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A multi-scale non-local means algorithm for image de-noising

A highly studied problem in image processing and the field of electrical engineering in general is the recovery of a true signal from its noisy version. Images can be corrupted by noise during their acquisition or transmission stages. As noisy images are visually very poor in quality, and complicate further processing stages of computer vision systems, it is imperative to develop algorithms which effectively remove noise in images. In practice, it is a difficult task to effectively remove the noise while simultaneously retaining the edge structures within the image. Accordingly, many de-noising algorithms have been considered attempt to intelligent smooth the image while still preserving its details. Recently, a non-local means (NLM) de-noising algorithm was introduced, which exploited the redundant nature of images to achieve image de-noising. The algorithm was shown to outperform current de-noising standards, including Gaussian filtering, anisotropic diffusion, total variation minimization, and multi-scale transform coefficient thresholding. However, the NLM algorithm was developed in the spatial domain, and therefore, does not leverage the benefit that multi-scale transforms provide a framework in which signals can be better distinguished by noise. Accordingly, in this paper, a multi-scale NLM (MS-NLM) algorithm is proposed, which combines the advantage of the NLM algorithm and multi-scale image processing techniques. Experimental results via computer simulations illustrate that the MS-NLM algorithm outperforms the NLM, both visually and quantitatively.