This article develops the mathematical algorithm of the Wavelet 2-D Transform not decimated (A trous algorithm) for the fusion of satellite images. Throughout the article three important themes are addressed, the first theme corresponds to the mathematical detail to implement the fusion of images using the Wavelet A trous transform; and the second theme to the implementation of the mathematical development of the Wavelet 2-D Transform using free and proprietary Python and Matlab software respectively, using a WorldView-2 satellite