A generalized study of the weighted least-squares measure for the selection of the regularization parameter in inverse problems

The weighted least-squares (WLS) measure is studied when linear and nonlinear estimators are considered. Nonlinear estimators become increasingly important in association with robust restoration schemes. Such estimators often lack analytic interpretation rendering the direct computation of the WLS measure useless. It is shown that the solution of a nonlinear equation. The approximation improves as the signal-to-noise ratio increases. The efficiency of this approximation is verified through restoration examples in Laplacian noise.<>