Wavelet-based filtering in scale space and image fusion

Multisensory images of the same scene, such as those obtained from Landsat Thematic Mapper and Satellite Pour 1{dollar}spprime{dollar} Observation de la Terre which are operated in different frequency bands, have different resolutions and different measurement noises. To integrate the multisensory information together and to remove the various noises, an image fusion process is performed to improve the quality of the resultant images. Wavelet-based multiresolution analysis provides a new approach to study the image fusion problem. Following the recent work of Chou and Willsky, et al. on signal processing, we have developed an efficient method for multisensory image fusion at the pixel level. Multiscale images can be well modelled by the two-dimensional wavelet transform in terms of the tensor product of two one-dimensional wavelet transforms, 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 Kalman theory, image fusion can be obtained by optimally estimating the finest scale original image from a set of multiscale noisy measurements, in a scale recursive form. Without the assumption of white processes for the wavelet coefficients and measurement noises at different scales, the matrix Ricatti equation, especially for image applications, would require huge computational effort. To overcome this difficulty, we have developed an efficient algorithm for pixel-level image fusion by using the wavelet packet transform which can be implemented in parallel for real-time processing. Furthermore, to model a broader class of multiscale images with more choices of analyzing wavelets, the wavelet-packet-based image fusion algorithm is also generalized to include the use of biorthogonal wavelets. This methodology is illustrated by an experiment performed on the fusion of a Landsat TM image and a SPOT image. Another example is also given to show the denoising of 1/f fractal textures by using our scale-recursive Kalman filtering.