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arXiv · 2006.09732

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

Zhen Gao·Felix Krahmer·Alexander M. Powell
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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 $\log_2( {\rm dim}(W_n)+1)$ 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.

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Zhen Gao, Felix Krahmer, Alexander M. Powell. 2020-06-17. High order low-bit Sigma-Delta quantization for fusion frames. https://doi.org/10.1142/s0219530520400096

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