Denoising by extracting fractional order singularities

In this paper we introduce a method of isolating and extracting a certain class of local singular behaviours of signals/images which in turn leads to a method of pointwise noise estimation and suppression. The underlying motivation is to decompose functions directly in terms of components which would naturally represent different orders of regular or singular behaviours defined by the local Holder exponents. We have shown that such a decomposition can lead to a factorization of the spectrum of the singular portion of the signal in terms of the spectrum of the original signal and that of a denoising filter.