Maureen Clerc and Jan Kybic 2007 Inverse Problems 23 2589 doi:10.1088/0266-5611/23/6/020
Maureen Clerc1 and Jan Kybic2
Show affiliationsThe Laplace–Cauchy problem of propagating Dirichlet and Neumann data from a portion to the rest of the boundary is an ill-posed inverse problem. Many regularizing algorithms have been recently proposed, in order to stabilize the solution with respect to noisy or incomplete data. Our main application is in electro-encephalography (EEG) where potential measurements available at part of the scalp are used to reconstruct the potential and the current on the inner skull surface. This problem, known as cortical mapping, and other applications—in fields such as nondestructive testing, or biomedical engineering—require us to solve the problem in realistic, three-dimensional geometry. The goal of this paper is to present a new boundary-element-based method for solving the Laplace–Cauchy problem in three dimensions, in a multilayer geometry. We validate the method experimentally on simulated data.
87.85.Ng Biological signal processing
87.19.R- Mechanical and electrical properties of tissues and organs
02.60.Lj Ordinary and partial differential equations; boundary value problems
65N38 Boundary element methods
92C55 Biomedical imaging and signal processing (See also 44A12, 65R10)
Issue 6 (December 2007)
Received 30 May 2007, in final form 28 September 2007
Published 23 November 2007
Maureen Clerc and Jan Kybic 2007 Inverse Problems 23 2589
Pedro Serranho 2006 Inverse Problems 22 663
Herbert Egger et al 2006 Inverse Problems 22 1247
Kamal Belkebir and Marc Saillard 2004 Inverse Problems 21 S1
Alan L Andrew 2005 Inverse Problems 21 223
A El Badia et al 2005 Inverse Problems 21 1121
M Bertero et al 1986 Inverse Problems 2 131
Hans Lundmark and Jacek Szmigielski 2003 Inverse Problems 19 1241
Koen Denecker et al 1998 Inverse Problems 14 615
J Madore 1992 Class. Quantum Grav. 9 69