Learning Dictionaries as a Sum of Kronecker Products

Abstract

The choice of an appropriate frame, or dictionary, is a crucial step in the sparse representation of a given class of signals. Traditional dictionary learning techniques generally lead to unstructured dictionaries that are costly to deploy and train, and do not scale well to higher dimensional signals. In order to overcome such limitation, we propose a learning algorithm that constrains the dictionary to be a sum of Kronecker products of smaller subdictionaries. This approach, named sum of Kronecker products, is demonstrated experimentally in an image denoising application.