An efficient structure and algorithm for image representation using nonorthogonal basis images

This paper presents a new recursive parallel mixed transform technique employing a projection algorithm for image representation. Image coders which employ subsets of nonorthogonal basis images chosen from two or more transform domains have been shown to consistently yield higher image quality than those based on one transform for a fixed compression ratio. However, these techniques have not been widely employed since existing formulations have either lacked rigorous development or suffered from high computational complexity and convergence problems. The algorithm presented herein overcomes these limitations. The algorithm is rigorously formulated, conditions for convergence are derived, and computational considerations are examined. Results of simulations are presented which demonstrate excellent performance in terms of energy compaction.