DEALing with Image Reconstruction: Deep Attentive Least Squares

State-of-the-art image reconstruction often relies on complex, abundantly parameterized deep architectures. We propose an alternative: a data-driven reconstruction method inspired by the classic Tikhonov regularization. Our approach iteratively refines intermediate reconstructions by solving a sequence of quadratic problems. These updates have two key components: (i) learned filters to extract salient image features; and (ii) an attention mechanism that locally adjusts the penalty of the filter responses. Our method matches leading plug-and-play and learned regularizer approaches in performance while offering interpretability, robustness, and convergent behavior. In effect, we bridge traditional regularization and deep learning with a principled reconstruction approach.

Image reconstruction is essential for obtaining high-quality images from limited or corrupted data, whether from cameras or medical scanners. We developed DEAL, a method that builds upon classical reconstruction techniques that account for the physics of image acquisition, and leveraged deep learning to enhance these models. A key component of our method is an attention mechanism that helps the model focus on important image features. DEAL performs well across tasks like MRI and super-resolution, and is more stable and interpretable than many existing deep learning models.