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Preprocessing for data fusion using fractal multiresolution analysis

In this paper, we introduce a preprocessing method for data fusion, based on multiresolution analysis using fractal functions. The reason for choosing this method is that many natural signals belong to the 1/f family and an important class of fractal signals is also of the 1/f type. Because of the self-affinity and the dilation properties, a finite set of fractal interpolation functions (FIF) is chosen for the multiresolution analysis. It is seen that a nested set of subspaces can be generated by the FIF which is equivalent to the set of wavelet subspaces. Through multiresolution analysis, it is possible to reduce the effect of high frequency noise and to keep useful information at the low frequency. Furthermore, such an approach has a localization effect. According to the characteristics of the FIF, the decomposition and reconstruction approach obtained from multiresolution analysis can be implemented by cascade filter banks. Computation complexity is thus also reduced. This method may provide a good way of preprocessing data in fusion.