Linear inverse problems

Abstract

This introductory treatment of linear inverse problems is aimed at students and neophytes. A historical survey of inverse problems and some examples of model inverse problems related to imaging are discussed to furnish context and texture to the mathematical theory that follows. The development takes place within the sphere of the theory of compact linear operators on Hilbert space, and the singular value decomposition plays an essential role. The primary concern is regularization theory: the construction of convergent well-posed approximations to ill-posed problems. For the most part, the discussion is limited to the familiar regularization method devised by Tikhonov and Phillips.