Quantized frame expansions with erasures

Frames have been used to capture significant signal characteristics, provid e numerical stability of reconstruction, and enhance resilience to additive noise. This paper places frames in a new setting, where some of the elemen ts are deleted. Since proper subsets of frames are sometimes themselves fra mes, a quantized frame expansion can be a useful representation even when s ome transform coefficients are lost in transmission. This yields robustness to losses in packet networks such as the Internet. With a simple model for quantization error, it is shown that a normalized frame minimizes mean-squ ared error if and only if it is tight. With one coefficient erased, a tight frame is again optimal among normalized frames, both in average and worst- case scenarios. For more erasures, a general analysis indicates some optima l designs. Being left with a tight frame after erasures minimizes distortio n, but considering also the transmission rate and possible erasure events c omplicates optimizations greatly. (C) 2001 Academic Press.