Noise properties of periodic interpolation methods with implications for few-view tomography

A number of methods exist specifically for the interpolation of periodic functions from a finite number of samples. When the samples are known exactly, exact interpolation is possible under certain conditions, such as when the function is band-limited to the Nyquist frequency of the samples. However, when the samples are corrupted by noise, it is just as important to consider the noise properties of the resulting interpolated curve as it is to consider its accuracy. In this work, we derive analytic expressions for the covariance and variance of curves interpolated by three periodic interpolation methods-the circular sampling theorem, zero padding and periodic spline interpolation-when the samples are corrupted by noise. We perform empirical studies for the special cases of white and Poisson noise and find the results to be in agreement with the analytic derivations. The implications of these findings for few-view tomography are also discussed.