Formal development and convergence analysis of the parallel adaptive mixed transform algorithm

Mixed transform techniques represent signals using combinations of basis functions, chosen from two or more transform domains simultaneously, to achieve higher energy compaction than can be achieved using a single transform. The parallel adaptive mixed transform (PAMT) technique has been shown to produce excellent energy compaction and greatly reduced computational burden compared with previous adaptive mixed transform techniques. In this paper, the PAMT algorithm is formally developed and its convergence properties examined. It is shown that convergence of the algorithm can be guaranteed independent of the transforms chosen, as long as those transforms are orthonormal in their own domains.