Research On Non-local Means And Its Applications

Noises are inevitably introduced in digital image acquisition, and thus denoising is still a very active area in image processing. Its goal is to reduce noise artifacts while retaining good details of observed images as much as possible. To this end, many noise filters have been proposed separately. Among of them, non-local means filter(NLM) proposed by Buades et al in 2005 is the beginning of non-local denoising methods. Unlike its precursors typically operating in a local neighborhood and based on singal pixels, NLM operates in a non-local area(even the whole image) by using a dissimilarity measure between patches and clearly outperform other classic filters. As a result, NLM has motivated many successors proposed. And non-local method has become a kind of state-of-the-art denoising strategy.Similarly to NLM itself, its successors of NLM mainly focus on removing Gaussian noise. However, the image noises in real world can belong to different levels, different types and even their mixtures. Meanwhile, the denoising strategy of NLM is only based on intuition and lack of theoretical basis which is benefit for experts to analyze the existing non-local filters and develop novel ones. For the reasons above, we mainly work on two aspects in this paper: one is modifying NLM to remove the complicated noises and the other is proposing a mathematical framework for this filter. We summarize the contributions of this paper as follows:1) Modify NLM to a universal filter. Due to totally different image degrading mechanisms brought out by Gaussian noise and impulse noise, up to date, just few works focus on the removal of the mixture of the two noises, though such a mixture is common in the real world. Though a state-of-the-art filter for removing Gaussian noise, NLM, like its local counterpart(mean filter), is no longer so effective in removing salt-pepper nois. Inspired by the Adaptive Median Filter(AMF) filtering strategies, in this paper, we modify NLM to a novel non-local universal filter(UNLM) which can remove not only either of Gaussian noise and salt-pepper noise but also their mixture.2) Improve non-local median filter: Non-Local Euclidean Medians(NLEM) has recently been proposed and shows more effective than NLM in removing heavy noise. In this paper, we find the inconsistency between the two dissimilarity measures in NLEM can affect its robustness, thus develop an improved version(INLEM) to compensate such an inconsistency. Further we provide a concise convergence proof for optimization iterations of both NLEM and INLEM.3) Propose a general non-local model(GNLMKIM) using multi-kernel-induced measures.Inspired by multi-kernel methods in machine learning which have been proved more robust and effective in tackling complex learning problems than single-kernel ones, in this paper, we propose a general non-local model(GNLMKIM) for image denoising based on multi-kernel-induced measures. Based on GNLMKIM, we further extend NLM to its multi-kernel counterpart with encouraging experimental results.4) Establish a two-step regularization framework for NLM. Though such a two-step viewpoint on NLM has appeared in several literatures, our framework is more general and flexible than the existing ones. To illustrate the effectiveness of the framework, based on it, we reinterpret several non-local filters in the unified view. Further, taking the framework as a design platform, we develop a novel non-local filter with encouraging experimental results.