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

A number of methods exist specifically for the interpolation of periodic fu nctions from a finite number of samples. When the samples are known exactly , exact interpolation is possible under certain conditions, such as when th e function is bandlimited to the Nyquist frequency of the samples. However, when the samples are corrupted by noise, it is just as important to consid er the noise properties of the resulting interpolated curve as it is to con sider its accuracy. In this work, we derive analytic expressions for the co variance and variance of curves interpolated by three periodic interpolatio n methods-circular sampling theorem, zero-padding, and periodic spline inte rpolation-when the samples are corrupted by noise. We perform empirical stu dies for the special cases of; white and Poisson noise and find the results to be in agreement with the analytic derivations. The implications of thes e findings for few-view tomography are also discussed.