Sampling and reconstruction for biomedical image registration

We investigate the problem of sampling and reconstruction of signals in the context of biomedical image registration. Given a finite energy input signal, a band limited point spread function, and Nyquist sampling scheme, we characterize the basis functions that can be used in reconstructing the signals so that the shift (pure translation) between two such input signals can be recovered exactly. Computational results using reconstruction using B-spline function spaces show that perfect reconstruction nor interpolation are not necessary for exact recovery of shifts between two signals.