Iterative Least-Square Method for 1-D Inversion Problems in Optical Tomography

Tadi, M.
December 2007
International Journal of Computational & Applied Mathematics;2007, Vol. 2 Issue 3, p253
Academic Journal
This note considers two coefficient identification problems for a one-dimensional parabolic equation. It introduces a similar algorithm for both problems that is iterative in nature. The algorithm assumes an initial guess for the unknown function and obtains a background field. After linearizing around the background field, it obtains an integral equation for the correction to the assumed function. At every iteration the algorithm needs to solve an integral equation. It uses Tikhonov regularization to stabilize the solution of the integral equation. A number of examples are used to demonstrate the applicability of the proposed method.


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