Sampling method based projection approach for the reconstruction of 3D acoustically penetrable scatterers. (English) Zbl 1333.65124
Summary: We present a projection based regularization parameter choice approach within the framework of the linear sampling method for the reconstruction of acoustically penetrable objects. Using the Golub-Kahan bidiagonalization algorithm and the Lanczos tridiagonalization process we form appropriate subspaces which generate a sequence of regularized solutions. As a result two new and efficient methods are developed and used for the solution of problems that involve large systems of linear equations. The effectiveness of our approach is illustrated with reconstructions of three dimensional objects.
MSC:
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 35R30 | Inverse problems for PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 65F22 | Ill-posedness and regularization problems in numerical linear algebra |
Keywords:
linear sampling method; factorization method; acoustic scattering; far-field matrix; generalized discrepancy principle; Helmholtz equation; inverse problem; numerical example; regularization; Golub-Kahan bidiagonalization algorithm; Lanczos tridiagonalization processReferences:
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