Compressed sensing

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

FSCT -- University of Luxembourg