I plan to write an easy understanding review of compressed sensing, which is a popular topic that attracts considerable attention from 2004 and appears being related to more and more fields in recent years. The review will be posted in this blog as a series of notes about several aspects of compressed sensing:

**Compressed sensing reconstruction algorithms** ( minimization, sparse signal recovery, reweighted/adaptive );
**Sparse coding** (dictionary learning, K-SVD, MOD, MoTIF, FOCUSS);
**Compressed sensing measurement** (RIPs);
**Why compressed sensing can exactly recover a sparse signal?** (Incoherence, uncertainty principles)
**Compressed sensing and statistics** (feature selection, lasso, structure sparsity, covariance selection, group testing, permutation test)
**Compressed sensing and learning** (sparse dimension reduction, sparse PCA, data/label compression, model selection)

**A brief history of compressed sensing:**

The fundamental ideas of compressed sensing can be found from some literatures since 1960. David Dohono develops and completes the theories of compressed sensing in his early papers, e.g., *UNCERTAINTY PRINCIPLES AND SIGNAL RECOVERY. *Terence Tao and Emmanuel Candes construct the whole theoretical framework in several papers they published from 2005-2006, which can be found here. The rest, as they say, is history.

**A brief introduction to compressed sensing:**

For a sparse signal , a few measurements (often linear and random, for example, ) much less than what Shannon-Nyquist sampling theorem determines are sufficient to exactly recover the signal by simple convex optimization.

Below is an illustration:

Illustration of compressed sensing

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## About tianyizhou

Research Assistant at University Washington, Seattle,
Working on Machine Learning & Statistics in
MODE lab leaded by Prof. Carlos Guestrin, and
MELODI lab leaded by Prof. Jeff Bilmes.

Nice graph~~

that’s a great start!