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Undersampled inverse problems occur everywhere in the sciences including medical imaging, radar, astronomy etc., yielding underdetermined linear or non-linear reconstruction problems. There are now a myriad of techniques to design decoders…

Optimization and Control · Mathematics 2023-11-29 Nina Maria Gottschling , Paolo Campodonico , Vegard Antun , Anders C. Hansen

In this paper, we propose a new algorithm of iterative least squared (LS) channel estimation for 64 antennas Massive Multiple Input, Multiple Output (MIMO) turbo-receiver. The algorithm employs log-likelihood ratios (LLR) of low-density…

Signal Processing · Electrical Eng. & Systems 2020-09-29 Alexander Osinsky , Andrey Ivanov , Dmitry Lakontsev , Roman Bychkov , Dmitry Yarotsky

Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…

Optimization and Control · Mathematics 2014-01-28 Christos Thrampoulidis , Samet Oymak , Babak Hassibi

In the standard Gaussian linear measurement model $Y=X\mu_0+\xi \in \mathbb{R}^m$ with a fixed noise level $\sigma>0$, we consider the problem of estimating the unknown signal $\mu_0$ under a convex constraint $\mu_0 \in K$, where $K$ is a…

Statistics Theory · Mathematics 2022-01-24 Qiyang Han

We study the multi-target detection problem of recovering a target signal from a noisy measurement that contains multiple copies of the signal at unknown locations. Motivated by the structure reconstruction problem in cryo-electron…

Signal Processing · Electrical Eng. & Systems 2022-05-17 Ye'Ela Shalit , Ran Weber , Asaf Abas , Shay Kreymer , Tamir Bendory

A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…

Information Theory · Computer Science 2012-05-22 Shirin Jalali , Arian Maleki , Richard Baraniuk

In this paper, we study a fast approximation method for {\it large-scale high-dimensional} sparse least-squares regression problem by exploiting the Johnson-Lindenstrauss (JL) transforms, which embed a set of high-dimensional vectors into a…

Statistics Theory · Mathematics 2015-07-21 Tianbao Yang , Lijun Zhang , Qihang Lin , Rong Jin

A distributed lossy compression network with $L$ encoders and a decoder is considered. Each encoder observes a source and sends a compressed version to the decoder. The decoder produces a joint reconstruction of target signals with the mean…

Information Theory · Computer Science 2022-06-06 Siyao Zhou , Sadaf Salehkalaibar , Jingjing Qian , Jun Chen , Wuxian Shi , Yiqun Ge , Wen Tong

It is now well understood that $\ell_1$ minimization algorithm is able to recover sparse signals from incomplete measurements [2], [1], [3] and sharp recoverable sparsity thresholds have also been obtained for the $\ell_1$ minimization…

Probability · Mathematics 2009-04-07 Weiyu Xu , M. Amin Khajehnejad , Salman Avestimehr , Babak Hassibi

Many applications have benefited remarkably from low-dimensional models in the recent decade. The fact that many signals, though high dimensional, are intrinsically low dimensional has given the possibility to recover them stably from a…

Information Theory · Computer Science 2015-07-29 Raja Giryes , Yaniv Plan , Roman Vershynin

We consider the problem of estimating an unknown signal $x_0$ from noisy linear observations $y = Ax_0 + z\in R^m$. In many practical instances, $x_0$ has a certain structure that can be captured by a structure inducing convex function…

Information Theory · Computer Science 2013-11-07 Samet Oymak , Christos Thrampoulidis , Babak Hassibi

We study compressive sensing with a deep generative network prior. Initial theoretical guarantees for efficient recovery from compressed linear measurements have been developed for signals in the range of a ReLU network with Gaussian…

Signal Processing · Electrical Eng. & Systems 2022-05-24 Jorio Cocola

In the undersampled phase retrieval problem, the goal is to recover an $N$-dimensional complex signal $\mathbf{x}$ from only $M<N$ noisy intensity measurements without phase information. This problem has drawn a lot of attention to reduce…

Information Theory · Computer Science 2017-10-11 Tianyu Qiu , Daniel P. Palomar

This paper studies the problem of recovering a signal vector and the corrupted noise vector from a collection of corrupted linear measurements through the solution of a l1 minimization, where the sensing matrix is a partial Fourier matrix…

Information Theory · Computer Science 2016-01-25 Dongcai Su

This work focuses on the reconstruction of sparse signals from their 1-bit measurements. The context is the one of 1-bit compressive sensing where the measurements amount to quantizing (dithered) random projections. Our main contribution…

Signal Processing · Electrical Eng. & Systems 2020-08-25 Thomas Feuillen , Mike Davies , Luc Vandendorpe , Laurent Jacques

We consider the problem of imaging sparse scenes from a few noisy data using an $l_1$-minimization approach. This problem can be cast as a linear system of the form $A \, \rho =b$, where $A$ is an $N\times K$ measurement matrix. We assume…

Image and Video Processing · Electrical Eng. & Systems 2020-04-22 Miguel Moscoso , Alexei Novikov , George Papanicolaou , Chrysoula Tsogka

We address the problem of reconstructing a multi-band signal from its sub-Nyquist point-wise samples. To date, all reconstruction methods proposed for this class of signals assumed knowledge of the band locations. In this paper, we develop…

Cellular Automata and Lattice Gases · Physics 2007-09-12 Moshe Mishali , Yonina C. Eldar

Inverse scattering from discrete targets with the single-input-multiple-output (SIMO), multiple-input-single-output (MISO) or multiple-input-multiple-output (MIMO) measurements is analyzed by compressed sensing theory with and without the…

Mathematical Physics · Physics 2015-05-13 Albert C. Fannjiang

In this paper, we study the sample complexity and develop efficient optimal algorithms for 1-bit phase retrieval: recovering a signal $\mathbf{x}\in\mathbb{R}^n$ from $m$ phaseless bits…

Information Theory · Computer Science 2025-12-18 Junren Chen , Ming Yuan

Our aim of this article is to reconstruct a signal from undersampled data in the situation that the signal is sparse in terms of a tight frame. We present a condition, which is independent of the coherence of the tight frame, to guarantee…

Numerical Analysis · Mathematics 2011-05-24 Song Li , Junhong Lin