The goal of the sparse approximation problem is to approximate a target signal using a
linear combination of a few elementary signals drawn from a fixed collection. This paper …

This chapter surveys recent work in applying ideas from graphical models and message
passing algorithms to solve large-scale regularized regression problems. In particular, the …

This first chapter formulates the objectives of compressive sensing. It introduces the
standard compressive problem studied throughout the book and reveals its ubiquity in many …

Suppose we wish to recover a signal\input amssym \font\abc=cmmib10\def\bi#1\abc#1\bix∈
\BbbC^n from m intensity measurements of the form \font\abc=cmmib10\def\bi#1\abc#1|⟨\bix …

Wireless body sensor networks (WBSN) hold the promise to be a key enabling information
and communications technology for next-generation patient-centric telecardiology or mobile …

In recent years, compressed sensing (CS) has attracted considerable attention in areas of
applied mathematics, computer science, and electrical engineering by suggesting that it may …

We give algorithms with provable guarantees that learn a class of deep nets in the
generative model view popularized by Hinton and others. Our generative model is an n …

In a recent paper, the authors proposed a new class of low-complexity iterative thresholding
algorithms for reconstructing sparse signals from a small set of linear measurements. The …

We review connections between phase transitions in high-dimensional combinatorial
geometry and phase transitions occurring in modern high-dimensional data analysis and …

In this paper, we survey algorithms for sparse recovery problems that are based on sparse
random matrices. Such matrices has several attractive properties: they support algorithms …