Two-dimensional cubic convolution for one-pass image restoration and reconstruction

This paper formulates two-dimensional parametric cubic convolution for one-pass image restoration and reconstruction and derives a closed-form solution for the mean-square optimal parameters. The approach improves on traditional separable cubic convolution and relaxes the interpolation constraint to support restoration. The resulting kernel has five parameters and is designated 2D-5PCC-R. The closed-form solution for the optimal parameters is based on a continuous-discrete-continuous system model that accounts for the scene ensemble, acquisition blurring, sampling, noise, and processing. The analysis of the model leads to a simultaneous solution for five linear equations in the five parameters