INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL J. Phys. A: Math. Gen. 34 (2001) 1271–1283 www.iop.org/Journals/ja PII: S0305-4470(01)19639-3 A generalized information theoretical approach to tomographic reconstruction Amos Golan 1, 3 and Volker Dose 2 1 American University, Roper 200, 4400 Massachusetts Ave, NW Washington, DC20016-8029, USA 2 Centre for Interdisciplinary Plasma Science, Max-Planck-Institut f ¨ ur Plasmaphysik, EURATOM Association, D-85748 Garching b. M¨ unchen, Germany E-mail: agolan@american.edu Received 16 November 1999, in final form 4 January 2001 Abstract A generalized maximum-entropy-based approach to noisy inverse problems such as the Abel problem, tomography or deconvolution is presented. In this generalized method, instead of employing a regularization parameter, each unknown parameter is redefined as a proper probability distribution within a certain pre-specified support. Then, the joint entropies of both, the noise and signal probabilities, are maximized subject to the observed data. After developing the method, information measures, basic statistics and the covariance structure are developed as well. This method is contrasted with other approaches and includes the classical maximum-entropy formulation as a special case. The method is then applied to the tomographic reconstruction of the soft x-ray emissivity of the hot fusion plasma. PACS numbers: 4230W, 0250F, 0250P 1. Introduction A common problem in analysing physical systems is limited data. In most cases, these data are in terms of a small number of expectation values, or moments, representing the distribution governing the system or process to be analysed. Examples of limited data problems include: reconstructing an image from incomplete and noisy data; reconstruction problems in emission tomography such as estimating the spatial intensity function based on projection data; estimation of the local values of some quantity of interest from available chordal measurements of plasma diagnostics (the discrete Abel inversion problem); and simply reconstructing a discrete probability distribution from a small number of observed moments. When working with such limited data, an inversion procedure is required in order to obtain estimates of the unobserved parameters. But with limited data the problem may be 3 NSF/ASA/Census Senior Research Fellow. 0305-4470/01/071271+13$30.00 © 2001 IOP Publishing Ltd Printed in the UK 1271