# Lightweight Hypercomplex MRI Reconstruction: A Generalized Kronecker-Parameterized Approach

arXiv: https://arxiv.org/abs/2503.05063 · HTML: https://mlsanity.com/paper/2503.05063/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 7 Mar 2025.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Beyond Fully-Connected Layers with Quaternions: Parameterization of Hypercomplex Multiplications with 1/n Parameters](https://mlsanity.com/paper/2102.08597/) (2021)
- [Swin Transformer for Fast MRI](https://mlsanity.com/paper/2201.03230/) (2022)
- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [Data and Physics driven Deep Learning Models for Fast MRI Reconstruction: Fundamentals and Methodologies](https://mlsanity.com/paper/2401.16564/) (2024)
- [Generalizing Medical Image Representations via Quaternion Wavelet Networks](https://mlsanity.com/paper/2310.10224/) (2023)

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

- [Variational Network with Wavelet-based UNET in Accelerated MRI Reconstruction from Under Sampled K-space Data](https://mlsanity.com/paper/2606.15167/) (2026)

## Abstract (arXiv)

Magnetic Resonance Imaging (MRI) is crucial for clinical diagnostics but is hindered by prolonged scan times. Current deep learning models enhance MRI reconstruction but are often memory-intensive and unsuitable for resource-limited systems. This paper introduces a lightweight MRI reconstruction model leveraging Kronecker-Parameterized Hypercomplex Neural Networks to achieve high performance with reduced parameters. By integrating Kronecker-based modules, including Kronecker MLP, Kronecker Window Attention, and Kronecker Convolution, the proposed model efficiently extracts spatial features while preserving representational power. We introduce Kronecker U-Net and Kronecker SwinMR, which maintain high reconstruction quality with approximately 50% fewer parameters compared to existing models. Experimental evaluation on the FastMRI dataset demonstrates competitive PSNR, SSIM, and LPIPS metrics, even at high acceleration factors (8x and 16x), with no significant performance drop. Additionally, Kronecker variants exhibit superior generalization and reduced overfitting on limited datasets, facilitating efficient MRI reconstruction on hardware-constrained systems. This approach sets a new benchmark for parameter-efficient medical imaging models.