Nonstationary iterated thresholding algorithms for image deblurring

We propose iterative thresholding algorithms based on theiterated Tikhonov method for image deblurring problems.Our method is similar in idea to the modified linearized Bregman algorithm (MLBA) sois easy to implement. In order to obtain good restorations, MLBA requires an accurate estimate of the regularization parameter α whichis hard to get in real applications.Based on previous results in iterated Tikhonov method, we designtwo nonstationary iterative thresholding algorithms which give nearoptimal results without estimating α. One of them is basedon the iterative soft thresholding algorithm and the other is basedon MLBA. We show that the nonstationary methods,if converge, will converge to the same minimizers ofthe stationary variants.Numerical resultsshow that the accuracy and convergence of our nonstationary methods are very robustwith respect to the changes in the parameters and the restorationresults are comparable to those of MLBA with optimal α.