Two-parameter cubic convolution for image reconstruction

This paper presents an analysis of a recently-proposed two-parameter piecewise-cubic convolution algorithm for image reconstruction. The traditional cubic convolution algorithm is a one-parameter, interpolating function. With the second parameter, the algorithm can also be approximating. The analysis leads to a Taylor series expansion for the average square error due to sampling and reconstruction as a function of the two parameters. This analysis indicates that the additional parameter does not improve the reconstruction fidelity-the optimal two-parameter convolution kernel is identical to the optimal kernel for the traditional one-parameter algorithm. Two methods for constructing the optimal cubic kernel are also reviewed.