A 2-STEP LINEAR INVERSION OF 2-DIMENSIONAL ELECTRICAL-CONDUCTIVITY

We introduce a novel approach to the inversion of two-dimensional dist ributions of electrical conductivity illuminated by line sources. The algorithm stems from the newly developed extended Born approximation [ 1], which sums in a simple analytical expression an infinitude of term s contained in the Neumann series expansion of the electric field resu lting from multiple scattering. Comparisons of numerical performance a gainst a finite-difference code show that the extended Born approximat ion remains accurate up to conductivity contrasts of 1:1000 with respe ct to a homogeneous background, even with large-size scatterers and fo r a wide frequency range. Moreover, the new approximation is nearly as computationally efficient as the first-order Born approximation. Most importantly, we show that the mathematical form of the extended Born approximation allows one to express the nonlinear inversion of electro magnetic fields scattered by a line source as the sequential solution of two Fredholm integral equations. We compare this procedure against a more conventional iterative approach applied to a limited-angle tomo graphy experiment. Our numerical tests show superior CPU time performa nce of the two-step linear inversion process.