Image reconstruction by bivariate quadratic splines

An approximation method for reconstructing the smooth image from a set of pixel data is described. The approximation space used is the space of bivariate piecewise polynomials of total degree two on the crisscross triangulation that have continuous first partial derivatives everywhere. This space is known to have a basis consisting of minimally supported functions, called B-splines for convenience. An iterative algorithm is developed to increase the accuracy of approximation and demonstrated numerically to be convergent. Numerical comparisons to other approximation and interpolation techniques are presented using two different error measures. Examples of image reconstructions are included