Filter design for directional multiresolution decomposition

Arthur L. Cunha; Minh N. Do

doi:10.1117/12.618314

17 September 2005 Filter design for directional multiresolution decomposition

Arthur L. Cunha, Minh N. Do

Proceedings Volume 5914, Wavelets XI; 59140V (2005) https://doi.org/10.1117/12.618314
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

Abstract

In this paper we discuss recent developments on design tools and methods for multidimensional filter banks in the context of directional multiresolution representations. Due to the inherent non-separability of the filters and the lack of multi-dimensional factorization tools, one generally has to overcome factorization by indirect methods. One such method is the mapping technique. In the context of contourlets we review methods for designing filters with directional vanishing moments (DVM). The DVM property is crucial in guaranteeing the non-linear approximation efficacy of contourlets. Our approach allows for easy design of two-channel linear-phase filter banks with DVM of any order. Next we study the design via mapping of nonsubsampled filter banks. Our methodology allows for a fast implementation through ladder steps. The proposed design is then used to construct the nonsubsampled contourlet transform which is particularly efficiently in image denoising, as experiments in this paper show.

Citation Download Citation

Arthur L. Cunha and Minh N. Do "Filter design for directional multiresolution decomposition", Proc. SPIE 5914, Wavelets XI, 59140V (17 September 2005); https://doi.org/10.1117/12.618314

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