High order low-bit Sigma-Delta quantization for fusion frames

Abstract

We construct high order low-bit Sigma-Delta $(\Sigma \Delta )$ quantizers for the vector-valued setting of fusion frames. We prove that these $\Sigma \Delta$ quantizers can be stably implemented to quantize fusion frame measurements on subspaces $W_n$ using ${\log }_2(\dim (W_n)+1)$ bits per measurement. Signal reconstruction is performed using a version of Sobolev duals for fusion frames, and numerical experiments are given to validate the overall performance.

18 pages, 2 figures

References in corpus (1)

• An RIP-based approach to $\Sigma \Delta$ quantization for compressed sensing