ABSTRACT
This chapter discusses a method for analytical inversion of incomplete Fourier transform data. It uses the Paley-Wiener-Schwartz theorem for deriving a basic result of analytical inversion of the Fourier transform data. The chapter considers different numerical aspects for performing the analytical inversion of incomplete Fourier transform data and constructs an algorithm for the data inversion. It discusses a Filtered backprojection method for inversion of the limited-angle tomographic data, and a modified filtered backprojection algorithm is developed. The chapter reviews the extrapolation problem based on available tomographic data. It uses the classical idea of the Lagrange interpolation formula for entire spheroidal functions.
