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dc.contributor.advisorAl-Naffouri, Tareq Y.
dc.contributor.authorAlrashdi, Ayed
dc.date.accessioned2016-12-04T13:01:24Z
dc.date.available2016-12-04T13:01:24Z
dc.date.issued2016-11
dc.identifier.doi10.25781/KAUST-67083
dc.identifier.urihttp://hdl.handle.net/10754/621924
dc.description.abstractThe amount of data that has been measured, transmitted/received, and stored in the recent years has dramatically increased. So, today, we are in the world of big data. Fortunately, in many applications, we can take advantages of possible structures and patterns in the data to overcome the curse of dimensionality. The most well known structures include sparsity, low-rankness, block sparsity. This includes a wide range of applications such as machine learning, medical imaging, signal processing, social networks and computer vision. This also led to a specific interest in recovering signals from noisy compressed measurements (Compressed Sensing (CS) problem). Such problems are generally ill-posed unless the signal is structured. The structure can be captured by a regularizer function. This gives rise to a potential interest in regularized inverse problems, where the process of reconstructing the structured signal can be modeled as a regularized problem. This thesis particularly focuses on finding the optimal regularization parameter for such problems, such as ridge regression, LASSO, square-root LASSO and low-rank Generalized LASSO. Our goal is to optimally tune the regularizer to minimize the mean-squared error (MSE) of the solution when the noise variance or structure parameters are unknown. The analysis is based on the framework of the Convex Gaussian Min-max Theorem (CGMT) that has been used recently to precisely predict performance errors.
dc.language.isoen
dc.subjectNon-parametric regression
dc.subjectRegularization
dc.subjectLeast squares
dc.subjectGeneralized LASSO
dc.subjectCGMT
dc.subjectStructured signals
dc.subjectBig data
dc.titleOn the MSE Performance and Optimization of Regularized Problems
dc.typeThesis
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
thesis.degree.grantorKing Abdullah University of Science and Technology
dc.contributor.committeememberAlouini, Mohamed-Slim
dc.contributor.committeememberLaleg-Kirati, Taous-Meriem
dc.contributor.committeememberBallal, Tarig
thesis.degree.disciplineElectrical Engineering
thesis.degree.nameMaster of Science
refterms.dateFOA2017-12-05T00:00:00Z


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