Online dictionary learning algorithm with periodic updates and its application to image denoising

We introduce a coe cient update procedure into existing batch and online dictionary learning algorithms. We rst propose an algorithm which is a coe cient updated version of the Method of Optimal Directions (MOD) dictionary learning algorithm (DLA). The MOD algorithm with coe cient updates presents a computationally expensive dictionary learning iteration with high convergence rate. Secondly, we present a periodically coe cient updated version of the online Recursive Least Squares (RLS)-DLA, where the data is used sequentially to gradually improve the learned dictionary. The developed algorithm provides a periodical update improvement over the RLS-DLA, and we call it as the Periodically Updated RLS Estimate (PURE) algorithm for dictionary learning. The performance of the proposed DLAs in synthetic dictionary learning and image denoising settings demonstrates that the coe cient update procedure improves the dictionary learning ability.