**
Borhan Sanandaji, Department of EE and CS, Colorado School of Mines**

Harold Frank Hall, Room 4164 (ECE Conference Room)

Over the past several years, Compressive Sensing (CS) has appeared as a powerful paradigm in signal processing which enables recovery of a sparse high-dimensional vector from a small number of noisy measurements. In this talk, I will illustrate how the tools in CS can be used in the analysis of high-dimensional but sparse dynamical systems.

To begin, I will consider recovering the ﬁnite impulse response of an LTI system from few measurements, when the impulse response is known to be sparse a priori. I will show how this problem can be formulated as the recovery of a sparse high-dimensional signal from its product with an underdetermined Toeplitz matrix. To this end, I will derive Concentration of Measure (CoM) inequalities for Toeplitz matrices, and show how the CoM inequalities can be used in establishing the Restricted Isometry Property (RIP) and in applications such as the binary detection problem. I will then consider the observability of linear systems from few measurements when the initial state of the system is known to be sparse. I will show how this problem can be formulated as recovering a sparse high-dimensional signal from its product with an underdetermined block- diagonal matrix. Similarly, I will establish a bound on the required number of measurements for stable recovery of the initial state.

**About Borhan Sanandaji:**

Borhan M. Sanandaji is currently a Ph.D. candidate in the Electrical Engineering and Computer Science department at the Colorado School of Mines. In the Fall of 2012 he will join the Electrical Engineering and Computer Sciences department at the University of California, Berkeley as a postdoctoral researcher. His research interests lie at the intersection of signal processing,dynamical systems, and control theory. In particular, the current focus of his research is on compressive sensing, sparse signal processing, and applications in the analysis of high-dimensional dynamical systems.

**Hosted by: Professor Upamanyu Madhow**