Speaker: C. Sinan Güntürk, Associate Professor,  Courant Institute of Mathematical Sciences

Abstract:
Compressive sensing has changed the theoretical landscape of signal acquisition in the recent years and is aiming to become a serious practical alternative to conventional techniques. Discrete encoding of measurements in compressive sensing is typically justified by the celebrated robustness result for the basis pursuit reconstruction algorithm. Under generic conditions on the measurement operator, such as the restricted isometry property, this result guarantees that if each measurement of a sparse signal is separately quantized to a given resolution epsilon, then the approximate recovery of this signal via ell-1 minimization is guaranteed to be within O(epsilon) of the original. However, this result does not provide a satisfactory performance guarantee from an information theory viewpoint. In this talk, we will present how frame theory techniques coupled with "noise-shaping" quantization algorithms and random matrix theory methods can be utilized to significantly improve quantization accuracy for sparse signals.