Extracting Signals and Graphical Models from Compressed Measurements

Abstract

The thesis is to give an integrated approach to efficiently learn the interdependency relation among high dimensional signal components and reconstruct signals from observations collected in a linear sensing system, Broadly speaking, the research topics consists of three parts: (i) interdependency relation learning; (ii) sensing system design; and (iii) signal reconstruction. In the interdependency relation learning part, we considered both the parametric and non-parametric methods to learn the graphical structure under the noisy indirect measurements. In the sensing system design part, we introduced a density evolution framework to design sensing systems for compressive sensing for the first time. In the signal reconstruction part, we focused on the signal reconstruction with a given sensing system, which consists of three parts: signal reconstruction with inexact knowledge of the sensing system; signal reconstruction with the signal being contaminated by undesired noise; signal reconstruction with the signal belonging to a union of convex sets.