### CAS Seminar

# Palina Salanevich

### (Jacobs University)

## "The restricted isometry property for time-frequency structured random matrices using suprema of chaos processes (Compressed Sensing seminar 2)"

** Date: ** |
Tue, December 15, 2015 |

** Time: ** |
16:00 |

** Place: ** |
Research I Seminar Room |

**Abstract:** Compressive sensing is a method aimed at recovering sparse vectors from highly incomplete information using efficient algorithms. The restricted isometry property is a standard tool for studying how efficiently the measurement matrix captures information about sparse signals. It is also supports the analysis of various reconstruction algorithms, including l_1 minimization and greedy algorithms. Remarkably, Gaussian matrices are optimal for sparse recovery, but they have limited appeal in practice because most applications impose structure on the measurement matrix. We are going to discuss a compressive sensing problem for the time-frequency structured measurement matrices. Measurement matrices of this form are relevant for many practical applications, such as channel identification and high resolution radar.

In the proof of RIP for time-frequency matrices the key ingredients are estimates for suprema of second order chaos, which is accomplished using a Dudley-type inequality due to Talagrand. This approach involves an estimate of the covering numbers of the set of unit-norm s-sparse vectors with respect to two metrics induced by the random process.