Optimized Spline Interpolation

TL;DR

This paper develops an optimized compact support spline interpolation method using calculus of variations, achieving high SNR and low computational complexity, outperforming conventional methods like cubic splines.

Contribution

It introduces a novel optimization approach for designing compact support interpolation kernels with guaranteed high SNR and computational efficiency.

Findings

Optimized splines outperform cubic splines in SNR.

The method reduces the optimization problem to a finite linear case.

Simulation results confirm superior performance of the proposed splines.

Abstract

In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite dimensional linear case, and then find the optimum compact support function that best approximates a given filter in the least square sense (l2 norm). The benefit of compact support interpolants is the low computational complexity in the interpolation process while the optimum compact support interpolant gaurantees the highest achivable Signal to Noise Ratio (SNR). Our simulation results confirm the superior performance of the proposed splines compared to other conventional compact support interpolants such as cubic spline.