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Limited-data tomography, to which electromagnetic geotomography belongs, is analyzed in this paper. In this technique, a discrete forward projection model may be expressed by a rank-deficient system of linear equations whose the nullspace is non-trivial. This means that some image components may fall into the nullspace, and hence the minimal-norm least-square solution, to which many image reconstructions methods converge, may be different from the true one. The Algebraic Reconstruction Technique (ART), Simultaneous Iterative Reconstruction Technique (SIRT), or Conjugate Gradients Least Squares (CGLS) are examples of such methods. In this paper, we deal with the question of how to partially recover the missing image components. First, we analyze the advantages of using the iterative Tikhonov regularization and the Maximum A Posteriori (MAP) algorithm with Gibbs prior. Then, we conclude that the missing (nullspace) image components can be partially recovered if the MAP algorithm is implemented through a multigrid technique.The results, which are presented for synthetic noise-free and noisy data, demonstrate the validity of our assumption. The problem of estimating the regularization and scaling parameters in the MAP algorithm is also addressed.

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application/pdf

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oai:lib.psnc.pl:633

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limited-data tomography, multigrid image reconstruction, hyperparameter estimation, electromagnetic geotomography

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PSNC Institutional Repository > Computational Methods in Science and Technology

PSNC Institutional Repository > Computational Methods in Science and Technology > 2007

PSNC Institutional Repository > Computational Methods in Science and Technology > 2007 > Volume 13(1)2007

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Aug 18, 2014

In our library since:

Jun 2, 2014

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179

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https://lib.psnc.pl/publication/807

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Volume 13(1) 2007

Edition name	Date
Multigrid Regularized Image Reconstruction for Limited-Data Tomography	Aug 18, 2014

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