Wavelet iterative regularization for image restoration with varying scale parameter

We first generalize the wavelet-based iterative regularization method and the wavelet-based inverse scale space to shift invariant wavelet-based cases for image restoration. Then, a method to estimate the scale parameter is proposed from wavelet-based iterative regularization; different parameters with different iterations are obtained. The wavelet-based iterative regularization with the new parameter, which controls the extent of denoising more precisely in the wavelet domain, leads to iterative global wavelet shrinkage. We also obtain a time adaptive wavelet-based inverse scale space from the iterative procedure with the proposed parameter. We provide a proof of the convergence and obtain a stopping criterion for the iterative procedure with the new scale parameter based on wavelet transform. The proposed iterative regularized method obtains quite accurate results on a variety of images. Numerical experiments show that the proposed methods can efficiently remove noise and well preserve the details of images.