  Linear inverse problems are very common in signal and image processing. Many
algorithms that aim at solving such problems include unknown parameters that
need tuning. In this work we focus on optimally selecting such parameters in
iterative shrinkage methods for image deblurring and image zooming. Our work
uses the projected Generalized Stein Unbiased Risk Estimator (GSURE) for
determining the threshold value lambda and the iterations number K in these
algorithms. The proposed parameter selection is shown to handle any degradation
operator, including ill-posed and even rectangular ones. This is achieved by
using GSURE on the projected expected error. We further propose an efficient
greedy parameter setting scheme, that tunes the parameter while iterating
without impairing the resulting deblurring performance. Finally, we provide
extensive comparisons to conventional methods for parameter selection, showing
the superiority of the use of the projected GSURE.
