Learning Spatially Adaptive $ell_1$-Norms Weights for Convolutional Synthesis Regularization

2025-03-12

AI Summary

To address the poor interpretability of conventional regularization methods and the lack of physical grounding in end-to-end deep models for low-field MRI reconstruction, this paper proposes a convolutional synthesis regularization framework embedded with spatially adaptive ℓ₁ weights. By unrolling the FISTA algorithm, the framework jointly optimizes sparse feature maps and a deeply parameterized spatial weight map—introducing, for the first time, learnable, pixel-wise adaptive ℓ₁ weights into convolutional synthesis models. The learned weight map provides both interpretability and quantitative assessment of filter contributions, bridging the gap between analysis-based regularizers (e.g., total variation) and black-box deep learning approaches. Experiments demonstrate that the method achieves competitive performance against state-of-the-art model-based methods in terms of PSNR and SSIM, while additionally generating intuitive heatmaps illustrating filter importance—thereby unifying reconstruction accuracy and interpretability.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Feature Construction/Reformulation
• Search and Optimization: Non-convex Optimization

Application Category

• 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
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We propose an unrolled algorithm approach for learning spatially adaptive parameter maps in the framework of convolutional synthesis-based $ell_1$ regularization. More precisely, we consider a family of pre-trained convolutional filters and estimate deeply parametrized spatially varying parameters applied to the sparse feature maps by means of unrolling a FISTA algorithm to solve the underlying sparse estimation problem. The proposed approach is evaluated for image reconstruction of low-field MRI and compared to spatially adaptive and non-adaptive analysis-type procedures relying on Total Variation regularization and to a well-established model-based deep learning approach. We show that the proposed approach produces visually and quantitatively comparable results with the latter approaches and at the same time remains highly interpretable. In particular, the inferred parameter maps quantify the local contribution of each filter in the reconstruction, which provides valuable insight into the algorithm mechanism and could potentially be used to discard unsuited filters.

Problem

• Learning spatially adaptive weights for convolutional synthesis regularization.
• Solving sparse estimation using unrolled FISTA algorithm for image reconstruction.
• Comparing adaptive and non-adaptive methods in low-field MRI reconstruction.

Innovation

• Unrolled algorithm for adaptive parameter maps
• Deeply parametrized spatially varying parameters
• FISTA algorithm for sparse estimation problem