Design of Optimal Quincunx Filter Banks for Image Coding
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Research Article Design of Optimal Quincunx Filter Banks for Image Coding Yi Chen, Michael D. Adams, and Wu-Sheng Lu Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC, Canada V8W 3P6 Received 31 December 2005; Revised 8 June 2006; Accepted 16 July 2006 Recommended by Ivan Selesnick Two new optimization-based methods are proposed for the design of high-performance quincunx filter banks for the application of image coding. These new techniques are used to build linear-phase finite-length-impulse-response (FIR) perfectreconstruction (PR) systems with high coding gain, good frequency selectivity, and certain prescribed vanishing-moment properties. A parametrization of quincunx filter banks based on the lifting framework is employed to structurally impose the PR and linear-phase conditions. Then, the coding gain is maximized subject to a set of constraints on vanishing moments and frequency selectivity. Examples of filter banks designed using the newly proposed methods are presented and shown to be highly effective for image coding. In particular, our new optimal designs are shown to outperform three previously proposed quincunx filter banks in 72% to 95% of our experimental test cases. Moreover, in some limited cases, our optimal designs are even able to outperform the well-known (separable) 9/7 filter bank (from the JPEG-2000 standard). Copyright © 2007 Yi Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Filter banks have proven to be a highly effective tool for image coding applications [1]. In such applications, one typically desires filter banks to have perfect reconstruction (PR), linear-phase, high coding gain, good frequency selectivity, and satisfactory vanishing-moment properties. The PR property facilitates the construction of a lossless compression system. The linear-phase property is crucial to avoiding phase distortion. High coding gain leads to filter banks with good energy compaction capabilities. The presence of vanishing moments helps to reduce the number of nonzero coefficients in the highpass subbands and tends to lead to smoother synthesis basis functions. Good frequency selectivity serves to minimize aliasing in the subband signals. Designing nonseparable two-dimensional (2D) filter banks with all of the preceding properties is an extremely challenging task. In the one-dimensional (1D) case, various filter-bank design techniques have been successfully developed. In the nonseparable 2D case, however, far fewer effective methods have been proposed. Variable transformation methods are commonly used for the design of 2D filter banks. With such methods, a 1D prototype filter bank is first designed, and then mapped into a 2D filter bank through a transformation of variables [2–6]. For example, the McClellan transformation [7] has been used in numerous design approaches.
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