Use of Wirtinger calculus in Gauss-Newton inversion of microwave tomography data

In microwave tomography inversion, it is often desirable to use complex-domain derivative operators toward reconstructing the unknown complex contrast profile of the target. However, the cost functionals to be optimized are often not complex differentiable with respect to the unknown by the strict definition of complex differentiability. This paper utilizes the so-called Wirtinger calculus in the infinite dimensional space to bypass this strict definition so as to provide closed-form expressions for the complex-domain derivative operators that, when discretized, can be used in Gauss-Newton inversion of microwave tomography data.