A new method for complete-to-overcomplete discrete wavelet transforms

Overcomplete discrete wavelet transforms (ODWT) are used in a number of applications because they provide shift invariance, a property extremely useful in wavelet-based image processing and video coding. In this paper, we propose a new construction of the ODWT starting from the subbands of the critically sampled (complete) DWT. The most straightforward application of our theory is scalable video coding with in-band prediction, for which it has been shown that the proposed method achieves lower complexity.