An orthogonal wavelet representation of multivalued images

In this paper, a new orthogonal wavelet representation of multivalued images is presented. The idea for this representation is based on the concept of maximal gradient of multivalued images. This concept is generalized from gradients toward linear vector operators in the image plane with equal components along rows and columns. Using this generalization, the pyramidal dyadic wavelet transform algorithm using quadrature mirror filters is modified to be applied to multivalued images. This results in a representation of a single image, containing multiscale detail information from all component images involved. This representation leads to multiple applications ranging from multispectral image fusion to color and multivalued image enhancement, denoising and segmentation. In this paper, the representation is applied for fusion of images. More in particular, we will introduce a scheme to merge high spatial resolution greylevel images with low spatial resolution multivalued images to improve spatial resolution of the latter while preserving spectral resolution. Two applications are studied: demosaicing of color images and merging of multispectral remote sensing images.