Academic Commons

Articles

Overcomplete Lifted Wavelet Representations for Multiscale Feature Analysis

Shim, Minbo; Laine, Andrew F.

The lifting scheme was introduced as a flexible tool to construct compactly supported second generation wavelets and the wavelet transform. However because it is not translation invariant, the traditional lifting framework may not be good for multiscale feature analysis where translation-invariant characteristics are highly desirable. In this paper we address the following question: can the lifting scheme be used as a framework for overcomplete wavelet representations with multiscale feature analysis in mind? We address this question by investigating each stage of the multiscale analysis: split, dual lifting and primal lifting. We introduce a smoothing lazy wavelet in the split stage. We then show that only the dual lifting is necessary since the primal lifting required to compensate for the aliasing needs no longer exist. We also demonstrate that the proposed scheme achieves better performance without introducing boundary artifacts that exist in the traditional methods.

Files

Also Published In

Title
1998 International Conference on Image Processing : proceedings : ICIP 98 : October 4-7, 1998, Chicago, Illinois, USA, vol. 2
DOI
https://doi.org/10.1109/ICIP.1998.723356

More About This Work

Academic Units
Biomedical Engineering
Publisher
IEEE
Published Here
August 17, 2010
Academic Commons provides global access to research and scholarship produced at Columbia University, Barnard College, Teachers College, Union Theological Seminary and Jewish Theological Seminary. Academic Commons is managed by the Columbia University Libraries.