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3年的研究中，我们专注于开发最佳的一维（1-D）和二维（2-D）可变分数延迟（VFD）数字滤波器的高分辨率图像插值。由于2-D VFD滤波器可以由一对具有不同延迟元件的1-D VFD滤波器级联而成，因此开发用于设计和实现1-D VFD滤波器的新算法尤为重要，这是获得良好的2-D VFD滤波器的基本步骤。因此，我们首先开发了几种新的方法来设计和实现1-D VFD滤波器，然后将1-D VFD滤波器推广到2-D的情况下，高精度的图像插值。本文主要研究了以下几个方面的新技术：（1）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）基于矢量阵列分解的VFD滤波器设计;（4）基于系数对称的VFD滤波器设计;（5）Lagrange型VFD滤波器的理论证明;（6）二维Lagrange型VFD滤波器在高分辨率图像插值中的应用我们用大量的图像例子说明，用二维VFD滤波器进行图像插值，在高分辨率图像插值方面上级现有的其他图像插值技术。准确性和降低的计算复杂度。

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

Variable fractional-delay filter design using weighted-least-squares singular-value decomposition

使用加权最小二乘奇异值分解的可变分数延迟滤波器设计

• DOI: 10.1109/tencon.2004.1414352
• 发表时间: 2004
• 期刊: The 2004 47th Midwest Symposium on Circuits and Systems, 2004. MWSCAS '04.
• 作者: T. 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)。