Abstract
Magnetic tomography is an ill-posed and ill-conditioned inverse problem since, in general, the solution is non-unique and the measured magnetic field is affected by high noise.
We use a joint sparsity constraint to regularize the magnetic inverse problem. This leads to a minimization problem whose solution can be approximated by an iterative thresholded Landweber algorithm. The algorithm is proved to be convergent and an error estimate is also given.
Numerical tests on a bidimensional problem show that our algorithm outperforms Tikhonov regularization when the measurements are distorted by high noise.
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Pitolli, F., Bretti, G. (2010). An Iterative Algorithm with Joint Sparsity Constraints for Magnetic Tomography. In: Dæhlen, M., Floater, M., Lyche, T., Merrien, JL., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2008. Lecture Notes in Computer Science, vol 5862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11620-9_21
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DOI: https://doi.org/10.1007/978-3-642-11620-9_21
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