Adaptive Wavelet Transforms via Lifting

Roger Claypoole (clayporl@rice.edu)
Electrical and Computer Engineering, Rice University

Richard Baraniuk (richb@rice.edu)
Electrical and Computer Engineering, Rice University

Robert Nowak (nowak@rice.edu)
Electrical and Computer Engineering, Rice University

This paper develops two new adaptive wavelet transfosm based on the lifting scheme. The lifting construction exploits a spatial-domain, prediction-error interpretation of the wavelet transofm and provides a powerful framework for designing customized transforms. We use the lifting construction to adaptively tune a wavelet transform to a desired signal by optimizing data-based prediction error criteria. The performance of the new transforms are compared to existing wavelet transforms, and applications to signal denoising are investigated.