Optimal Linear Interpolation of Images with Known Point Spread Function

The need for interpolation between pixels arises in many contexts. Kriging provides a general theory for optimal linear interpolation, which can be implemented and interpreted in either spatial or frequency domains. Of critical importance is knowledge of the autocorrelation function of the image at sub-pixel distances or, equivalently, the form of the spectrum near the Nyquist frequency. Although neither of these will typically be known, in many applications the point spread function of the imaging sensor is either known or can be estimated. We show how this knowledge can be combined with an assumption that the true scene is a Matern process, to derive a linear interpolant with minimum variance which takes account of the effects of aliasing in the sampled image. We apply the new method to both simulated and X-ray computed tomography images, and show it to be superior to bicubic and sinc interpolation for images that are not band-limited at the Nyquist frequency.