Smooth wavelet frames with application to denoising

Abstract

This paper considers the design and application of wavelet tight frames based on iterated oversampled filter banks. The greater design freedom available makes possible the construction of wavelets with a high degree of smoothness, in comparison with orthonormal wavelet bases. Grobner bases are used to obtain the solutions to the nonlinear design equations. Following the dual-tree DWT of Kingsbury (see Proceedings of the Eighth IEEE DSP Workshop, Utah, 1998, and Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (ICASSP), Phoenix, 1999), one goal is to keep the redundancy-factor bounded by 2, instead of allowing it to grow as it does for the undecimated DWT (which is exactly shift-invariant). For the tight frame presented here, optimal-tree based denoising algorithms can be directly applied.