Filter Bank Fusion Frames

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.

keywords: filter banks, frames, tight, fusion, erasures, polyphase

Cited by in corpus (7)

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• A combinatorial characterization of tight fusion frames
• Preconditioning filter bank decompositions using structured normalized tight frames
• J-fusion frame for Krein spaces
• Approximative Atomic Systems for operators in Banach spaces
• Auto-tuning unit norm frames
• Non-orthogonal fusion frames and the sparsity of fusion frame operators