Theory and methods of processing speckle interferometry data from close visual binary stars are presented and implemented. The effects of the optical systems used for observing close visual binary stars are explained and simulated from both the geometrical and physical optical viewpoints. The atmospheric phase distortion and shot noise responsible for the observed speckle patterns are simulated. The deconvolution technique originally presented by Labeyrie is implemented to extract astrometric data from close visual binary stars. This method is applied to both simulated and experimental data from Kitt Peak National Observatory as validation. Parts of the deconvolution process are optimized to allow for near real time calculations in an automated observatory.