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Multidimensional Directional Filter Banks and Surfacelets

机译:多维定向滤波器组和表面

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In 1992, Bamberger and Smith proposed the directional filter bank (DFB) for an efficient directional decomposition of 2-D signals. Due to the nonseparable nature of the system, extending the DFB to higher dimensions while still retaining its attractive features is a challenging and previously unsolved problem. We propose a new family of filter banks, named NDFB, that can achieve the directional decomposition of arbitrary N-dimensional (Nges2) signals with a simple and efficient tree-structured construction. In 3-D, the ideal passbands of the proposed NDFB are rectangular-based pyramids radiating out from the origin at different orientations and tiling the entire frequency space. The proposed NDFB achieves perfect reconstruction via an iterated filter bank with a redundancy factor of N in N-D. The angular resolution of the proposed NDFB can be iteratively refined by invoking more levels of decomposition through a simple expansion rule. By combining the NDFB with a new multiscale pyramid, we propose the surfacelet transform, which can be used to efficiently capture and represent surface-like singularities in multidimensional data
机译:1992年,Bamberger和Smith提出了定向滤波器组(DFB),用于有效地二维信号的定向分解。由于系统的不可分割的性质,将DFB扩展到更高的尺寸,同时仍保留其吸引人的功能是一个具有挑战性且以前尚未解决的问题。我们提出了一个新的滤波器组系列,称为NDFB,它可以通过简单高效的树状结构实现任意N维(Nges2)信号的定向分解。在3-D中,建议的NDFB的理想通带是基于矩形的金字塔,该金字塔从原点以不同的方向辐射出去,并拼接整个频率空间。提议的NDFB通过N-D中N为冗余因子的迭代滤波器组实现了完美的重构。通过使用简单的扩展规则调用更多分解级别,可以迭代地完善所提议的NDFB的角分辨率。通过将NDFB与新的多尺度金字塔相结合,我们提出了表面波变换,该变换可用于有效捕获和表示多维数据中的表面状奇点

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