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.