A normalized Information based method for efficient signal representation

Function approximation in Hilbert spaces is a well studied problem but the automatic selection of the optimal set of coefficients of the expan- sion of a function on a basis still represents a challenging issue. In this paper a model for automatic selection of coefficients, based on informa- tion measures, is further studied. In particular its extension to wavelet bases is investigated. The model aims at finding the set of coefficients for optimal function reconstruction by maximizing the information measure named ENID, defined on the sequence of decreasingly sorted coefficients. The use of ENID in wavelet basis highlights some issues in its definition. As a result, two different solutions are proposed and investigated through numerical experiments in the MatLab environment.