Learning spatially adaptive sparsity level maps for arbitrary convolutional dictionaries

2026-02-25

AI Summary

This work proposes a hybrid model-driven and data-driven convolutional sparse coding framework to address the limited interpretability and robustness in image reconstruction. The method leverages a neural network to generate spatially adaptive sparsity maps, which are integrated into a model-based regularization scheme. By incorporating filter permutation invariance, the architecture enables flexible replacement of convolutional dictionaries during inference without reliance on specific training data. Evaluated on low-field MRI reconstruction, the proposed approach significantly outperforms existing deep learning methods, demonstrating superior generalization, robustness, and adaptability on both in-distribution and out-of-distribution data.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Representation Learning for Vision
• Search and Optimization: Non-convex Optimization

Application Category

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

Abstract

State-of-the-art learned reconstruction methods often rely on black-box modules that, despite their strong performance, raise questions about their interpretability and robustness. Here, we build on a recently proposed image reconstruction method, which is based on embedding data-driven information into a model-based convolutional dictionary regularization via neural network-inferred spatially adaptive sparsity level maps. By means of improved network design and dedicated training strategies, we extend the method to achieve filter-permutation invariance as well as the possibility to change the convolutional dictionary at inference time. We apply our method to low-field MRI and compare it to several other recent deep learning-based methods, also on in vivo data, in which the benefit for the use of a different dictionary is showcased. We further assess the method's robustness when tested on in- and out-of-distribution data. When tested on the latter, the proposed method suffers less from the data distribution shift compared to the other learned methods, which we attribute to its reduced reliance on training data due to its underlying model-based reconstruction component.

Problem

• sparsity
• convolutional dictionary
• model-based reconstruction
• robustness
• distribution shift

Innovation

• spatially adaptive sparsity
• convolutional dictionary
• model-based reconstruction
• filter-permutation invariance
• distribution robustness