Anisotropic diffusion for noise removal of band pass signals

Abstract

A noise removal method for band pass signals based on anisotropic diffusion algorithm is proposed in this paper. This anisotropic smoothing algorithm is for band pass signals with a constant frequency and is an extension of the anisotropic diffusion method proposed by Perona and Malik. Band pass signals are considered as complex valued vectors here. To this end, real valued band pass signals are therefore converted to complex valued signals by using Hilbert transform. An appropriate linear operator is considered here for such complex valued signals to form an anisotropic diffusion algorithm. A partial differential equation to smooth band pass noisy signals is therefore driven. The propagator of this differential equation is a complex valued Gabor filter. The algorithm proposed here demonstrates better performance for band pass noisy signals containing discontinuities in comparison with the traditional Perona-Malik (PM) algorithm and is robust at the presence of excessive noise with SNR less than unity

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