A fast nonlocally centralized sparse representation algorithm for image denoising

摘要

The sparsity from self-similarity properties of natural images, which has received significant attention in the image processing community of researchers, is widely applied for image denoising. The recently proposed nonlocally centralized sparse representation (NCSR) algorithm that takes advantage of the sparse representations (SRs) and the nonlocal estimate of sparse coefficients (NESCs) has shown promising results with respect to noise reduction. Despite successful combination of the above two techniques, the iterative dictionary learning and the nonlocal estimate of unknown sparse coefficients make this algorithm computationally demanding, which largely limits its applicability in many applications. To address this problem, a fast version of the NCSR algorithm called FNCSR algorithm, which is based on pre-learned dictionary and adaptive parameter setting approaches, was proposed in this paper. Specifically, we adopted the same dictionary learning approach, i.e, the K-means and principal component analysis (PCA), with the NCSR algorithm to obtain a dictionary for each image in a selected image dataset including high-quality natural and texture images. Then we applied PNSR index to objectively assess the image quality of the reconstructed images using these dictionaries throughout the image dataset. The dictionary providing the best average reconstructed quality was selected as fixed dictionary, i.e., the pre-learned dictionary, for sparse coding throughout the iterative denoising process, which implies that it no longer requires dictionary learning procedure within the framework of the proposed FNCSR algorithm, resulting in greatly decreased execution time. In order to further improve computational efficiency, we employed quality-aware features and support vector regression (SVR) technique to build a fast noise level estimator (NLE) to estimate the noise level from a single noisy image. The parameters related to the NESC, i.e., the search window and the search step, which influences the computational performance of the NCSR algorithm strongly, were chosen automatically according to the estimated noise level. Compared to the original NCSR algorithm, these modifications lead to substantial benefits in computational efficiency (a performance gain of about 90% can be achieved) without sacrificing image quality too much (the largest decline is less than 0.55 dB and 0.014 in terms of PSNR and SSIM indices). Compared with other state-of-the-art denoising algorithms, experimental results show that the proposed FNCNR algorithm also achieves comparable performance in terms of both quantitative measures and visual quality.