1. A method for hierarchical sparse dictionary learning (“HiSDL”) to construct a learned dictionary regularized by an a priori over-complete dictionary, comprising: providing at least one a priori over-complete dictionary for regularization; performing sparse coding of the at least one a priori over-complete dictionary to provide a sparse coded dictionary; using a processor, updating the sparse coded dictionary with regularization using auxiliary variables to provide a learned dictionary; determining whether the learned dictionary converges to an input data set; and outputting the learned dictionary regularized by the at least one a priori over-complete dictionary when the learned dictionary converges to the input data set.