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The effectiveness of using model sparsity as a priori information when solving linear inverse problems is studied. We investigate the reconstruction quality of such a method in the non-idealized case and compute some typical recovery errors…

Numerical Analysis · Mathematics 2010-07-19 Ignace Loris , Caroline Verhoeven

The support recovery problem consists of determining a sparse subset of variables that is relevant in generating a set of observations. In this paper, we study the support recovery problem in the phase retrieval model consisting of noisy…

Information Theory · Computer Science 2020-09-29 Lan V. Truong , Jonathan Scarlett

Sparse phase retrieval with redundant dictionary is to reconstruct the signals of interest that are (nearly) sparse in a redundant dictionary or frame from the phaseless measurements via the optimization models. Gao [7] presented conditions…

Information Theory · Computer Science 2025-06-06 Haiye Huo , Li Xiao

We consider the problem of exact recovery of a $k$-sparse binary vector from generalized linear measurements (such as logistic regression). We analyze the linear estimation algorithm (Plan, Vershynin, Yudovina, 2017), and also show…

Machine Learning · Statistics 2025-02-25 Arya Mazumdar , Neha Sangwan

This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering…

Statistics Theory · Mathematics 2016-09-05 Rui M. Castro , Ervin Tánczos

One-bit compressive sensing (CS) is an advanced version of sparse recovery in which the sparse signal of interest can be recovered from extremely quantized measurements. Namely, only the sign of each measurement is available to us. In many…

Information Theory · Computer Science 2019-10-22 Hossein Beheshti , Sajad Daei , Farzan Haddadi

Compressed Sensing (CS) is an effective approach to reduce the required number of samples for reconstructing a sparse signal in an a priori basis, but may suffer severely from the issue of basis mismatch. In this paper we study the problem…

Information Theory · Computer Science 2014-02-04 Yuejie Chi

We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…

Information Theory · Computer Science 2015-06-17 Jeremy Vila , Philip Schniter

We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…

Optimization and Control · Mathematics 2023-01-19 Arthur Marmin , Marc Castella , Jean-Christophe Pesquet , Laurent Duval

Sparsity driven signal processing has gained tremendous popularity in the last decade. At its core, the assumption is that the signal of interest is sparse with respect to either a fixed transformation or a signal dependent dictionary. To…

Computer Vision and Pattern Recognition · Computer Science 2014-06-10 Yuanming Suo , Minh Dao , Umamahesh Srinivas , Vishal Monga , Trac D. Tran

Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…

Machine Learning · Computer Science 2020-03-23 Luiz F. O. Chamon , Yonina C. Eldar , Alejandro Ribeiro

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

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 joint sparse recovery problem is a generalization of the single measurement vector problem which is widely studied in Compressed Sensing and it aims to recovery a set of jointly sparse vectors. i.e. have nonzero entries concentrated at…

Information Theory · Computer Science 2017-01-10 Changlong Wang , Jigen Peng

In compressive sensing, a small collection of linear projections of a sparse signal contains enough information to permit signal recovery. Distributed compressive sensing (DCS) extends this framework by defining ensemble sparsity models,…

Information Theory · Computer Science 2013-03-29 Marco F. Duarte , Michael B. Wakin , Dror Baron , Shriram Sarvotham , Richard G. Baraniuk

In the paper, we proposed the Dantzig selector based on the $l_{p-q}$ ($0<p\leq1, 1<q\leq2$) minimization for the signal recovery. First, we establish the convex combination representation of sparse vectors under the $l_{p-q}$ minimization…

Optimization and Control · Mathematics 2024-01-26 Jie Li , Chaohong Deng , Baode Li

The task of finding a sparse signal decomposition in an overcomplete dictionary is made more complicated when the signal undergoes an unknown modulation (or convolution in the complementary Fourier domain). Such simultaneous sparse recovery…

Information Theory · Computer Science 2019-10-02 Youye Xie , Michael B. Wakin , Gongguo Tang

We propose a compressed sampling and dictionary learning framework for fiber-optic sensing using wavelength-tunable lasers. A redundant dictionary is generated from a model for the reflected sensor signal. Imperfect prior knowledge is…

Methodology · Statistics 2017-06-13 Christian Weiss , Abdelhak M. Zoubir

Sparse signal recovery problems from noisy linear measurements appear in many areas of wireless communications. In recent years, deep learning (DL) based approaches have attracted interests of researchers to solve the sparse linear inverse…

Signal Processing · Electrical Eng. & Systems 2021-01-28 Wei Chen , Bowen Zhang , Shi Jin , Bo Ai , Zhangdui Zhong

The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…

Optimization and Control · Mathematics 2019-07-24 Sophie M. Fosson , Mohammad Abuabiah