= Tikhonov reconstruction from two-plane scattering data
{c}
{title2=$J_\alpha(V)=\|A_+V-d_+\|^2+\|A_-V-d_-\|^2+\alpha\|V\|^2$}
The two <Born approximation> measurement operators $A_\pm$ map a supported <scattering potential> to fields on planes above and below it. The displayed <Tikhonov regularization> functional balances their residuals against a positive quadratic penalty. With an $L^2$ penalty, the unconstrained minimizer is $(A^*A+\alpha I)^{-1}A^*d$, where $A=(A_+,A_-)$. Regularization stabilizes estimation but cannot remove the nonuniqueness of <Born non-scattering contrasts at one incident direction> without extra information.
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