ABSTRACT

The basic idea of local tomography is to compute not the original function, but the result of action of an elliptic pseudodifferential operator. This chapter introduces a family of local tomography functions, and describes the generalizations of local tomography to the exponential and generalized Radon transforms. It develops a local tomography for the limited-angle problem. The chapter discusses Krein-Rutman theorem and provides an algorithm for finding values of jumps of a function. It introduces the cartesian coordinate system and provides a density plot of the local tomography function computed from the limited angle data. The chapter provides an illustration of the notation used for finding asymptotics of pseudodifferential operator, symbols of which have discontinuities on a conical surface.