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Algorithms for Sparse Signal Recovery in Compressed Sensing

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.advisor Ollila, Esa
dc.contributor.author Ejaz, Aqib
dc.date.accessioned 2015-06-24T11:33:11Z
dc.date.available 2015-06-24T11:33:11Z
dc.date.issued 2015-06-10
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/16850
dc.description.abstract Compressed sensing and sparse signal modeling have attracted considerable research interest in recent years. The basic idea of compressed sensing is that by exploiting the sparsity of a signal one can accurately represent the signal using fewer samples than those required with traditional sampling. This thesis reviews the fundamental theoretical results in compressed sensing regarding the required number of measurements and the structure of the measurement system. The main focus of this thesis is on algorithms that accurately recover the original sparse signal from its compressed set of measurements. A number of greedy algorithms for sparse signal recovery are reviewed and numerically evaluated. Convergence properties and error bounds of some of these algorithms are also reviewed. The greedy approach to sparse signal recovery is further extended to multichannel sparse signal model. A widely-used non-Bayesian greedy algorithm for the joint recovery of multichannel sparse signals is reviewed. In cases where accurate prior information about the unknown sparse signals is available, Bayesian estimators are expected to outperform non-Bayesian estimators. A Bayesian minimum mean-squared error (MMSE) estimator of the multichannel sparse signals with Gaussian prior is derived in closed-form. Since computing the exact MMSE estimator is infeasible due to its combinatorial complexity, a novel algorithm for approximating the multichannel MMSE estimator is developed in this thesis. In comparison to the widely-used non-Bayesian algorithm, the developed Bayesian algorithm shows better performance in terms of mean-squared error and probability of exact support recovery. The algorithm is applied to direction-of-arrival estimation with sensor arrays and image denoising, and is shown to provide accurate results in these applications. en
dc.format.extent 9+65
dc.format.mimetype application/pdf en
dc.language.iso en en
dc.title Algorithms for Sparse Signal Recovery in Compressed Sensing en
dc.type G2 Pro gradu, diplomityö en
dc.contributor.school Sähkötekniikan korkeakoulu fi
dc.subject.keyword compressed sensing en
dc.subject.keyword sparse modeling en
dc.subject.keyword greedy algorithms en
dc.subject.keyword MMSE en
dc.subject.keyword Bayesian en
dc.subject.keyword multichannel sparse recovery en
dc.identifier.urn URN:NBN:fi:aalto-201506303499
dc.programme.major Signal Processing fi
dc.programme.mcode S3013 fi
dc.type.ontasot Master's thesis en
dc.type.ontasot Diplomityö fi
dc.contributor.supervisor Koivunen, Visa
dc.programme TLT - Master’s Programme in Communications Engineering fi
dc.location P1 fi
local.aalto.openaccess yes
dc.rights.accesslevel openAccess
local.aalto.idinssi 51907
dc.type.publication masterThesis
dc.type.okm G2 Pro gradu, diplomityö

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