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

I. Introduction

This paper develops an efficient cubic convolution filter that effectively restores and reconstructs digital images in a single pass. Image restoration is the process of recovering a more accurate image of a scene by removing or reducing degradations such as acquisition blurring, aliasing, and noise [1]. Basic methods for image restoration include deconvolution, least-squares filters, and iterative approaches [2], [3]. Image reconstruction is the process of defining a spatially continuous image from a set of discrete samples. Reconstruction is fundamental to many digital image processing operations such as geometric transforms, geometric corrections, and image registration [4]. Popular methods for reconstruction include nearest neighbor interpolation, bi-linear interpolation, cubic-spline interpolation, and piecewise cubic convolution [5].