The approximate inverse is presented as general regularization method that allows for including invariances of the underlying mathematical model. First, for a given mollifier, a reconstruction kernel is computed independently of the data yb solving an auxiliary problem. The invariances result in fast implementations.
Especially, if the same problem has to solved repeatedly, as in scanning devices e.g., this method brings many advantages. Applications in three-dimensional x-ray tomography are discussed, reconstrucitons from measured data are presented showing the power of the method.
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