Limited-angle tomography using constrained sinogram restoration

Summary form only given. An algorithm that calculates the maximum a posteriori estimate of the complete sinogram has been developed. It uses prior knowledge of the smoothness of the sinogram, fundamental mathematical constraints on the Radon transform, and a complete probabilistic characterization of the observation noise. The object is reconstructed using convolution backprojection applied to the restored sinogram. The observation that many objects of interest tend to have smooth sinograms, although the objects themselves may not be smooth, has been incorporated by defining a Markov random field prior probability on full sinograms, rather than on objects. The Markov random field used is of the simplest kind--nearest neighbor with quadratic potential terms--although more elaborate models can be used. Using a known noise model (zero-mean, Gaussian), the maximum a posteriori solution to the sinogram restoration problem can be formulated. The solution to this problem is a constrained optimization algorithm, and because of the simple form of both the prior and the observation noise, it was possible to develop an iterative primal-dual algorithm that converges quite rapidly to the desired solution.