Non-smooth image restoration via Nesterov-smoothed Bilevel Learnable Descent Algorithm

Image denoising is a fundamental but challenging task due to the balance between noise removal and fine detail/textural preservation. We propose a bilevel optimization framework with a novel Bilevel Learnable Descent Algorithm (BLDA) for image restoration in this paper. The model allows non-smooth fidelity terms for robust suppression of complex noises, such as impulse noise, and uses space-variant regularization weights to avoid artifacts, like staircasing. Incorporating the CNN-based regularizer into a bilevel scheme, the proposed Nesterov smoothing treats the lower-level problem non-differentiable for efficient gradient-based updates. The proposed algorithm has both convergence guarantees of the smoothed lower-level solver and also for the overall bilevel method. Experimental results on standard benchmark datasets, such as BSD68, and real-world noisy images, including a COVID-19 CT scan, demonstrate the performance of the proposed BLDA. Particularly, higher PSNR and SSIM values than existing approaches are obtained by BLDA. With PSNR improvements of about 0.3 dB over the best competing methods on benchmark data, BLDA leads to better preservation of important image structures. These results emphasize both theoretical advances of our bilevel formulation and its empirical effectiveness in challenging image denoising tasks.