A new sensor, the Advanced Electro-Optical System (AEOS) Spectral Imaging Sensor (ASIS) has been developed at the Maui Space Surveillance Complex (MSSC). ASIS is capable of collecting resolved imagery of space objects in 10\u27s-100\u27s of spectral bands while using an adaptive optics system. However, the stringent requirements of collecting ground-based images requires a sensor that induces spectral blurring. Post-processing algorithms to remove this blurring are required to fully exploit these spectral images. This research focuses on developing the reconstruction algorithms, based on proven estimation theories, required to spectrally deblur the images collected from ASIS. Additionally, the research will expand the algorithm to also estimate the linear polarizations of the scene. The Cramer-Rao lower bounds on two key performance parameters, the spectral resolution and accuracy, of the reconstruction algorithm will also be calculated. Through the examination of these lower bounds a performance metric can be determined. This metric can be used to compare the ability of the algorithm to work on different spectral sensors