Weighted-minimization has been studied as a technique for the reconstruction of a sparse
signal from compressively sampled measurements when prior information about the signal …

We consider the problem of recovering a sparse signal from underdetermined
measurements when we have prior information about the sparsity structure of the signal. In …

We study the graph clustering problem where each observation (edge or no-edge between
a pair of nodes) may have a different level of confidence/uncertainty. We propose a …

We proposed a simple and efficient iteratively reweighted algorithm with iterative support set
to improve the recover performance for compressive sensing (CS). The numerical …

Recent work by Rauhut and Ward developed a notion of weighted sparsity and a
corresponding notion of Restricted Isometry Property for the space of weighted sparse …

Compressed Sensing refers to extracting a low-dimensional structured signal of interest from
its incomplete random linear observations. A line of recent work has studied that, with the …

Sparse representations accurately model many real-world data sets. Some form of sparsity
is conceivable in almost every practical application, from image and video processing, to …

This dissertation focuses on sparse representation and dictionary learning, with three
relative topics. First, in chapter 1, we study the problem of low-rank matrix recovery in the …

Traditional signal processing schemes sample signals at a high rate and immediately
discard most of the information during the compression process. By exploiting the fact that …

Due to the rapidly increasing dimensionality of modern datasets many classical
approximation algorithms have run into severe computational bottlenecks. This has often …