DEALing with Image Reconstruction: Deep Attentive Least Squares

2025-02-06

AI Summary

Existing image reconstruction methods often struggle to simultaneously achieve high performance, interpretability, and theoretical convergence guarantees. To address this, we propose a novel iterative reconstruction framework that unifies classical Tikhonov regularization with deep learning—yielding both interpretability and provable convergence. Specifically, we embed a local adaptive attention mechanism into a weighted least-squares optimization, formulating a differentiable attention-weighted quadratic objective. This model is trained end-to-end via optimization unfolding, enabling data-driven regularization while preserving rigorous convergence properties. Unlike conventional deep unrolling or plug-and-play methods, our approach requires no complex network architecture. Experimental results demonstrate reconstruction quality on par with state-of-the-art learned and plug-and-play regularizers, along with significant improvements in noise robustness, solution interpretability, and convergence stability.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Non-convex Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• Improves image reconstruction efficiency
• Simplifies deep learning architectures
• Enhances interpretability and robustness

Innovation

• Data-driven Tikhonov regularization method
• Iterative quadratic problem solving
• Learned filters and attention mechanism