High order low-bit Sigma-Delta quantization for fusion frames
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We construct high order low-bit Sigma-Delta (ΣΔ) quantizers for the vector-valued setting of fusion frames. We prove that these ΣΔ 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.
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