Image denoising by linear regression on non-local means algorithm

Abstract

Non-local means (NL-Means) algorithm which removes the noise from the image have been used in the field widely due to its good performance especially for magnetic resonance images which consists of three dimensional data. Its main idea is using all the pixels which are local and non-local in an image and taking weighted averaging of all values. One negative side of this method is that it considers all pixels in the image without looking at their similarity. This paper proposes an NL-Means algorithm with pixel selection by applying linear regression analysis using root mean squared error (RMSE) value. After regression analysis, RMSE of the neighborhoods is used to exclude non-similar pixels during the noise removal. Lastly, obtained results were compared by four different methods which are NL-Means algorithm and, Gaussian, anisotropic diffusion and median filterings. All of the methods were outperformed by our method on structured similarity index and peak signal-to-noise ratio quantitative metrics. Moreover, the level of increase on visual qualities are also represented as a qualitative analysis. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2024.