Continuous wavelet transform with arbitrary scales and O(N) complexity

Authors:
Arrate Muñoz;Raphaël Ertlé;Michael Unser
Affiliations:
Department of Microtechnology, Biomedical Imaging Group/DMT, Swiss Federal Institute of Technology Lausanne, CH-1O15 Lausanne EPEL, Switzerland;Department of Microtechnology, Biomedical Imaging Group/DMT, Swiss Federal Institute of Technology Lausanne, CH-1O15 Lausanne EPEL, Switzerland;Department of Microtechnology, Biomedical Imaging Group/DMT, Swiss Federal Institute of Technology Lausanne, CH-1O15 Lausanne EPEL, Switzerland
Venue:
Signal Processing
Year:
2002

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Abstract

The continuous wavelet transform (CWT) is a common signal-processing tool for the analysis of nonstationary signals. We propose here a new B-spline-based method that allows the CWT computation at any scale. A nice property of the algorithm is that the computational cost is independent of the scale value. Its complexity is of the same order as that of the fastest published methods, without being restricted to dyadic or integer scales. The method reduces to the filtering of an auxiliary (pre-integrated) signal with an expanded mask that acts as a kind of modified a trous' filter. The algorithm is well-suited for a parallel implementation.