# Geometric Approaches to Increase the Expressivity of Deep Neural Networks for MR Reconstruction

arXiv: https://arxiv.org/abs/2003.07740 · HTML: https://mlsanity.com/paper/2003.07740/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Mar 2020.

## Built on by (most cited first, 3 of 3)

- [AI-based Reconstruction for Fast MRI -- A Systematic Review and Meta-analysis](https://mlsanity.com/paper/2112.12744/) (2021)
- [Simultaneous super-resolution and motion artifact removal in diffusion-weighted MRI using unsupervised deep learning](https://mlsanity.com/paper/2105.00240/) (2021)
- [DUN-SRE: Deep Unrolling Network with Spatiotemporal Rotation Equivariance for Dynamic MRI Reconstruction](https://mlsanity.com/paper/2506.10309/) (2025)

## Abstract (arXiv)

Recently, deep learning approaches have been extensively investigated to reconstruct images from accelerated magnetic resonance image (MRI) acquisition. Although these approaches provide significant performance gain compared to compressed sensing MRI (CS-MRI), it is not clear how to choose a suitable network architecture to balance the trade-off between network complexity and performance. Recently, it was shown that an encoder-decoder convolutional neural network (CNN) can be interpreted as a piecewise linear basis-like representation, whose specific representation is determined by the ReLU activation patterns for a given input image. Thus, the expressivity or the representation power is determined by the number of piecewise linear regions. As an extension of this geometric understanding, this paper proposes a systematic geometric approach using bootstrapping and subnetwork aggregation using an attention module to increase the expressivity of the underlying neural network. Our method can be implemented in both k-space domain and image domain that can be trained in an end-to-end manner. Experimental results show that the proposed schemes significantly improve reconstruction performance with negligible complexity increases.