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Solving a 1-D inverse medium scattering problem using a new multi-frequency globally strictly convex objective functional
- Publication Year :
- 2019
-
Abstract
- We propose a new approach to constructing globally strictly convex objective functional in a 1-D inverse medium scattering problem using multi-frequency backscattering data. The global convexity of the proposed objective functional is proved using a Carleman estimate. Due to its convexity, no good first guess is required in minimizing this objective functional. We also prove the global convergence of the gradient projection algorithm and derive an error estimate for the reconstructed coefficient. Numerical results show reasonable reconstruction accuracy for simulated data.<br />Comment: 30 pages
- Subjects :
- Mathematics - Numerical Analysis
35R30, 35L05, 78A46
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1901.03183
- Document Type :
- Working Paper