This thesis investigates a technique known as "coring" which can be used to reduce noise in two-dimensional video images. Coring passes the high spatial frequency components of a noisy image through a non-linear "coring function". This function operates on each pixel and is a function of pixel intensity. This thesis provides a theoretical justification for the success of coring in noise reduction. Coring functions are generated using the theoretical results and then tested on a set of images. Finally, this thesis develops an algorithm for noise reduction given a statistical characterization of the noise.