Convergent convolutional dictionary learning using Adaptive Contrast Enhancement (CDL-ACE): Application of CDL to image denoising
Convolutional dictionary learning (CDL) has great potential to “learn” rich sparse representations from training datasets, by training translation-invariant filters. However, the performance of applying learned filters from CDL to inverse problems has not yet been fully maximized because training data preprocessing in training stage is not fully compensated in testing stage. We propose CDL using Adaptive Contrast Enhancement (CDL-ACE) that additionally models the preprocessing in CDL, and image denoising model using learned filters from CDL-ACE. For CDL-ACE, we apply a practically feasible and convergent Block Proximal Gradient method using Majorizer (BPG-M) with a momentum coefficient formula and an adaptive restarting rule. Numerical experiments show that, for strong additive white Gaussian noise, the proposed image denoiser using learned filters by CDL outperforms existing image denoising methods using Wiener filtering and total variation; and learned filters by CDL-ACE further improves the denoiser.