Maximum Entropy (ME) techniques have found widespread applicability in the reconstruction of incomplete or noisy data. These techniques have been applied in many areas of data analysis including imaging, spectroscopy, and scattering [Gull and Skilling, 1984]. The techniques have proven particularly useful in astronomy [Narayan and Nityanada, 1984]. In many of these applications the goal of the reconstruction is the detection of point objects against a noisy background. In this work we investigate the applicability of ME techniques to data sets which have strong components which are periodic...