ABSTRACT

Some of the restoration methods discussed in the previous chapters can be easily extended to the restoration of color images and other vector-valued data. However, there are several problems that have to be considered. We mention some of them. First, the notion of image edges identified using the norm of the gradient for scalar images has several different extensions in the vectorial case. The gradient is now a matrix and we can define different gradient norms |∇u| of the Jacobian matrix ∇u when u is a vector-valued function; such gradient norms could define edges in different ways. Second, care has to be taken when processing color images; new colors should not be introduced in the restored image by the diffusion process.