Abstract:

A formula for inverting the control submatrix of the singular value decomposition of the Radon transform is obtained. We prove that the pseudoinverse matrix is expressed in terms of the submatrix itself and its calculation does not require the use of linear algebra packages. The formula and proof are given.  The practical value lies in the ability to control the components of the singular value decomposition of the Radon transform and to filter and analyze images. The numerical experiments on real-world images demonstrate the efficiency of the techniques proposed.