v1.0

v1.0

The first release.

A tutorial on compressed sensing, written as a single LaTeX document. It answers one question: if a signal is sparse in some basis, how few measurements does it take to recover it exactly? The Nyquist rate is the classical answer for band-limited signals, and compressed sensing shows that sparsity buys far more.

The tutorial builds up in three parts. It begins with the transforms that make sparsity meaningful, then develops the concepts the theory needs, and only then reaches compressed sensing itself.

Contents

• Signal transformation — the discrete Fourier transform and its non-uniform variant, the discrete cosine transform, the short time Fourier transform, and the continuous and discrete wavelet transforms.
• Basic Concepts — sparsity, norms, convex optimization, and the projection matrix.
• Compressed Sensing — the definition, the observation matrices that make recovery possible, and greedy pursuit.
• Afterword and References.

Building

Requires a TeX distribution with XeLaTeX, and a full TeX Live installation rather than a minimal one. elegantbook.cls is bundled in the repository, so there is nothing extra to install.