Insights into analysis operator learning: From patch-based sparse models to higher-order MRFs
This work addresses image restoration problems for computer vision researchers, offering an incremental improvement in training efficiency and performance.
The paper tackles the problem of learning analysis operators for co-sparse models by introducing a bi-level optimization technique, showing that it outperforms existing analysis operator learning methods and matches state-of-the-art image denoising algorithms in numerical experiments.
This paper addresses a new learning algorithm for the recently introduced co-sparse analysis model. First, we give new insights into the co-sparse analysis model by establishing connections to filter-based MRF models, such as the Field of Experts (FoE) model of Roth and Black. For training, we introduce a technique called bi-level optimization to learn the analysis operators. Compared to existing analysis operator learning approaches, our training procedure has the advantage that it is unconstrained with respect to the analysis operator. We investigate the effect of different aspects of the co-sparse analysis model and show that the sparsity promoting function (also called penalty function) is the most important factor in the model. In order to demonstrate the effectiveness of our training approach, we apply our trained models to various classical image restoration problems. Numerical experiments show that our trained models clearly outperform existing analysis operator learning approaches and are on par with state-of-the-art image denoising algorithms. Our approach develops a framework that is intuitive to understand and easy to implement.