A Bottom-Up Design Approach of Critically Sampled Contourlet Transform for Efficient Image Representation

Seisuke KYOCHI  Shizuka HIGAKI  Yuichi TANAKA  Masaaki IKEHARA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.3   pp.762-771
Publication Date: 2009/03/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.762
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Latest Advances in Fundamental Theories of Signal Processing)
Category: 
Keyword: 
critical sampling,  contourlet,  directional filter bank,  wavelet transform,  non-linear approximation,  

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Summary: 
In this paper, a novel design method of critically sampled contourlet transform (CSCT) is proposed. The original CT which consists of Laplacian pyramid and directional filter bank provides efficient frequency plane partition for image representation. However its overcompleteness is not suitable for some applications such as image coding, its critical sampling version has been studied recently. Although several types of the CSCT have been proposed, they have problems on their realization or unnatural frequency plane partition which is different from the original CT. In contrast to the way in conventional design methods based on a "top-down" approach, the proposed method is based on a "bottom-up" one. That is, the proposed CSCT decomposes the frequency plane into small directional subbands, and then synthesizes them up to a target frequency plane partition, while the conventional ones decompose into it directly. By this way, the proposed CSCT can design an efficient frequency division which is the same as the original CT for image representation can be realized. In this paper, its effectiveness is verified by non-linear approximation simulation.