Learning image models for optimal information extraction: image registration from first principles

We demonstrate an unbiased method of image registration which has errors consistent with the Cramer-Rao bound (CRB) by using Super Registration: learning an optimal model for the underlying image and shifting that tomatch the data. Image registration is the inference of transformations relating noisy and distorted images. Fundamental in computer vision, experimental physics, and medical imaging, even in the simplest case of translation, known methods are biased and none achieve the CRB. Cutting edge experiments operator at extreme limits of signal-to-noise, for example, low-dose TEM imaging of sensitive biological materials. It is in these high-noise scenarios when existing registration techniques fail to correctly infer shifts. Following Bayesian inference, we prove that the standard method of shifting one image to match another cannot reach the CRB. We reach the theoretical lower bound in shift resolution and extract a higher resolution, de-noised model of the latent image. Finally, while sub-pixel errors in shift inference do not dramatically change the reconstructed image for oversampled data, we show that using our new registration method can lead to 10× more precise particle tracking.