LOCAL TOMOGRAPHY

Tomography produces the reconstruction of a function f from a large nu mber of line integrals of f. Conventional tomography is a global proce dure in that the standard convolution formulas for reconstruction at a single point require the integrals over all lines within some plane c ontaining the point. Local tomography, as introduced initially, produc ed the reconstruction of the related function LAMBDA-f where LAMBDA is the square root of -DELTA, the positive Laplace operator. The reconst ruction of LAMBDA-f is local in that reconstruction at a point require s integrals only over lines passing infinitesimally close to the point , and Af has the same smooth regions and boundaries as f However, LAMB DA-f is cupped in regions where f is constant. LAMBDA-1f, also amenabl e to local reconstruction, is smooth everywhere and contains a counter -cup. This article provides a detailed study of the actions of LAMBDA and LAMBDA-1, and shows several examples of what can be achieved with a linear combination. It includes the results of x-ray experiments in which the line integrals are obtained from attenuation measurements on two-dimensional image intensifiers and fluorescent screens, instead o f the usual linear detector arrays.