Constrained image representation using multi-transforms

A technique is presented to represent images employing two or more mutually non-orthogonal transforms. First, the image is divided into smaller non-overlapping subimages. Then, each subimage is resolved into two dimensional (2-D) subsignals such that each of the subsignals is compactly represented in a particular transform domain. This leads to an efficient representation of the subimage by superimposing the dominant coefficients corresponding to each subsignal. The residual error, which is the difference between the original subimage and the reconstructed subimage is properly formulated. An adaptive algorithm in conjunction with a strategy is developed to minimize this error for a fixed number of transform coefficients. The feasibility of the method is established through a synthetic image example. It is also shown that the DCT-Haar combination offers a percentage reduction of up to 15.0 to 17.0% in the Root Mean Square Error (RMSE) for the test images as compared to the DCT alone