Iterative weighted risk estimation for nonlinear image restoration with analysis priors
2012
Image acquisition systems invariably introduce blur, which necessitates the use of deblurring algorithms
for image restoration. Restoration techniques involving regularization require appropriate
selection of the regularization parameter that controls the quality of the restored result. We focus
on the problem of automatic adjustment of this parameter for nonlinear image restoration using
analysis-type regularizers such as total variation (TV). For this purpose, we use two variants of
Stein's unbiased risk estimate (SURE), Predicted-SURE and Projected-SURE, that are applicable
for parameter selection in inverse problems involving Gaussian noise. These estimates require
the Jacobian matrix of the restoration algorithm evaluated with respect to the data. We derive
analytical expressions to recursively update the desired Jacobian matrix for a fast variant of the
iterative reweighted least-squares restoration algorithm that can accommodate a variety of regularization
criteria. Our method can also be used to compute a nonlinear version of the generalized
cross-validation (NGCV) measure for parameter tuning. We demonstrate using simulations that
Predicted-SURE, Projected-SURE, and NGCV-based adjustment of the regularization parameter
yields near-MSE-optimal results for image restoration using TV, an analysis-type 1-regularization,
and a smooth convex edge-preserving regularizer.
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