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Denoising is an important task inside the image processing area. In order to overcome this challenging problem, diverse proposals have been done, like Non-Local means (NL-means) algorithm. In this paper, we present a fast algorithm that uses a preliminary segmentation combined with NL-means for image denoising. Firstly, the algorithm performs a subsampling, called Preliminary Segmentation-Based Subsampling (PSB Subsampling) while reducing the data quantity to be processed, based in the preliminary segmentation information given by the noisy image. This preliminary segmentation finds out an image partition where regions are labeled as significant or non-significant. In a second step, the denoising procedure is done, but NL-means is applied only on some pixels, reducing the data quantity again. The selection of these pixels is done based on information contributed by a segmentation of the subsampled image. Experimental results show that the implementation of this proposal is quite faster than existing bibliography and it could be used in other image processing tasks like segmentation.