Filter Bank Fusion Frames

TL;DR

This paper introduces novel oversampled filter bank constructions that implement fusion frames, enabling robust and redundant signal encoding with stable inversion, using polyphase domain characterizations and specific wavelet and Gabor transforms.

Contribution

It provides the first practical constructions of fusion frames via oversampled filter banks, including finite impulse response filters with well-behaved frequency responses.

Findings

Constructed filter bank fusion frames using polyphase domain analysis.

Developed fusion frame versions of wavelet and Gabor transforms.

Demonstrated robustness and stability in signal encoding.

Abstract

In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly designed, fusion frames can provide redundant encodings of signals which are optimally robust against certain types of noise and erasures. However, up to this point, few implementable constructions of such frames were known; we show how to construct them using oversampled filter banks. In this work, we first provide polyphase domain characterizations of filter bank fusion frames. We then use these characterizations to construct filter bank fusion frame versions of discrete wavelet and Gabor transforms, emphasizing those specific finite impulse response filters whose frequency responses are well-behaved.