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This paper describes the algorithms and procedures developed for reconstructing images using the hexagonal bar positron camera. This camera has six continuous position-sensitive detectors which are completely stationary, and it has some special software requirements. In particular, spatial nonlinearities in the detectors must be removed in software, the large but sparsely populated data matrix must be reduced in size, and the gaps in the data from the intersections of the detectors must be compensated for. These problems have been investigated, and an appropriate algorithm for this system has been implemented. The effectiveness of this algorithm was evaluated by reconstructing both real and simulated data.