Metropolis Monte Carlo for tomographic reconstruction with prior smoothness information

The Metropolis Monte Carlo algorithm was applied to produce tomographic reconstructions from scarce projection data supplemented by prior information about the smoothness of the object. The prior information is represented by means of local energy functions, which are added to the projection error. The proposed prior function is an extension of previous proposals of border filters, the novelty introduced here being an adaptive control of the filter during the reconstruction process. The method was tested on synthetic phantoms and the reconstructions of a real object from a small number of projections. The technique shows good results in images with piecewise homogeneous regions, and can be useful in certain applications, where the scanning views are within an angular range that is either limited or sparsely sampled, as the detection of material defects in non-destructive testing or special anatomical components in medical images. Finally, the method is applied to the reconstruction of an industrial application of a stainless-steel BNC elbow from very few projections.