A formula for least-squares projection and its application in image reconstruction

A novel method for the interpolation of sampled images is presented. It makes use of a recently discovered formula for the least-squares projection of an arbitrary function onto a repetitive basis. The proposed interpolation formula differs from standard techniques such as cubic spline convolution in that the image samples are modified by a discrete convolution operator prior to the reconstruction summation. The visual performance of the method is shown to be superior to that of cubic spline convolution, which is the best current algorithm. The main attraction of the method is that the algorithm is automatically tailored to the spatial resolution of the image sensor. The exact computational cost of the method, in terms of reconstruction sum size, depends on the sensor PSF (point spread function) but is likely to be only slightly greater than that for spline convolution. All the results given hold good in a general N-dimensional space