This paper presents a two-dimensional (2-D) eigenfilter technique to design 2-D perfect reconstruction (PR) filterbanks with directional vanishing moment (DVM). In this paper, we first introduce the DVM constraint for 2-D directional filterbank design. The proposed DVM constraint is imposed in 2-D eigenfilter formulation to obtain maximally flat 2-D low-pass analysis filter. Then, we use this designed analysis filter in 2-D time-domain formulation of PR condition to obtain complementary low-pass synthesis filters. The PR and DVM constraints are imposed to obtain 2-D low-pass synthesis filter. It is shown that the proposed 2-D filters satisfy the PR criteria with prescribed DVM. The performance of 2-D PR filters is evaluated in image denoising application. The performance of designed filterbank is compared with well-known existing methods in terms of peak signal-to-noise ratio to validate the results.

中文翻译：

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基于特征滤波法的具有方向消失矩的二维梅花形滤波器组设计

本文提出了一种二维 (2-D) 特征滤波器技术来设计具有方向消失矩 (DVM) 的二维完美重构 (PR) 滤波器组。在本文中，我们首先介绍了二维方向滤波器组设计的 DVM 约束。建议的 DVM 约束被强加在 2-D 特征滤波器公式中，以获得最大平坦的 2-D 低通分析滤波器。然后，我们在 PR 条件的二维时域公式中使用这种设计的分析滤波器来获得互补的低通合成滤波器。施加 PR 和 DVM 约束以获得二维低通合成滤波器。结果表明，所提出的二维滤波器满足具有规定 DVM 的 PR 标准。在图像去噪应用中评估二维 PR 滤波器的性能。