High-Accuracy Image Interpolation Using Multi-dimensional Variable Fractional-Delay Digital Filters

使用多维可变分数延迟数字滤波器进行高精度图像插值

• 批准号: 14550379
• 负责人: ITO Noboru
• 金额: $ 1.98万
• 依托单位: Toho University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14550379/
• 关键词: digital filter; Variable digital filter; fractional-delay filter; image interpolation; resolution conversion; Lagrange interpolation; one-dimensional VFD filter; two-dimensional VFD filter; 可変フィルタ; 非整数遅延; ラグランジュ型フィルタ; 位相遅延; 多次元フィルタ; 解像度; 再帰形

During this 3-year research, we focused on developing optimal one-dimensional (1-D) and two-dimensional (2-D) variable fractional-delay(VFD) digital filters for high-resolution image interpolation. Since 2-D VFD filters can be constructed by cascading a pair of 1-D VFD filters with different delay elements, so developing new algorithms for designing and implementing 1-D VFD filters is particularly important, which is the basic step for obtaining good 2-D VFD filters. Therefore, we first developed several new methods for designing and implementing 1-D VFD filters, then generalized the 1-D VFD filters to the 2-D case for high-accuracy image interpolation. The new techniques developed during this research are as follows :(1)weighted-least-squares method for designing VFD filters with also tunable magnitude ;(2)SVD-based design and new structures for VFD filters ;(3)VFD filter design using vector-array decomposition ;(4)VFD filter design using coefficient-symmetry ;(5)theoretical proof of Lagrange-type VFD filters ;(6)2-D Lagrange-type VFD filters for high-resolution image interpolation.We have used many image examples to show that the image interpolation using 2-D VFD filter is superior to other existing image interpolation techniques in terms of high-accuracy and reduced computational complexity.

在这项为期 3 年的研究中，我们专注于开发用于高分辨率图像插值的最佳一维 (1-D) 和二维 (2-D) 可变分数延迟 (VFD) 数字滤波器。由于二维VFD滤波器可以通过级联一对具有不同延迟元件的一维VFD滤波器来构造，因此开发用于设计和实现一维VFD滤波器的新算法尤为重要，这是获得良好的2维VFD滤波器的基本步骤。 -D VFD 滤波器。因此，我们首先开发了几种设计和实现一维 VFD 滤波器的新方法，然后将一维 VFD 滤波器推广到二维情况以进行高精度图像插值。本研究中开发的新技术如下：（1）用于设计幅度可调的VFD滤波器的加权最小二乘法；（2）基于SVD的VFD滤波器设计和新结构；（3）使用向量阵列分解；(4)利用系数对称性的VFD滤波器设计；(5)拉格朗日型VFD滤波器的理论证明；(6)二维拉格朗日型VFD滤波器高分辨率图像插值。我们使用许多图像示例来表明，使用二维VFD滤波器进行图像插值在高精度和降低计算复杂度方面优于其他现有图像插值技术。

项目成果

Tian-Bo Deng: "Weighted least-Squares design and parallel implementation of variable FIR filters"Proc. ITC-cscc 2002. 1. 686-689 (2002)

邓天波：“可变 FIR 滤波器的加权最小二乘设计与并行实现”Proc.

SVD-based important theorem for designing variable fractional-delay filters

基于 SVD 的可变分数延迟滤波器设计重要定理

• 发表时间: 2003
• 期刊: Proc. IEEE ICICS-PCM 2003 1
• 作者: T.-B.Deng;Y.Nakagawa;T.-B.Deng;Tian-Bo Deng;Tian-Bo Deng;Tian-Bo Deng;Tian-Bo Deng;Tian-Bo Deng;Tian-Bo Deng
• 通讯作者: Tian-Bo Deng

Tian-Bo Deng: "SVD-Based important theorem for designing variable fractional delay filters"Proc.ISPACS 2003. 1. 446-449 (2003)

邓天波：“基于SVD的可变分数延迟滤波器设计的重要定理”Proc.ISPACS 2003. 1. 446-449 (2003)

Tian-Bo Deng: "SVD-based design of fractional-delay 2-D digital filters exploiting specification symmetries"第18回ディジタル信号処理シンポジウム講演論文集. 1. C2-2-C2-2 (2003)

Tian-Bo Deng：“利用规范对称性的分数延迟二维数字滤波器的 SVD 设计”第 18 届数字信号处理研讨会论文集 1. C2-2-C2-2 (2003)。

Tian-Bo Deng: "Vector-array decomposition-based design of variable digital filters"Proc. 2002 International Symposium on New Paradigm VLSI Computing. 1. 91-94 (2002)

邓天波：“基于向量阵列分解的可变数字滤波器设计”。