than done by conventional means employing Nyquist sampling theorem. Since many naturally occurring signals are…

Signal Processing · Electrical Eng. & Systems 2023-03-29 Aditi Kathpalia , Nithin Nagaraj

Inspired by significant real-life applications, in particular, sparse phase retrieval and sparse pulsation frequency detection in Asteroseismology, we investigate a general framework for compressed sensing, where the measurements are…

Numerical Analysis · Mathematics 2017-09-04 Martin Ehler , Massimo Fornasier , Juliane Sigl

Compressed Sensing aims to capture attributes of $k$-sparse signals using very few measurements. In the standard Compressed Sensing paradigm, the $\m\times \n$ measurement matrix $\A$ is required to act as a near isometry on the set of all…

Information Theory · Computer Science 2015-05-14 Robert Calderbank , Stephen Howard , Sina Jafarpour

The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry…

Optimization and Control · Mathematics 2017-08-29 Angang Cui , Jigen Peng , Haiyang Li

Traditional compressed sensing considers sampling a 1D signal. For a multidimensional signal, if reshaped into a vector, the required size of the sensing matrix becomes dramatically large, which increases the storage and computational…

Information Theory · Computer Science 2016-11-17 Hao Fang , Sergiy A. Vorobyov , Hai Jiang , Omid Taheri

A new class of cost functionals for optimal control of quantum systems which produces controls which are sparse in frequency and smooth in time is proposed. This is achieved by penalizing a suitable time-frequency representation of the…

Optimization and Control · Mathematics 2016-07-15 Gero Friesecke , Felix Henneke , Karl Kunisch

Compressive sensing (CS) is a signal processing technique that enables sub-Nyquist sampling and near lossless reconstruction of a sparse signal. The technique is particularly appealing for neural signal processing since it avoids the issues…

Signal Processing · Electrical Eng. & Systems 2021-02-02 Hyunseok Park , Xilin Liu

Motivated by applications in unsourced random access, this paper develops a novel scheme for the problem of compressed sensing of binary signals. In this problem, the goal is to design a sensing matrix $A$ and a recovery algorithm, such…

Information Theory · Computer Science 2021-09-21 Elad Romanov , Or Ordentlich

We propose a sampling-based trajectory optimization methodology for constrained problems. We extend recent works on stochastic search to deal with box control constraints,as well as nonlinear state constraints for discrete dynamical…

Optimization and Control · Mathematics 2019-11-13 George I. Boutselis , Ziyi Wang , Evangelos A. Theodorou

We consider the problem of reconstructing time sequences of spatially sparse signals (with unknown and time-varying sparsity patterns) from a limited number of linear "incoherent" measurements, in real-time. The signals are sparse in some…

Information Theory · Computer Science 2016-11-17 Namrata Vaswani

Bagging, a powerful ensemble method from machine learning, improves the performance of unstable predictors. Although the power of Bagging has been shown mostly in classification problems, we demonstrate the success of employing Bagging in…

Machine Learning · Statistics 2019-05-03 Luoluo Liu , Sang Peter Chin , Trac D. Tran

This paper considers a simple on-off random multiple access channel, where n users communicate simultaneously to a single receiver over m degrees of freedom. Each user transmits with probability lambda, where typically lambda n < m << n,…

Information Theory · Computer Science 2009-03-09 Alyson K. Fletcher , Sundeep Rangan , Vivek K Goyal

Recovering a sparse signal from an undersampled set of random linear measurements is the main problem of interest in compressed sensing. In this paper, we consider the case where both the signal and the measurements are complex. We study…

Information Theory · Computer Science 2015-03-19 Arian Maleki , Laura Anitori , Zai Yang , Richard Baraniuk

Parsimony in signal representation is a topic of active research. Sparse signal processing and representation is the outcome of this line of research which has many applications in information processing and has shown significant…

Computer Vision and Pattern Recognition · Computer Science 2018-05-15 Hojjat Seyed Mousavi

The least squares problem with L1-regularized regressors, called Lasso, is a widely used approach in optimization problems where sparsity of the regressors is desired. This formulation is fundamental for many applications in signal…

Optimization and Control · Mathematics 2021-04-26 Andreea B. Alexandru , Anastasios Tsiamis , George J. Pappas

We introduce the sparse direct sampling method (DSM) to estimate properties of a region from signals that probe the region. We demonstrate the sparse-DSM on two separate problems: estimating both the angle-of-arrival of a radio wave…

Analysis of PDEs · Mathematics 2020-10-19 Isaac Harris , Jacob D Rezac

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