Differential SART for sub-Nyquist tomographic reconstruction in presence of misalignments

In this paper we study tomographic reconstruction methods in the case that prior knowledge about the object is available. In particular, we consider the case that a reference object that is similar in shape and orientation is available, which is very common in non-destructive testing applications. We demonstrate that a differential version of existing reconstruction methods can easily be derived which reconstructs only the deviation between test and reference object. Since this difference volume is significantly more sparse, the differential reconstruction can be implemented very efficiently. We also discuss the case where knowledge about the misalignment between test and reference object is available, in which case the efficiency of the differential reconstruction can be improved even further. The resulting algorithm is faster, more accurate, and less sensitive to the choice of the step size parameters and regularization than state of the art reconstruction methods.