K-Plane Clustering Algorithm For Analysis Dictionary Learning | ||

Ye Zhang, Haolong Wang, Wenwu Wang, Saeid Sanei |

**Abstract:**

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.