DEALing with Image Reconstruction: Deep Attentive Least Squares

ICML 2025

[Denoising Task] \( {\bf{x}}_k \) represents the output of the \( k \)-th step of DEAL. Each pixel of the outputs is a weighted average of the data, with weights well-adapted to the image structure.

Abstract

State-of-the-art image reconstruction often relies on complex, highly 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 filter responses. Our method achieves performance on par with leading plug-and-play and learned regularizer approaches while offering interpretability, robustness, and convergent behavior. In effect, we bridge traditional regularization and deep learning with a principled reconstruction approach.

BibTeX

@article{pourya2025dealing,
  title={DEALing with Image Reconstruction: Deep Attentive Least Squares},
  author={Pourya, Mehrsa and Kobler, Erich and Unser, Michael and Neumayer, Sebastian},
  journal={arXiv preprint arXiv:2502.04079},
  year={2025}
}