2D and 3D Bayesian displacement estimation

Bayesian displacement estimation has been previously demonstrated in 1D and shown to reduce estimation and jitter and often bias. Here it is shown that the 1D implementation is directly extendable to 2D and 3D. 2D simulations are used to determine the validity of the perturbed likelihood function and empirically determine values for the scaling term α. 3D translation stage and in vivo cardiac experiments are used to examine the algorithm's performance for estimating displacements. The 2D simulations determined that a cap should be placed on the full scaling term (SNR/α). The 3D translation stage experiments show better performance in all three dimensions, and the 3D in vivo results show significant qualitative improvements as well as improvements in estimated levels of estimation variance.