Reconstruction of characteristic functions in two-dimensional Radon tomography

Abstract

Contents § 1. Introduction. The mathematical model of a tomograph § 2. Statement of results § 3. Reconstruction errors and series of oscillatory integrals § 4. Analysis of critical points § 5. Estimate of the discretization error 5.1. Preliminary remarks 5.2. Proof of Lemma 5.1 5.3. Proof of assertions 1 and 2 of Theorem 2.1 5.4. Proof of assertion 3 of Theorem 2.1 5.5. The formal convergence exponent and sharpness of the estimates 5.6. Concluding remarks Appendix. Estimates of oscillatory integrals 1. Integration by parts 2. The remainder term in the stationary phase method 3. Uniform estimates of one-dimensional oscillatory integrals 4. The regularization error 5. A special class of two-dimensional oscillatory integrals 6. Estimates of principal values of oscillatory integrals Index of notationBibliography