RESOLVING IMAGES IN MULTIPLE TRANSFORM DOMAINS WITH APPLICATIONS

A technique is presented to represent images employing two or more mut ually non-orthogonal transforms. First, the image is divided into smal ler non-overlapping subimages. Then, each subimage is resolved into tw o-dimensional subsignals such that each subsignal is compactly represe nted in a particular transform domain. This leads to an efficient repr esentation of the subimage by superimposing the dominant coefficients corresponding to each subsignal. The residual error, which is the diff erence between the original subimage and the reconstructed subimage, i s properly formulated. Adaptive algorithms in conjunction with an opti mization strategy are developed to minimize this error. Finally, resul ts are presented where first the feasibility of the method is establis hed through a synthetic image example and then applications to compact ly represent test images are presented. The number of transform coeffi cients is reduced by a factor ranging from 5 to 40. It is verified tha t, for a given coefficient reduction factor, the direct cosine transfo rm (DCT)-Haar representation of test images yields a more compact repr esentation than using DCT or Haar alone. It is shown that the DCT-Haar combination offers a reduction of up to 15.0 to 17.0% in the root mea n square error as compared to the DCT alone. (C) 1995 Academic Press, Inc.