Rayan Saab : Quantization of compressed sensing measurements and frame expansions (Oct 17, 2011 4:25 PM)

Compressed sensing, as a signal acquisition technique, has been shown to be highly effective for dimensionality reduction. On the other hand, reconstruction from compressed sensing measurements is highly non-linear and requires digital computers. Thus, quantizing (i.e., digitizing) compressed sensing measurements is an important, albeit under-addressed topic. In this talk, we show that by using $\Sigma\Delta$ quantization instead of the most commonly assumed approach (uniform quantization), a significant reduction in the reconstruction error is possible. In particular, we prove error decay rates of $\lambda^{-c r}$ where $\lambda$ is the ratio of the number of measurements to the sparsity of the underlying signal, and $r$ is the order of the $\Sigma\Delta$ scheme. In addition to the compressed sensing scenario we also consider the quantization of frame expansions, where one collects more measurements than the ambient dimension. We show state of the art results for certain frames (including random frames) and $\Sigma\Delta$ schemes. In particular, we prove error rates of $e^{-c\sqrt{\lambda}}$, where $\lambda$ is the oversampling ratio.

• Category: Applied Math and Analysis
• Duration: 01:34:53
• Date:  October 17, 2011 at 4:25 PM
• Views: 111
• Tags:   seminar, Applied Math And Analysis Seminar