Cardinal MK-spline signal processing: Spatial interpolation and frequency domain filtering

Abstract

Altering the sampling rate of a digital signal by interpolation is a very important task in many digital signal processing applications. MK-spline is a kind of promising cardinal spline or explicit interpolation spline, which can achieve the purpose of interpolation without solving systems of coefficient equations, and which can inherit almost all good properties of B-splines, such as local support, high order smoothness, and central symmetry. For using MK-spline as a tool in signal and image processing, we first provide elementary theory which is composed of MK-spline convolution representation, related Fourier transform in continuous domain, and z transform of expanded MK-spline in discrete domain. Then, a cubic MK-spline interpolating filter (MKIF) is designed as a physically realizable FIR digital filter based on the discrete convolution operation which outputs directly a discrete smoothed signal from an input discrete signal. Next, frequency domain MK-spline lowpass and highpass filters are also devised in this study for image smoothing, sharpening, and denoising. Finally, simulated experiments are presented in different dimensional data formats in order to verify that the convolution-based MKIF is faster than those based on traditional continuous method, and that the proposed MK-spline filters have significantly good characteristics in the processes of signal reconstruction, image enlargement, and image denoising, when compared with traditional linear filters and classical B-spline filters.