Local tomography .2.

Standard, or global, tomography involves the reconstruction of a function f from line integrals. Local tomography, in this paper, involves the reconstruction of a related function, Lf = alpha(Lambda f + mu Lambda(-1)f), where is is the square root of the positive Laplacian, -Delta. This article is a sequel to the article ''Local Tomography'' [SIAM J. Appl. Math., 52 (1992), pp. 459-484, 1193-1198] by Faridani, Ritman, and Smith. The principal new results are (1) good bounds for Lambda f and Lambda(-1)f outside the support of f, particularly when f has 0 moments up to some order; (2) identification and reduction of global effects in local tomography, i.e., identification and reduction of the dependence of Lf(x) on the values of f at points at an intermediate distance from 2; (3) an algorithm for computing approximate density jumps from Lambda f when f is a linear combination of characteristic functions and a smooth background. Several examples are given: some from real x-ray data, some from mathematical phantoms. They include three-dimensional 7-micron resolution reconstructions from microtomographic scans.