Estimating homeomorphic deformations of multi-dimensional signals - An accuracy analysis

Consider the problem of estimating a multi-dimensional signal in the presence of an unknown deformation of its coordinates and additive Gaussian noise. This problem arises in a wide range of engineering applications including image registration, image classification, and speech processing. A fundamental solution to this problem involves estimating the unknown parameters of a model for the distorting function. The achievable parameter estimation accuracy for this problem is evaluated using the Cramer Rao lower bound. The performance of a recently developed low complexity linear estimator is analyzed.