2014/08/04 by Michael V. Klibanov, Klibanov, Michael V., Nguyễn Trung Thành +2
Engineering · Mathematics · Physics and Astronomy · #35L05 #35R30 #78A46 #FOS: Physical sciences #Mathematical Physics (math-ph) #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Ultrasonics and Acoustic Wave Propagation #math-ph #math.MP #msc:35L05 #msc:35R30 #msc:78A46
paper · pdf · doi:10.48550/arxiv.1408.0583
Keywords: Coefficient inverse problem, Laplace transform, Carleman weight function, strictly convex cost functional, global convergence, Laguerre functions, numerical experiments
arxiv created 2014/08/04 · openalex publication_date 2014/08/04 · arxiv updated 2014/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The inverse problem of estimating dielectric constants of explosives using boundary measurements of one component of the scattered electric field is addressed. It is formulated as a coefficient inverse problem for a hyperbolic differential equation. After applying the Laplace transform, a new cost functional is constructed and a variational problem is formulated. The key feature of this functional is the presence of the Carleman Weight Function for the Laplacian. The strict convexity of this functional on a bounded set in a Hilbert space of an arbitrary size is proven. This allows for establishing the global convergence of the gradient descent method. Some results of numerical experiments are presented.