Conventional wisdom and common practice in acquisition and reconstruction of images from
frequency data follow the basic principle of the Nyquist density sampling theory. This …

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 …

This paper investigates the problem of estimating the frequency components of a mixture of
s complex sinusoids from a random subset of n regularly spaced samples. Unlike previous …

This paper introduces a simple and very general theory of compressive sensing. In this
theory, the sensing mechanism simply selects sensing vectors independently at random …

These notes give a mathematical introduction to compressive sensing focusing on recovery
using1-minimization and structured random matrices. An emphasis is put on techniques for …

Compressive sensing (CS) is a new approach to simultaneous sensing and compression of
sparse and compressible signals based on randomized dimensionality reduction. To …

This paper extends the concept of compressed sensing to signals that are not sparse in an
orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a …

We propose a variant of the classical conditional gradient method for sparse inverse
problems with differentiable observation models. Such models arise in many practical …

Compressive sensing is a new type of sampling theory, which predicts that sparse signals
and images can be reconstructed from what was previously believed to be incomplete …

This paper considers recovery of jointly sparse multichannel signals from incomplete
measurements. Several approaches have been developed to recover the unknown sparse …