# Learning spatially adaptive sparsity level maps for arbitrary convolutional dictionaries

arXiv: https://arxiv.org/abs/2602.21707 · HTML: https://mlsanity.com/paper/2602.21707/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 25 Feb 2026.

## Builds on (most cited first, 12 of 12)

- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Truncated Back-propagation for Bilevel Optimization](https://mlsanity.com/paper/1810.10667/) (2018)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [Measuring Robustness in Deep Learning Based Compressive Sensing](https://mlsanity.com/paper/2102.06103/) (2021)
- [Learned reconstruction methods with convergence guarantees](https://mlsanity.com/paper/2206.05431/) (2022)
- [Deep K-SVD Denoising](https://mlsanity.com/paper/1909.13164/) (2019)
- [Convolutional Dictionary Learning: A Comparative Review and New Algorithms](https://mlsanity.com/paper/1709.02893/) (2017)
- [DEALing with Image Reconstruction: Deep Attentive Least Squares](https://mlsanity.com/paper/2502.04079/) (2025)
- [Learning Spatially Adaptive ℓ1-Norms Weights for Convolutional Synthesis Regularization](https://mlsanity.com/paper/2503.09483/) (2025)

## Built on by (most cited first, 1 of 1)

- [Learning spatially varying regularisation parameters of low regularity for image reconstruction](https://mlsanity.com/paper/2608.25127/) (2026)

## Abstract (arXiv)

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, where the benefit of using a different dictionary is demonstrated. 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.