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

Abstract

We construct high-order low-bit Sigma-Delta [Formula: see text] quantizers for the vector-valued setting of fusion frames. We prove that these [Formula: see text] quantizers can be stably implemented to quantize fusion frame measurements on subspaces [Formula: see text] using [Formula: see text] 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.