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11) V Hence the scattered field can be seen as the result of a radiated field from a current distribution equal to the product of the field in the imaging domain and the object function. 7) are known as forward problems and provide expressions for the measurable field as function of the distribution of the object function. e. determine the distribution of the object function from measurements of the field. 7), the field at a given point in space is expressed as a function of the object function.

1 Determining the Update: Derivative of the Measured Signal In order to linearise the cost function, it is necessary to find the derivative of the measured scattered signal with respect to a change in the object function in a single subvolume. By following a procedure similar to that used in Sect. r0 / dv 0 . 40) rec tr @ q @ q 2V V Vq rec In this expression, E is the field in the subvolume Vq when the receiver is tr transmitting with an excitation voltage of V rec , and E is the field in the imaging domain when the transmitter is transmitting with excitation voltage V tr .

In: Proceedings of IEEE international conference on neural networks, vol 4, pp 1942–1948 [46] Landweber L (1951) An Iteration Formula for Fredholm Integral Equations of the First Kind. 2307/2372313 [47] Levenberg K (1944) A method for the solution of certain non-linear problems in least squares. Q Appl Math (USA) 2:164–168 [48] Marquardt DW (1963) An Algorithm for Least-Squares Estimation of Nonlinear Parameters. Journal of the Society for Industrial and Applied Mathematics 11(2):431–441 [49] Meaney PM, Demidenko E, Yagnamurthy NK, Li D, Fanning MW, Paulsen KD (2001a) A two-stage microwave image reconstruction procedure for improved internal feature extraction.