Nonlinear and Nonseparable Bidimensional Multiscale Representation Based on Cell-Average Representation

The aim of this paper is to construct a new nonlinear and nonseparable multiscale representation of piecewise continuous bidimensional functions. This representation is based on the definition of a linear projection and a nonlinear prediction operator, which locally adapts to the function to be represented. This adaptivity of the prediction operator proves to be very interesting for image encoding in that it enables a considerable reduction in the number of significant coefficients compared with other representations. Applications of this new nonlinear multiscale representation to image compression and super-resolution conclude this paper.