Interpolation and resampling in image processing and holography

In this paper, we present an overview of some recent advances in interpolation and resampling. We are particularly interested in the linear, convolution-based interpolation techniques where new image pixels are generated by first fitting a certain continuous function to the given uniformly sampled data and then resampled at the desired coordinates. We start with stating the interpolation problem in signal and frequeny domain and then continue with describing the interpolation artifacts and how to evaluate the interpolator's performance. We then review the class of piecewise-polynomial interpolators of minimal support as the best compromise between high performance and acceptable cost. We describe efficient filter structures, discuss different optimized designs and give comparative results both experimental and analytical.