The 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.
| Identifer | oai:union.ndltd.org:kaust.edu.sa/oai:repository.kaust.edu.sa:10754/621924 |
| Date | 11 1900 |
| Creators | Alrashdi, Ayed |
| Contributors | Al-Naffouri, Tareq Y., Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division, Alouini, Mohamed-Slim, Laleg-Kirati, Taous-Meriem, Ballal, Tarig |
| Source Sets | King Abdullah University of Science and Technology |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Rights | 2017-12-05, At the time of archiving, the student author of this thesis opted to temporarily restrict access to it. The full text of this thesis became available to the public after the expiration of the embargo on 2017-12-05. |
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