Residual method for variational regularization
= Residual method for variational regularization
Given $\|f_\delta-f\|\leq\delta$, the residual method minimizes a penalty $J(u)$ subject to $\|Au-f_\delta\|\leq\delta$. Every exact solution is feasible, so a reconstruction $u_\delta$ has penalty no larger than that of any <J-minimizing solution>.