A new formula of the Radon transform inversion

In this paper the well-known Radon transform inversion problem is considered. An approach to optimal reconstruction from a finite number of arbitrary directed projections within the framework of the conventional parallel beam geometry is suggested. The method considered converges to the minimal solution of the Radon problem, and a linear system of the Fredholm integral equations of the third kind in terms of one-dimensional functions is derived. As a consequence of the approach a new formula of the Radon transform inversion and a functional determining projection information content are obtained. The results of computer modelling are presented.