A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing and provides a detailed account of the core theory upon which the field is build.Expand

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 information.Expand

We show that a Legendre s-sparse polynomial of maximal degree N can be recovered from [emailÂ protected]?slog^4(N) random samples that are chosen independently according to the Chebyshev probability measure. As an efficient recovery method, @?"1-minimization can be used.Expand

We show that a matrix, which is a composition of a random matrix of certain type and a deterministic dictionary, has small restricted isometry constants and can be recovered via basis pursuit from a small number of random measurements.Expand

We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements with an error of the order of the best $k$-rank approximation.Expand

A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certainâ€¦ Expand

We show how to compute solutions of linear inverse problems with joint sparsity regularization constraints by fast thresholded Landweber algorithms.Expand

Functions of interest are often smooth and sparse in some sense, and both priors should be taken into account when interpolating sampled data. Classical linear interpolation methods are effectiveâ€¦ Expand

We consider the application of compressed sensing (CS) to the estimation of doubly selective channels within pulse-shaping multicarrier systems (which include orthogonal frequency-division multiplexing (OFDM) systems as a special case).Expand