Spatial enhancement of satellite images using data fusion algorithms in the wavelet domain

Image processing is becoming one of the most demanding domains of satellite imaging for remote sensing applications. Whatever the application, image processing evolves in the way different sensors are asked to contribute to the decision of combining the observation they get on the object of interest. In this paper, we present some tools used to make a fusion of images and we discuss the fundamentals of these tools. We present the mathematical theory of multiresolution analysis then develop wavelets. In fact, there are mathematical tools for hierarchically decomposing functions. They allow a function to be described in terms of a coarse overall shape, plus details that range from broad to narrow. We develop and discuss the case of Haar, Daubechies and biorthogonal (linear B-spline and quadratic B-spline) wavelets in two dimensions and show how they can be used for image fusion. A quantitative comparison of all developed methods is achieved using a SPOT image of the Australian region including urban areas (SPOT-XS 20m and Panchromatic 10m).