Smooth Adaptation by Sigmoid Shrinkage

Abdourrahmane Atto (1) , Dominique Pastor (1, 2) , Grégoire Mercier (1, 3)

1 Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
2 SC - Département Signal et Communications
3 ITI - Département Image et Traitement Information

This work addresses the properties of a sub-class of sigmoid based shrinkage functions: the non zero-forcing 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 sub-class. 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 perform weak 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 property makes it possible to smoothly tune contrast (enhancement - reduction).

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Abdourrahmane Atto, Dominique Pastor, Grégoire Mercier. Smooth Adaptation by Sigmoid Shrinkage. EURASIP Journal on Image and Video Processing, 2009, pp.532312. ⟨10.1155/2009/532312⟩. ⟨hal-00732347⟩