K-plane clustering algorithm for analysis dictionary learning

Analysis dictionary learning (ADL) aims to adapt dictionaries from training data based on an analysis sparse representation model. In a recent work, we have shown that, to obtain the analysis dictionary, one could optimise an objective function defined directly on the noisy signal, instead of on the estimated version of the clean signal as adopted in analysis K-SVD. Following this strategy, a new ADL algorithm using K-plane clustering is proposed in this paper, which is based on the observation that, the observed data are co-planer in the analysis sparse model. In other words, the columns of the observed data form multi-dimensional subspaces (hyperplanes), and the rows of the analysis dictionary are the normal vectors of the hyper-planes. The normal directions of the K-dimensional concentration hyper-planes can be estimated using the K-plane clustering algorithm, and then the rows of the analysis dictionary which are the normal vectors of the hyper-planes can be obtained. Experiments on natural image denoising demonstrate that the K-plane clustering algorithm provides comparable performance to the baseline algorithms, i.e. the analysis K-SVD and the subset pursuit based ADL.