WAVELET-BASED KALMAN FILTERING IN SCALE SPACE FOR IMAGE FUSION

In this chapter, a 2-dimensional (2D) dynamic system of images is formulated in the scale space based on the 2D wavelet transform. The original image is assigned to the highest index (the finest scale) and the decomposed approximations at successively coarser scales (lower indices) are interpreted as the state variables at the corresponding scales. The state transition takes place from a coarse scale to a fine scale. Through the use of the Kalman filtering, the optimal estimation of the finest scale original image from a set of multiscale noisy measurements can be obtained in a scale recursive form. This can be applied to multiresolution image fusion. An efficient filtering algorithm has been developed by using the orthogonal wavelet packet transform that greatly reduces its computational complexity. This methodology is illustrated by experiments including one performed on the fusion of a Landsat TM band 1 image and a SPOT image.