Efficient implementation of all-digital interpolation

Abstract

B-splines are commonly used for continuous representation of discrete time signals. This kind of representation proves to be very useful in applications such as image interpolation, rotation and edge detection. In all these applications, the first step is to compute the B-spline coefficients of the signal, and this involves the use of an IIR noncausal filter called the direct B-spline filter. The signal reconstruction is achieved using the indirect B-spline filter, which in many applications operates at a higher rate. In this paper, we introduce a simplified implementation of the signal reconstruction part that will significantly reduce the overall complexity. We also show that the direct B-spline filter can safely be replaced with a short FIR filter, without compromising the performance of the traditional method. Numerous examples show both visually and numerically that the differences between this method and the traditional one are indeed very small. Finally, we report the performance of these newly proposed methods in other image processing applications such as edge detection and least squares approximation.