Frame decompositions of bounded linear operators in Hilbert spaces with applications in tomography

We consider the decomposition of bounded linear operators on Hilbert spaces in terms functions forming frames. Similar to singular-value decomposition, resulting frame decompositions encode information structure and ill-posedness problem can be used as basis for design implementation efficient numerical solution methods. In contrast presented derived explicitly a wide class operators, particular those satisfying certain stability condition. order show usefulness this approach, we different examples from field tomography.