Redundancy is a key to practical and reliable data representation in
many settings. Frame theory provides a mathematical framework for stably
representing signals as linear combinations of an overcomplete collection
of "basic building blocks." We shall discuss the problem of quantization
(analog-to-digital conversion) for redundant finite frame expansions. Our
focus will be on a special class of
algorithms, known as Sigma-Delta schemes, which are related to error
diffusion. We explain the basics of how Sigma-Delta schemes work in this
setting and point to current directions of research (including error
estimates, stability theorems, and reconstruction procedures).
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