Linear inversion methods

The most common approach to the solution of nonlinear electromagnetic inverse problems is based on linearization of the forward modeling operator. This approach has found wide practical application because of the ease of its implementation, the accessibility of software for linear inversion, and the speed of numerical calculations. Linearization uses the family of linear and nonlinear approximations based on the Born method, described in Chapter 9. 

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Note that the quasi-linear inversion method, outlined above, can be easily extended to the case of the vector wavefield. We leave the detailed derivation of the corresponding formulae (which look very similar to the analogous formulae for electromagnetic field QL inversion) as an exercise for the interested reader. 

Hagen, D.E., Alofs, D.J., 1983. Linear inversion method to obtain aerosol size distributions from measurements with a differential mobihty analyzer. Aerosol Sci. Technol. 2, 465-475. 

Zhu X, Ballard B, Predecki P. Determination of Z-profiles of diffraction data from profiles using a numerical linear inversion method. Adv X-Ray Anal 1995 38 255-262. 

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