Globally optimal filters for multiresolution image decomposition

The performance of multiresolution image coding schemes depends strongly on the employed filters for up and down conversion. Minimization of the variances of the error images between successive levels is often used as optimality criterion (local optimality). In this contribution we propose the use of a slightly different criterion. Instead of the error variance between successive levels we consider the error between the original image and the lower resolution renditions at the finest scale (global optimality). Both approaches (local vs. global) differ, because iterated orthogonal projections lead only in special cases to orthogonal projections. The “global” approach is better suited than the “local” one for the design of progressive coding schemes, where the low resolution approximations are not rendered at intermediate resolutions but to the full resolution