# Sigma-net: Systematic Evaluation of Iterative Deep Neural Networks for Fast Parallel MR Image Reconstruction

arXiv: https://arxiv.org/abs/1912.09278 · HTML: https://mlsanity.com/paper/1912.09278/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2019.

## Built on by (most cited first, 7 of 7)

- [Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction](https://mlsanity.com/paper/2102.06665/) (2021)
- [HUMUS-Net: Hybrid unrolled multi-scale network architecture for accelerated MRI reconstruction](https://mlsanity.com/paper/2203.08213/) (2022)
- [Model Adaptation for Image Reconstruction using Generalized Stein's Unbiased Risk Estimator](https://mlsanity.com/paper/2102.00047/) (2021)
- [AAPM DL-Sparse-View CT Challenge Submission Report: Designing an Iterative Network for Fanbeam-CT with Unknown Geometry](https://mlsanity.com/paper/2106.00280/) (2021)
- [Estimating MRI Image Quality via Image Reconstruction Uncertainty](https://mlsanity.com/paper/2106.10992/) (2021)
- [Training Adaptive Reconstruction Networks for Blind Inverse Problems](https://mlsanity.com/paper/2202.11342/) (2022)
- [MosaicMRI: A Diverse Dataset and Benchmark for Raw Musculoskeletal MRI](https://mlsanity.com/paper/2604.11762/) (2026)

## Abstract (arXiv)

Purpose: To systematically investigate the influence of various data consistency layers, (semi-)supervised learning and ensembling strategies, defined in a Sigma-net, for accelerated parallel MR image reconstruction using deep learning. Theory and Methods: MR image reconstruction is formulated as learned unrolled optimization scheme with a Down-Up network as regularization and varying data consistency layers. The different architectures are split into sensitivity networks, which rely on explicit coil sensitivity maps, and parallel coil networks, which learn the combination of coils implicitly. Different content and adversarial losses, a semi-supervised fine-tuning scheme and model ensembling are investigated. Results: Evaluated on the fastMRI multicoil validation set, architectures involving raw k-space data outperform image enhancement methods significantly. Semi-supervised fine-tuning adapts to new k-space data and provides, together with reconstructions based on adversarial training, the visually most appealing results although quantitative quality metrics are reduced. The Sigma-net ensembles the benefits from different models and achieves similar scores compared to the single state-of-the-art approaches. Conclusion: This work provides an open-source framework to perform a systematic wide-range comparison of state-of-the-art reconstruction approaches for parallel MR image reconstruction on the fastMRI knee dataset and explores the importance of data consistency. A suitable trade-off between perceptual image quality and quantitative scores are achieved with the ensembled Sigma-net.