Exact reconstruction filters to invert Radon transforms with finite elements (Q1819558)

Let R be the Radon transform and \(R^*\) its adjoint. It has been known for a long time that \((R*g)*f=R*(g*Rf)\). This formula is extensively used in computerized tomography to derive inversion algorithms. The idea is to prescribe R*g freely (e.g. as an approximate \(\delta\)-function), to determine g which defines the reconstruction filter. The author constructs pairs R*g, g for two and three dimensions. He suggests to use these functions as trial functions in a Ritz method for inverting R.