K-Plane Clustering Algorithm For Analysis Dictionary Learning
Ye Zhang, Haolong Wang, Wenwu Wang, Saeid Sanei

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.