Oversampling and Coarse Quantization for Signals

CSIC Building (#406), Seminar Room 4122.
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Sigma-delta Quantization of
Finite Frames - Part 2

Dr. Alex Powell

Department Of Mathematics at Princeton University

Abstract:   Redundancy is a key to practical and reliable data representation in many settings. The standard example is sampling theory for (bandlimited) audio signals, where oversampling is used to ensure numerical stability. Frame theory provides a mathematical framework for stably representing signals as linear combinations of "basic building blocks" that constitute an overcomplete collection. Finite frames are the piece of this theory that is tailored for finite, but potentially high dimensional, data. We address the problem of how to accurately and efficiently quantize redundant finite frame expansions. We analyze the performance of certain second order Sigma-Delta quantization schemes in this setting, and derive rigorous approximation error estimates as well as new stability theorems. This is joint work with J. Benedetto and O. Yılmaz. This talk can be viewed as a sequel to O. Yılmaz's "Part 1" talk.