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

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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.