# Learning Regularization Parameter-Maps for Variational Image Reconstruction using Deep Neural Networks and Algorithm Unrolling

arXiv: https://arxiv.org/abs/2301.05888 · HTML: https://mlsanity.com/paper/2301.05888/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2023.

## Built on by (most cited first, 14 of 14)

- [Learning Regularization Functionals for Inverse Problems: A Comparative Study](https://mlsanity.com/paper/2510.01755/) (2025)
- [DEALing with Image Reconstruction: Deep Attentive Least Squares](https://mlsanity.com/paper/2502.04079/) (2025)
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- [Iteratively Refined Image Reconstruction with Learned Attentive Regularizers](https://mlsanity.com/paper/2407.06608/) (2024)
- [Deep unrolling for learning optimal spatially varying regularisation parameters for Total Generalised Variation](https://mlsanity.com/paper/2502.16532/) (2025)
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- [Learning Spatially Adaptive ℓ1-Norms Weights for Convolutional Synthesis Regularization](https://mlsanity.com/paper/2503.09483/) (2025)
- [MRpro: open framework for model-based, learned, and quantitative MR imaging](https://mlsanity.com/paper/2507.23129/) (2025)
- [Patch-based learning of adaptive Total Variation parameter maps for blind image denoising](https://mlsanity.com/paper/2503.16010/) (2025)
- [An incremental algorithm for non-convex AI-enhanced medical image processing](https://mlsanity.com/paper/2505.08324/) (2025)
- [Deep regularization networks for inverse problems with noisy operators](https://mlsanity.com/paper/2506.07008/) (2025)
- [Rasterized Steered Mixture of Experts for Efficient 2D Image Regression](https://mlsanity.com/paper/2510.05814/) (2025)
- [Learnable Total Variation with Lambda Mapping for Low-Dose CT Denoising](https://mlsanity.com/paper/2511.10500/) (2025)

## Abstract (arXiv)

We introduce a method for fast estimation of data-adapted, spatio-temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV)-minimization. Our approach is inspired by recent developments in algorithm unrolling using deep neural networks (NNs), and relies on two distinct sub-networks. The first sub-network estimates the regularization parameter-map from the input data. The second sub-network unrolls T iterations of an iterative algorithm which approximately solves the corresponding TV-minimization problem incorporating the previously estimated regularization parameter-map. The overall network is trained end-to-end in a supervised learning fashion using pairs of clean-corrupted data but crucially without the need of having access to labels for the optimal regularization parameter-maps. We prove consistency of the unrolled scheme by showing that the unrolled energy functional used for the supervised learning Gamma-converges as T tends to infinity, to the corresponding functional that incorporates the exact solution map of the TV-minimization problem. We apply and evaluate our method on a variety of large scale and dynamic imaging problems in which the automatic computation of such parameters has been so far challenging: 2D dynamic cardiac MRI reconstruction, quantitative brain MRI reconstruction, low-dose CT and dynamic image denoising. The proposed method consistently improves the TV-reconstructions using scalar parameters and the obtained parameter-maps adapt well to each imaging problem and data by leading to the preservation of detailed features. Although the choice of the regularization parameter-maps is data-driven and based on NNs, the proposed algorithm is entirely interpretable since it inherits the properties of the respective iterative reconstruction method from which the network is implicitly defined.