Theory and Design of Local Interpolators

This paper shows that an error spectrum can be used to describe the performance of any convolutional interpolator used to shift an oversampled image. This spectrum is linear in the image power spectrum and in an error factor that depends only on the interpolator and the shift. The same form is shown to describe the interpolation of undersampled data, in an average sense. Simple formulas are derived for the error factor in either Fourier or real space, and standard interpolators are evaluated with them. Optimal interpolators are derived for various theoretical spectra: constant inband, Lorentzian, power law, and Gaussian. Practical methods of interpolator design are devised for use with image spectra that are known only partially or are not easily characterized analytically.