146 
\\ 
\\ 
147 
\end{array} 
\end{array} 
148 
\end{equation} 
\end{equation} 
149 
We also need to provide an approximation of the inverse of the Hessian operator. The operator evaluation is executes as a solution 
We also need to provide an approximation of the inverse of the Hessian operator as discussed in section~\ref{chapter:ref:inversion cost function:gradient}. 

of a linear PDE which is solved using \escript \class{LinearPDE} class. In the \escript notation we need to provide 


\begin{equation}\label{ref:EQU:REG:600} 


\begin{array}{rcl} 


A_{kilj} & = & \displaystyle{\frac{\partial X_{ki}}{\partial m_{l,j}}} \\ 


D_{kl} & = & \displaystyle{\frac{\partial Y_{k}}{\partial m_{l}}} 


\end{array} 


\end{equation} 

150 
For the case of a single valued level set function $m$ we get 
For the case of a single valued level set function $m$ we get 
151 
\begin{equation}\label{ref:EQU:REG:601} 
\begin{equation}\label{ref:EQU:REG:601} 
152 
\begin{array}{rcl} 
\begin{array}{rcl} 