Automatic parameter tuning for image denoising with learned sparsifying transforms

Data-driven and learning-based sparse signal models outperform analytical models (e.g, wavelets), for image denoising, but require careful parameter tuning to reach peak performance. In this work, we provide a solution to the problem of parameter tuning for image denoising with transform sparsity regularization. We show that by viewing a learned sparsifying transform as a filter bank we can utilize the SURELET denoising algorithm to automatically tune parameters for an image denoising task. Numerical experiments show that combining SURELET with a learned sparsifying transform provides the best of both worlds. Our approach requires no parameter tuning for image denoising, yet outperforms SURELET with analytic transforms and matches the performance of transform learning denoising with hand-tuned parameters.