Ridge functions, natural pixels and minimal norm reconstruction

In this work reconstruction from a finite number of projections using ridge functions within the framework of parallel beam geometry is considered. Theoretically, ridge functions are continuous solutions of a system of integral equations and their sum results in the minimal norm solution of the reconstruction problem. In practice, discretized versions of ridge functions are considered to obtain reconstruction from real data. Discrete projection data are modeled with the help of natural pixels. Analytical inversion formulas based both on ridge functions and natural pixels are derived. Results of numerical experiments are discussed.