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Compressive Sensing in Signal Processing: Performance Analysis and Applications

Tesfamicael, Solomon Abedom
Doctoral thesis
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URI
http://hdl.handle.net/11250/2399472
Date
2016
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Abstract
This thesis deals with an emerging area of signal processing, called Compressive Sensing (CS),

that allows the reconstruction of sparse or compressible signals from fewer measurements than

are used in traditional schemes. Like traditional signal representation schemes, CS follows a similar

framework: encoding, transmission/storing, and decoding. The encoding part is done using

random projection (RP) or random sensing, and the decoding is done via nonlinear reconstruction

algorithms from a reduced amount of measurements. The performance of the reconstruction

schemes used and the application of such paradigm are the two main focuses of the thesis. It

has three parts: the introduction, performance analysis of recovery algorithms in CS and some

applications of CS.

The introductory part provides the background for the following four chapters. It begins by defining

the basic concepts used in CS theory and presents the Bayesian framework. Further, an analytical

tool from statistical mechanics for performance analysis of physical systems is introduced

applied on a non-noisy CS problem. The Bayesian framework is given ample emphasis in the

thesis for two reasons. First, it serves as a bridge between the recovery algorithms used in CS

and a tool from the statistical mechanics, called the replica method. Second, it is used as main

framework to incorporate different prior signal information, like sparsity and clusteredness. Furthermore,

a short description of CS applications is given before the introduction concludes by

presenting the scope and the contribution of the thesis.

The second part of the thesis deals with the study of the performance of recovery methods in CS

systems using the Replica Method. At the beginning, the study of the performance of the recovery

algorithms in CS was focused on the ratio of the amount of measurement used, the sparsity

level, and how accurate the recovered information is. However, there was a luck of universal

performance analysis. The Replica method provides this by considering large size systems. This

thesis contributes to such analysis via the Bayesian framework. In this work noisy CS systems

are considered and the recovering algorithms are reinterpreted as a maximum a posteriori (MAP)

estimator. It, therefore, provides replica analysis including one step replica breaking ansatz for

CS systems as an extension of similar analysis done for other systems like multiple input/multiple

output (MIMO).

The CS application is the third part of the thesis. The theory of CS has been applied in many

signal processing fields such as image processing, communication, networks and so on. There

are hundreds, if not thousands of articles on this subject at present. In this thesis, there are novel

results that contribute to the application of CS theory. The theory is applied to limited feedback in

temporally correlated MIMO channels, where the sparsity property was used to reduce feedback

overhead significantly while delivering the same performance. Further, including another assumption,

i.e., more structure among the sparse entries, to the sparsity of signals, and modeling it as

a modified Laplacian prior in Bayesian setting, a novel way of compressive sensing is presented

in this thesis. It can have potential impact on medical imaging processing, especially to magnetic

resonance imaging (MRI).
Has parts
Tesfamicael, Solomon A. "Compressive Sensing Performance Analysis via Replica Method using the Bayesian Framework" International Journal of Simulation Systems, Science & Technology (IJSSST), vol. 16, no. 3, 2016. DOI 10.5013/IJSSST.a.16.03.16

Tesfamicael, Solomon Abedom; Barzideh, Faraz; Lundheim, Lars Magne. "Improved Reconstruction in Compressive Sensing of Clustered Signals." IEEE AFRICON 2015 http://dx.doi.org/10.1109/AFRCON.2015.7331947 (c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.

Tesfamicael, Solomon Abedom; Faraz, Barzideh. "Clustered Compressed Sensing Via Bayesian Framework. UKSim-AMSS 17th International Conference on Modeling and Simulation" (c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.

Tesfamicael, Solomon Abedom; Lundheim, Lars. "Compressed Sensing Based Rotative Quantization in Temporally Correlated MIMO Channels." Proceedings of Recent Developments on Signal Processing (RDSP) 2013
Publisher
NTNU
Series
Doctoral thesis at NTNU;2016:182

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