Three-dimensional reconstructions from projections are usually ridden by noise from different sources. A common problem among many three-dimensional reconstruction techniques is the systematic absence of certain projections, but also the accidental absence of spurious projections. In these three-dimensional reconstructions such absences are visible as directional smearing due to convolution. Other convolution effects such as those due to the optics of the instrument used to record the data usually cause severe damping of high frequencies and even contrast reversal (common in images from electron microscopes).

Several approaches to overcome these ‘noise’ effects in three-dimensional reconstructions have been developed, but they usually suffer from the very small radius of convergence. Very easily and commonly, the refinement iterations end up stuck in a premature choice of a minimum. We have developed another algorithm, constrained maximum entropy tomography (COMET), that in practice has been shown to overcome these problems.