Iteratively Refined Image Reconstruction with Learned Attentive Regularizers
This work addresses the need for interpretable and theoretically sound models in image reconstruction for researchers and practitioners, though it is incremental as it builds on existing variational models.
The authors tackled the problem of interpretability and theoretical guarantees in deep-learning-based image reconstruction by proposing a regularization scheme that iteratively refines spatial regularization strength using learned masks, matching state-of-the-art performance in inverse problems.
We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze theoretically. In contrast, our scheme is interpretable because it corresponds to the minimization of a series of convex problems. For each problem in the series, a mask is generated based on the previous solution to refine the regularization strength spatially. In this way, the model becomes progressively attentive to the image structure. For the underlying update operator, we prove the existence of a fixed point. As a special case, we investigate a mask generator for which the fixed-point iterations converge to a critical point of an explicit energy functional. In our experiments, we match the performance of state-of-the-art learned variational models for the solution of inverse problems. Additionally, we offer a promising balance between interpretability, theoretical guarantees, reliability, and performance.