| This thesis pursues a statistical investigation of a multi-frame image restoration technique, and in particular derived estimates on the statistical uncertainty associated with one commonly used image displacement estimation algorithm. Such displacement uncertainty is then leveraged to provide implicit kernelling of image pixels when they are recombined in a composite image of possibly higher sampling density and lower noise than any constituent image. In the course of this statistical investigation, a novel orthogonal regression routine was developed that extends any desirable ordinary regression algorithm to the case where some or all of the "independent" regression variables have measurement errors in addition to the measurement error of the notionally "dependent" variable. This novel orthogonal regression algorithm was then further developed into the Method of Orthogonal Excision, providing a technique equivalent to Principal Component Decomposition, but with the benefits of alternative error metrics and outlier rejection associated with any desirable ordinary regression technique. |
