Near-orthogonal and adaptive affine lifting scheme on vector-valued signals

Lifting Scheme is actually a widely used second generation multi-resolution technique in image and video processing field. It permits to easily create fast, reversible, separable or no, not necessarily linear, multi-resolution analysis for sound, image, video or even 3D graphics. An interesting feature of lifting scheme is the ability to build adaptive transforms, more easily than with other decompositions. Many works have already be done in this subject, especially in lossless or near-lossless compression framework where there is no orthogonal constraint. However, some applications as lossy compression or de-noising requires well conditioned transforms. Indeed, this is due to the use of shrinking or quantization which has not controlled propagation through inverse transform. Authors have recently presented a technique permitting to determine some lifting scheme filters in order to obtain a high level of adaptivity combined with near-orthogonal properties, useful for most of these applications. Naturly coming into the adaptive near orthogonal framework, the point of interest of this article is affine algebraic filters. Color images and video have especially been studied through point of view of compression. In this way, the treatment of the vector aspect of signal, not only by processing channels independently, becomes the focus point of the article.