22 March 1996 Wavelet filtering in the scale domain
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Abstract
It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform establishes a one-to-one correspondence between frequency filters (system or transfer functions) and scale filters, which are defined as multiplication operators in the scale domain, subject to the convergence of the defining integrals. Applications to the denoising of random signals are proposed. We argue that the present method is more suitable for removing the effects of atmospheric turbulence than the conventional procedures based on Fourier analysis because it is ideally suited for resolving spectral power laws.
© (1996) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Gerald Kaiser, "Wavelet filtering in the scale domain", Proc. SPIE 2762, Wavelet Applications III, (22 March 1996); doi: 10.1117/12.236038; https://doi.org/10.1117/12.236038
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