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A modified gradient method for two-dimensional problems in tomography. (English) Zbl 0757.65133

A method for reconstruction of a bounded two-dimensional inhomogeneous object from a measured scattered field is presented. The governing domain integral equation is solved iteratively by a successive overrelaxation technique.
Convergence of this process is established for indices of refraction much larger than required for convergence of the Born approximation. Numerical results are presented for a number of representative two-dimensional objects.

MSC:

65R10 Numerical methods for integral transforms
65R30 Numerical methods for ill-posed problems for integral equations
44A12 Radon transform
92C55 Biomedical imaging and signal processing
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