Two dimensional synthesis sparse model

Sparse representation has been proved to be very efficient in machine learning and image processing. Traditional image sparse representation formulates an image into a one dimensional (1D) vector which is then represented by a sparse linear combination of the basis atoms from a dictionary. This 1D representation ignores the local spatial correlation inside one image. In this paper, we propose a two dimensional (2D) sparse model to much efficiently exploit the horizontal and vertical features which are represented by two dictionaries simultaneously. The corresponding sparse coding and dictionary learning algorithm are also presented in this paper. The 2D synthesis model is further evaluated in image denoising. Experimental results demonstrate our 2D synthesis sparse model outperforms the state-of-the-art 1D model in terms of both objective and subjective qualities.