Image de-noising based on Hodrick-Prescott filtering

Abstract

It is of great interest to effectively deal with noise that imaging sensors or external sources may have introduced to a digital image. During the years, de-noising techniques have been proposed to attenuate additive random noise but without a doubt it can be said that no algorithm exist that can completely eliminate it. Unfortunately this paper will not make such a claim but it changes the approach point of view on how to de-noise an image that has been corrupted by additive noise. The problem is viewed as having an original image represented by a stochastic trend component added to a random irregular term but in a similar way to what has been done by Hodrick and Prescott in the area of economics to study rapid fluctuations i.e. noise, that are too rapid with respect to a slower trend in a time series i.e. image. The method qualitatively produced good results when comparing it to wavelet based and adaptive Wiener filtering techniques. The proposed technique has also shown to be robust for the case of multiplicative noise.