Single-rate calculation of overcomplete discrete wavelet transforms for scalable coding applications

A number of emerging resolution-scalable image and video coding algorithms have recently shown very promising performance due to the use of overcomplete wavelet representations. In these applications, the overcomplete discrete wavelet transform (ODWT) is derived starting from the critically-sampled subbands of the DWT (complete representation) of a certain decomposition (resolution) level. This process, which is a complete-to-overcomplete DWT (CODWT), is used for wavelet domain operations that require shift invariance. Specifically, both the encoder and decoder independently construct the overcomplete representation at the best accuracy possible, given the critically-sampled subbands of a certain resolution level. In contrast to the classical approach for performing the CODWT, which is a multi-rate calculation scheme that requires the reconstruction of the input spatial-domain signal, in this paper we propose a new, single-rate calculation scheme, which is formalized for the general case of an arbitrary decomposition (resolution) level. Based on derived symmetry properties, a simple implementation structure of the proposed approach provides interesting tradeoffs for the required multiplication budget in comparison to the conventional approach. This leads to a complexity-scalable solution that fits the versatile requirements of scalable coding environments. The use of the proposed single-rate calculation scheme of the CODWT is demonstrated in several image and video coding systems.