Conductivity imaging by the Born approximation

Before moving to the iterative Born inversion technique, we introduce a fast imaging technique based on a Born approximation. Let us recall formula (5.91) for an approximate regularized solution of the linear inverse problem. In the case of equation (10.16), this formula takes the form 

Let us find, first, an explicit form of the adjoint Fr6chet derivative operator 

From the last formula we conclude that the adjoint Frechet derivative operator Fg is given by the formula  

In a similar way we can obtain the formula for the adjoint Pr6chet derivative operator Fjj  

Substituting expression (10.25) into formula (10.20), we finally arrive at the following imaging formula  

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