Compressive Sensing in Signal Processing: Performance Analysis and Applications
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.16.03.16Tesfamicael, 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