Quantization of compressed sensing measurements is typically justified by the
celebrated robustness result for $\ell_1$ recovery due to Donoho, and Candes et al.
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 quantized to a given resolution $\epsilon$, then the approximate recovery
of this signal is to within $O(\epsilon)$ of the original. While this result is
critical for the practical implementation of compressed sensing, it does not
guarantee that reconstruction accuracy can be improved by increasing the number
of measurements while keeping the resolution of measurements fixed, a standard
approach in mainstream oversampled A/D conversion. In this talk, we will present
how frame theory techniques coupled with "noise-shaping" quantization algorithms
can be utilized to significantly improve reconstruction accuracy for sparse
signals from their quantized measurements.