2D nonlocal sparse representation for image denoising

Two dimensional (2D) sparse representation provides promising performance in image denoising by cooperatively exploiting horizontal and vertical features inherent in images by two dictionaries. In this paper, we first propose integrating the 2D sparse model with clustering and nonlocal regularization into a unified variational framework, defined as 2D nonlocal sparse representation (2DNSR), for optimization. Within this framework, we then present a dictionary learning method for image denoising which jointly decomposes groups of similar noisy patches on subsets of 2D dictionaries. We finally present a 2DNSR-based algorithm for image denoising. Experimental results on image denoising show our proposed 2D nonlocal sparse representation outperforms the 2D sparse model and achieves competitive performance to state-of-the-art nonlocal sparse models whereas with much less memory costs.