Model selection for image processing

Parameter tuning is a critical point in image restoration techniques. When degraded data are simulated form a reference image, we can compare the restored image to the reference one, and then select the set of parameters providing the best restoration quality. This tuning is less trivial in real acquisition setting for which there are no reference images. In the case of simple degradation models, statistical tools can be used to estimate the square restoration error even though the reference image is unknown, we speak about “risk estimation”. To optimize this estimate with respect to the parameters of the method leads to a near optimal calibration. The Stein’s unbiased risk estimator (SURE, Stein 1981) is one of the most famous example, successfully applied to calibrate image restoration methods under Gaussian noise degradation (see e.g., Ramani et al., 2008). We focus in developing new estimators derived from the SURE for the calibration of parametres involved in recent methods, potentially highly parameterized, for the restoration of images with complex degradation models (blur, missing data, non-Gaussian, non-stationary and correlated noise).

Stein Unbiased GrAdient estimator of the Risk
Stein Consistent Risk Estimator for hard thresholding
Local Behavior of Sparse Analysis Regularization