Mr. Arthur L. Cunha Profile

Arthur L. Cunha

at Univ of Illinois

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Proceedings Article | 17 September 2005 Paper

Filter design for directional multiresolution decomposition

Arthur Cunha, Minh Do

Proceedings Volume 5914, 59140V (2005) https://doi.org/10.1117/12.618314

KEYWORDS: Optical filters, Linear filtering, Denoising, Nonlinear filtering, Wavelets, Prototyping, Finite impulse response filters, Image compression, Fluctuations and noise, Image filtering

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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.

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