Reconstruction algorithms of an inverse source problem for the Helmholtz equation
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Acosta, S., Chow, S., Taylor, J., Villamizar, V.: On the multi-frequency inverse source problem in heterogeneous media. Inverse Probl. 28(7), 075013 (2012)
Alves, C., Kress, R., Serranho, P.: Iterative and range test methods for an inverse source problem for acoustic waves. Inverse Probl. 25(5), 055005 (2009)
Alves, C., Mamud, R., Martins, N., Roberty, N.: On inverse problems for characteristic sources in Helmholtz equations. Math. Probl. Eng. 2017, 1–16 (2017)
Alves, C., Martins, N., Roberty, N.: Full identification of acoustic sources with multiple frequencies and boundary measurements. Inverse Probl. Imag. 3(2), 275–294 (2009)
Badia, A., Nara, T.: An inverse source problem for Helmholtz’s equation from the cauchy data with a single wave number. Inverse Probl. 27(10), 105001 (2011)
Coleman, T., Li, Y.: On the convergence of interior-reflective newton methods for nonlinear minimization subject to bounds. Math. Program. 67(1), 189–224 (1994)
Coleman, T., Li, Y.: An interior, trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6, 418–445 (1996)
Colton, D., Kress, R.: Inverse Acoustic and Electromagnetic Scattering Theory. Applied Mathematical Sciences, 2nd edn., p 93. Springer, New-York (1998)
Hamad, A., Tadi, M.: A numerical method for inverse source problems for poisson and Helmholtz equations. Phys. Lett. A 380(44), 3707–3716 (2016)
Hämäläinen, M., Hari, R., Ilmoniemi, R., Knuutila, J., Lounasmaa, O.: Magnetoencephalography-theory, instrumentation, and applications to noninvasive studies of the working human brain. Rev. Modern Phys. 65, 413–497 (1993)
Hanke, M., Rundell, W.: On rational approximation methods for inverse source problems. Inverse Probl. Imag. 5(1), 185–202 (2011)
He, S., Romanov, V.: Identification of dipole sources in a bounded domain for Maxwell’s equations. Wave Motion 28(1), 25–40 (1998)
Ikehata, M.: Reconstruction of a source domain from the cauchy data. Inverse Probl. 15(2), 637 (1999)
Isakov, V.: Inverse Source Problems. Mathematical Surveys and Monographs. American Mathematical Society (1990)
Kress, R., Rundell, W.: Reconstruction of extended sources for the Helmholtz equation. Inverse Probl. 29(3), 035005 (2013)
Levenberg, K.: A method for the solution of certain problems in least-squares. Q. Appl. Math. 2, 164–168 (1944)
Marquardt, D.: An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math. 11(2), 431–441 (1963)
Meyer, R., Roth, P.: Modified damped least squares: an algorithm for non-linear estimation. IMA J. Appl. Math. 9(2), 218–233 (1972)
Moré, J.: The Levenberg-Marquardt algorithm: implementation and theory. Lect. Notes Math. 630, 105–116 (1978)
Novikov, P.: Sur le probléme inverse du potentiel. Dokl.akad.nauk Sssr 18, 165–168 (1938)
Rainha, M., Roberty, N.: Integral and variational formulations for the Helmholtz equation inverse source problem. Math. Probl. Eng. 2012(1), 95–100 (2012)
Roberty, N., Alves, C.: On the identification of star-shape sources from boundary measurements using a reciprocity functional. Inverse Probl. Sci. Eng. 17 (2), 187–202 (2009)
Schuhmacher, A., Hald, J., Rasmussen, K., Hansen, P.: Sound source reconstruction using inverse boundary element calculations. J. Acous. Soc. America 113(1), 114 (2003)