Smooth adaptation by sigmoid shrinkage

Authors:
Abdourrahmane M. Atto;Dominique Pastor;Grégoire Mercier
Affiliations:
Lab-STICC, CNRS, UMR, TELECOM Bretagne, Technopôle Brest-Iroise, Brest Cedex 3, France;Lab-STICC, CNRS, UMR, TELECOM Bretagne, Technopôle Brest-Iroise, Brest Cedex 3, France;Lab-STICC, CNRS, UMR, TELECOM Bretagne, Technopôle Brest-Iroise, Brest Cedex 3, France
Venue:
Journal on Image and Video Processing
Year:
2009

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Abstract

This paper addresses the properties of a subclass of sigmoid-based shrinkage functions: the non zeroforcing smooth sigmoid-based shrinkage functions or SigShrink functions. It provides a SURE optimization for the parameters of the SigShrink functions. The optimization is performed on an unbiased estimation risk obtained by using the functions of this subclass. The SURE SigShrink performance measurements are compared to those of the SURELET (SURE linear expansion of thresholds) parameterization. It is shown that the SURE SigShrink performs well in comparison to the SURELET parameterization. The relevance of SigShrink is the physical meaning and the flexibility of its parameters. The SigShrink functions performweak attenuation of data with large amplitudes and stronger attenuation of data with small amplitudes, the shrinkage process introducing little variability among data with close amplitudes. In the wavelet domain, SigShrink is particularly suitable for reducing noise without impacting significantly the signal to recover. A remarkable property for this class of sigmoid-based functions is the invertibility of its elements. This propertymakes it possible to smoothly tune contrast (enhancement, reduction).