We propose a principal basis analysis(PBA)method over a learned overcomplete basis set(called dictionary).The proposed PBA makes use of a novel criterion:the frequency of basis vector(atom of the dictionary)over a data set.This proposed criterion is well adapted to sparse signal representation.Moreover it adapts to an intrinsic characteristic of the regularity of signals. The proposed PBA makes use of a novel criterion: the frequency of basis vector (atom of the dictionary) over a data set. This proposed criterion is well adapted to sparse signal representation. Moreover it adapts to an intrinsic characteristic of the regularity of signals.