Wavelet-Like Lifting-Based Transform for Decomposing Images in Accordance with the Inter-prediction Principles of Video Coding

In this paper, an innovative approach to image analysis-synthesis is presented, which follows the prediction principles of video coding. It consists in decomposing an image into four polyphase components, which are processed like video frames. One of them is made the essential reference frame, whereas each of the remaining components is predicted using the reference or any of previously encoded components. Such hierarchical prediction is adapted, being similar to the bidirectional motion estimation-compensation using two reference frames, known of the MPEG-4 AVC standard for video coding. On the other hand, obtainable residuals are similar to the results of lifting-based subband decompositions of images, or even to wavelet transforms, if the algorithm is applied iteratively to the reference. But, surprisingly, our computational scheme is most related to the known PLT and GTD algorithms, conceptually distant from both wavelets and video coding, and thus it can be called the hierarchical adaptive spatial triangular decomposition (HASTD). Owing to implementation advantages, our solution forms an interesting basis for developing a new class of image codecs.