Tomographic reconstruction from both interferometric and absorption data is a potentially powerful tool for experimental observations of compressible fluid mechanics, combustion, and heat transfer. In many of these cases, both flow field images and ensemble statistics are desired. The use of an ensemble of noisy tomographic data sets to synthesize image statistics and stabilize individual reconstructions using a Maximum A Posteriori (MAP) reconstruction technique is presented. The MAP technique uses the ensemble mean and variances of the source function to constrain individual reconstructions of the ensemble. In this paper, we show that by synthesizing the mean and variances using preliminary algebraic reconstructions, the reconstruction of the individual realizations can be improved. The technique is demonstrated using a group of source images generated with a fractal sum of pulses technique. The paper discusses a fractal model for turbulent mixing field images, the selection of the preliminary reconstruction technique, and the results of MAP and synthetic MAP reconstructions.