Highly Nonlinear Approximations for Sparse Signal Representation
say, we address now the issue of determining a partition , and sub-partitions , such that: a) and b) the partitions are suitable for generating a sparse representation of the signal in hand. As a first step we propose to tailor the partition to the signal by setting taking into account the critical points of the curvature function of the signal, i.e.,
ande.g. if and , we have The codes for creating a partition adapted to a given signal are ProducePartition.m and FinalProducePartition.m and the one code for creating the dictionaries for the space is CutDic.m.