## Generalised non-locally centralised image de-noising using sparse dictionary

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Recently, image de-noising algorithm based on sparse representation has received an increasing amount of attention. Such algorithms proposed a comprehensive sparse representation model, by solving the sparse coding problem and choosing the proper method for dictionary updating to achieve better de-noising results. Therefore, the construction of learning dictionary has become one of the key problems that limit the de-noising effectiveness. The non-locally centralised sparse representation de-noising algorithm uses principal component analysis method to achieve dictionary updating. Nevertheless, the instability of a single complete dictionary in sparse coding leads to erratic result in the process of the original image restoration. In this study, the authors present a new method named generalised non-locally centralised sparse representation algorithm. In the proposed method, the authors cluster the training patches extracted from a set of example images into subspaces, and then train dictionaries for subspaces by sparse analysis k-singular value decomposition dictionary, which is utilised to construct coded sub-block dictionary to avoid the instable results caused by a single dictionary. Experiments show that the improved method has better signal-to-noise ratio and de-noising effect compared with other methods.