Iterative Regularization and Nonlinear Inverse Scale Space Applied to Wavelet-Based Denoising

In this paper, we generalize the iterative regularization method and the inverse scale space method, recently developed for total-variation (TV) based image restoration, to wavelet-based image restoration. This continues our earlier joint work with others where we applied these techniques to variational-based image restoration, obtaining significant improvement over the Rudin–Osher–Fatemi TV-based restoration. Here, we apply these techniques to soft shrinkage and obtain the somewhat surprising result that a) the iterative procedure applied to soft shrinkage gives firm shrinkage and converges to hard shrinkage and b) that these procedures enhance the noise-removal capability both theoretically, in the sense of generalized Bregman distance, and for some examples, experimentally, in terms of the signal-to-noise ratio, leaving less signal in the residual.