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Many existing non-local means (NLM) methods either use Euclidean distance to measure the similarity between patches, or compute weight $\omega _{ij}$ only once and keep it unchanged during the subsequent denoising iterations, or use only the structure information of the denoised image to update weight $\omega _{ij}$. These may lead to the limited denoising performance. To address these issues, this paper proposes the non-local adaptive means (NLAM) for image denoising. NLAM treats weight $\omega _{ij}$ as an optimization variable and iteratively updates its value. We then introduce three unbiased distances, namely, pixel–pixel, patch–patch, and coupled unbiased distances. These unbiased distances are more robust to measure the image pixel/patch similarity than Euclidean distance. Using the coupled unbiased distance, we propose the unbiased distance non-local adaptive means (UD-NLAM). Because UD-NLAM uses only a single patch size to compute weight $\omega _{ij}$ , we introduce multipatch UD-NLAM (MUD-NLAM) to adapt different noise levels. To further improve denoising performance, we then propose a new denoising method called MUD-NLAM with wavelet shrinkage (MUD-NLAM-WS). Experimental results show that the proposed NLAM, UD-NLAM, and MUD-NLAM outperform existing NLM methods, and MUD-NLAM-WS achieves a better performance than the state-of-the-art denoising methods. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the iterative regularization method and the inverse scale space method, recently developed for total-variation (TV) based image restoration, to wavelet-based image restoration. This continues our earlier joint work with others where we applied these techniques to variational-based image restoration, obtaining significant improvement over the Rudin-Osher-Fatemi TV-based restoration. Here, we apply these techniques to soft shrinkage and obtain the somewhat surprising result that a) the iterative procedure applied to soft shrinkage gives firm shrinkage and converges to hard shrinkage and b) that these procedures enhance the noise-removal capability both theoretically, in the sense of generalized Bregman distance, and for some examples, experimentally, in terms of the signal-to-noise ratio, leaving less signal in the residual. [ABSTRACT FROM AUTHOR]