Title
Reconstruction of shapes and impedance functions using few far-field measurements
Abstract
We consider the reconstruction of complex obstacles from few far-field acoustic measurements. The complex obstacle is characterized by its shape and an impedance function distributed along its boundary through Robin type boundary conditions. This is done by minimizing an objective functional, which is the L^2 distance between the given far-field information g^~ and the far-field of the scattered wave u^~ corresponding to the computed shape and impedance function. We design an algorithm to update the shape and the impedance function alternatively along the descent direction of the objective functional. The derivative with respect to the shape or the impedance function involves solving the original Helmholtz problem and the corresponding adjoint problem, where boundary integral methods are used. Further we implement level set methods to update the shape of the obstacle. To combine level set methods and boundary integral methods we perform a parametrization step for a newly updated level set function. In addition since the computed shape derivative is defined only on the boundary of the obstacle, we extend the shape derivative to the whole domain by a linear transport equation. Finally, we demonstrate by numerical experiments that our algorithm reconstruct both shapes and impedance functions quite accurately for non-convex shape obstacles and constant or non-constant impedance functions. The algorithm is also shown to be robust with respect to the initial guess of the shape, the initial guess of the impedance function and even large percentage of noise.
Year
DOI
Venue
2009
10.1016/j.jcp.2008.09.029
J. Comput. Physics
Keywords
Field
DocType
impedance function,shape derivatives,inverse scattering,far-field measurement,level set method,computed shape derivative,non-constant impedance function,initial guess,far-field pattern data,boundary integral method,non-convex shape obstacle,complex obstacle,boundary integral methods,updated level set function,robin type boundary conditions,computed shape,level set methods,objective function,level set,boundary condition
Active shape model,Boundary value problem,Mathematical optimization,Mathematical analysis,Level set,Helmholtz free energy,Electrical impedance,Shape optimization,Mathematics,Inverse scattering problem,Shape analysis (digital geometry)
Journal
Volume
Issue
ISSN
228
3
Journal of Computational Physics
Citations 
PageRank 
References 
3
0.64
4
Authors
3
Name
Order
Citations
PageRank
Lin He130.64
Stefan Kindermann229319.60
M. Sini3256.70