An analysis dictionary learning algorithm based on recursive least squares

We consider the dictionary learning problem in sparse representations based on an analysis model with noisy observations. A typical limitation associated with several existing analysis dictionary learning (ADL) algorithms, such as Analysis K-SVD, is their slow convergence due to the procedure used to pre-estimate the source signal from the noisy measurements when updating the dictionary atoms in each iteration. In this paper, we propose a new ADL algorithm where the recursive least squares (RLS) algorithm is used to estimate the dictionary directly from the noisy measurements. To improve the convergence properties of the proposed algorithm, the initial dictionary is estimated from a small training set by using the K-plane clustering algorithm. The proposed algorithm, as shown by experiments, offers advantages over the Analysis K-SVD, in both the runtime and atom recovery rate.