A system, method and computer program product for hierarchical sparse dictionary learning (“HiSDL”) to construct a learned dictionary regularized by an a priori over-complete dictionary, includes 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 at least one auxiliary variable 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. The system and method includes, when the learned dictionary lacks convergence, repeating the steps of performing sparse coding, updating the sparse coded dictionary, and determining whether the learned dictionary converges to the input data set.