Polynomial spline signal processing algorithms

The authors describe a novel digital filtering algorithms for the processing and representation of signals using polynomial splines. The classical polynomial spline interpolation problem is considered. It is found that it can be solved efficiently by recursive digital filtering. This result also yields a simple procedure for signal differentiation. Filters that efficiently solve the problem of smoothing spline approximations are derived. This technique is a regularized version of spline interpolation and is therefore less sensitive to noise. It is applied to the design of a robust edge detection algorithm with an adjustable scale parameter. A filtering/sampling algorithm for least squares spline approximation is described. This data reduction technique is applied to the generation of a cubic spline image pyramid that is found to compare favorably with the Gauss/Laplace pyramid