2010
DOI: 10.1007/978-3-642-11620-9_21
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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 alg… Show more

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Cited by 3 publications
(1 citation statement)
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“…In contrast, one typically wants to obtain sparse sequences of dense vectors. A standard method for obtaining such results is the usage of a regularisation term that consists of the sum of the Euclidean norms of the coefficient vectors (see for instance [3,18,29,32]). Below, we also consider the setting where different norms than only the Euclidean one are used for the penalisation of the coefficient vectors.…”
Section: Joint Sparsitymentioning
confidence: 99%
“…In contrast, one typically wants to obtain sparse sequences of dense vectors. A standard method for obtaining such results is the usage of a regularisation term that consists of the sum of the Euclidean norms of the coefficient vectors (see for instance [3,18,29,32]). Below, we also consider the setting where different norms than only the Euclidean one are used for the penalisation of the coefficient vectors.…”
Section: Joint Sparsitymentioning
confidence: 99%