**Goal:**

Compressed sensing (CS) is a signal processing technique for efficiently
acquiring and reconstructing a sparse signal, by finding solutions to underdetermined linear systems. In 2004, Emmanuel Candès and Terence Tao, and David Donoho independently, proved that given knowledge about a signal's sparsity, the signal may be reconstructed with even fewer samples than the sampling theorem requires. Since then, CS has seen a impressive number of spectacular applications, in areas including photography, holography, facial recognition, astronomy, magnetic resonance imaging, shortwave-infrared cameras, etc.

The goals of this project was to

- Understand the proof of a version of the Candès-Tao theorem;

- Propose a program (in Matlab) to find the exact number of samples that are required to reconstruct a sparse signal exactly.

**Student:**
Lucien May.

**Supervisor:**
Ivan Nourdin.

**Difficulty level:**
Master student project

**Tools:**
Programs were coded in Matlab.

**Obtained results:**
Link to the master thesis of Lucien May