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.
An Iterative Algorithm with Joint Sparsity Constraints for Magnetic Tomography / Pitolli, Francesca; Gabriella, Bretti. - STAMPA. - 5862:(2010), pp. 316-328. (Intervento presentato al convegno 7th International Conference on Mathematical Methods for Curves and Surfaces tenutosi a Tonsberg, NORWAY nel JUN 26-JUL 01, 2008) [10.1007/978-3-642-11620-9_21].
An Iterative Algorithm with Joint Sparsity Constraints for Magnetic Tomography
PITOLLI, Francesca;
2010
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.