This research develops a model-based spectral image reconstruction (MBSIR) algorithm to reconstruct images collected from the Advanced Electro-Optical System (AEOS) Spectral Imaging Sensor (ASIS). The development of the algorithm requires two key elements: 1. the statistics of the photon arrival and 2. estimates of the spatial and spectral transfer functions. With these two elements, the MBSIR algorithm can, through image postprocessing, dramatically increase the resolution of the images as well as give insight into the performance of the imaging sensor itself. The MBSIR algorithm is designed to simultaneously improve both the spatial and spectral resolution, and is derived for the general case of a spectrally variant imaging system. While MBSIR algorithms can be developed for any spectral imaging system, this research focuses on ASIS, a new spectral imaging sensor installed with the 3.6-m AEOS telescope at the Maui Space Surveillance Complex (MSSC). The primary purpose of ASIS is to take spatially resolved spectral images of space objects. The low-light levels and object motion inherent in imaging some objects in space, such as satellites, lead to a sensor design with less spectral resolution than required for image analysis. However, by applying MBSIR to the collected data, the sensor will be capable of achieving a higher resolution, allowing for better spectral analysis. The algorithm is shown to work with simulated ASIS data and measured data from an ASIS-like sensor.