Enhancing proximity measure between residual and noise for image denoising

Sparse representation and dictionary learning-based image denoising algorithms approximate the clean image patch by linear combination of few dictionary atoms. Clearly, residue after completion of denoising must be similar to the contaminating noise. Ideally, clean image patch is perfectly recovered if residue is exactly contaminating noise. Hence, for better denoising, residue must be enforced to possess characteristics similar to the contaminating noise. In this paper, we model residue such that proximity between residue and contaminating noise is increased. The proposed mathematical model makes sure that the residue is as random in nature as contaminating noise. This is achieved by unique sparse coding and dictionary update stages developed based on modelling of randomness in residue. The proposed algorithm is tested on additive white Gaussian noise (AWGN), additive coloured Gaussian noise (ACGN) and Laplacian noise. Since performance of the image denoising algorithms also depend on image effective bandwidth, therefore, in this paper we have generated synthetic images with known effective image bandwidths. These images are generated using the discrete cosine transform (DCT). The proposed algorithm is also tested on these images. The proposed algorithm is compared with state-of-the-art algorithms. The comparison on the bases of peak signal-to-noise ratio (PSNR), structure similarity index measure (SSIM) and feature similarity index measure (FSIM) indicate that the proposed algorithm is able to produce often better and competitive results.