9 December 1997 Extension of Tikhonov regularization based on varying the singular values of the regularization operator
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Abstract
We consider the numerical solution of first kind Fredholm integral equations. Such integral equations occur in signal processing and image recovery problems among others. For this numerical study, the kernel k(x,t) is the sinc kernel. This study compares traditional Tikhonov regularization with an extension of Tikhonov regularization which updates the solution found by the usual method. In this work, both the identity, derivative and Laplacian operators are used as regularizers and tests were done with and without error in the image data g(x). The results indicate that the extension can provide a decrease in error of about two orders of magnitude.
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Monica M. Alger, John W. Hilgers, William R. Reynolds, Barbara S. Bertram, "Extension of Tikhonov regularization based on varying the singular values of the regularization operator", Proc. SPIE 3171, Computational, Experimental, and Numerical Methods for Solving Ill-Posed Inverse Imaging Problems: Medical and Nonmedical Applications, (9 December 1997); doi: 10.1117/12.279728; https://doi.org/10.1117/12.279728
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