The Stein unbiased risk estimator has become popular for parameter selection in image restoration algorithms. It estimates the square error loss between the reconstruction and the unknown image of interest, and hence, can be used as an objective for parameter selection. This estimator and its extensions all rely on modeling noise as perturbations whose distribution belongs to the exponential family. However, under non-Gaussian noise, we will show that optimizing the square error loss can lead to selecting irrelevant parameters. In this talk, we will consider more appropriate loss functions and will discuss the challenging problem of estimating them.