FaIMS
swMATH ID:  6425 
Software Authors:  Chaillat, St'ephanie; Biros, George 
Description:  FaIMS: A fast algorithm for the inverse medium problem with multiple frequencies and multiple sources for the scalar Helmholtz equation We propose an algorithm to compute an approximate singular value decomposition (SVD) of leastsquares operators related to linearized inverse medium problems with multiple events. Such factorizations can be used to accelerate matrixvector multiplications and to precondition iterative solvers.par We describe the algorithm in the context of an inverse scattering problem for the lowfrequency timeharmonic wave equation with broadband and multipoint illumination. This model finds many applications in science and engineering (e.g., seismic imaging, subsurface imaging, impedance tomography, nondestructive evaluation, and diffuse optical tomography).par We consider small perturbations of the background medium and, by invoking the Born approximation, we obtain a linear leastsquares problem. The scheme we describe in this paper constructs an approximate SVD of the Born operator (the operator in the linearized leastsquares problem). The main feature of the method is that it can accelerate the application of the Born operator to a vector.par If \(N_{omega }\) is the number of illumination frequencies, \(N_{s}\) the number of illumination locations, \(N_{d}\) the number of detectors, and N the discretization size of the medium perturbation, a dense singular value decomposition of the Born operator requires \(O(min(N_{s}N_{omega }N_{d},N)]^{2} imes max(N_{s}N_{omega }N_{d},N))\) operations. The application of the Born operator to a vector requires \(O(N_{omega }N_{s}mu (N))\) work, where \(mu (N)\) is the cost of solving a forward scattering problem. We propose an approximate SVD method that, under certain conditions, reduces these work estimates significantly. For example, the asymptotic cost of factorizing and applying the Born operator becomes \(O(mu (N)N_{omega })\). We provide numerical results that demonstrate the scalability of the method. 
Homepage:  http://www.cc.gatech.edu/~gbiros/papers/faims10.pdf 
Keywords:  inverse acoustic scattering; Born approximation; LippmannSchwinger integral equation; randomized singular value decomposition; recursive singular value decomposition; fullwaveform inversion; multiple sources 
Related Software:  LSQR; redbKIT; CLAIRE; Matlab; DOLFIN; Gmsh 
Cited in:  9 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

FaIMS: a fast algorithm for the inverse medium problem with multiple frequencies and multiple sources for the scalar Helmholtz equation. Zbl 1250.78023 Chaillat, Stéphanie; Biros, George 
2012

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Cited by 18 Authors
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Cited in 8 Serials
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