Learning $\ell_1$-based analysis and synthesis sparsity priors using bi-level optimization
This work addresses sparse representation learning for image processing tasks, but it appears incremental as it builds on existing ℓ1-based models and optimization techniques.
The paper tackles the problem of learning analysis and synthesis sparsity priors using a unified bi-level optimization framework, revealing internal relations between ℓ1-based models and applying the learned operators to image denoising with performance comparisons to state-of-the-art methods.
We consider the analysis operator and synthesis dictionary learning problems based on the the $\ell_1$ regularized sparse representation model. We reveal the internal relations between the $\ell_1$-based analysis model and synthesis model. We then introduce an approach to learn both analysis operator and synthesis dictionary simultaneously by using a unified framework of bi-level optimization. Our aim is to learn a meaningful operator (dictionary) such that the minimum energy solution of the analysis (synthesis)-prior based model is as close as possible to the ground-truth. We solve the bi-level optimization problem using the implicit differentiation technique. Moreover, we demonstrate the effectiveness of our leaning approach by applying the learned analysis operator (dictionary) to the image denoising task and comparing its performance with state-of-the-art methods. Under this unified framework, we can compare the performance of the two types of priors.