# PISCO: Self-Supervised k-Space Regularization for Improved Neural Implicit k-Space Representations of Dynamic MRI

arXiv: https://arxiv.org/abs/2501.09403 · HTML: https://mlsanity.com/paper/2501.09403/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 47 references that are in the map.
- First posted on arXiv 16 Jan 2025.

## Builds on (most cited first, 18 of 18)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [Plug and play methods for magnetic resonance imaging (long version)](https://mlsanity.com/paper/1903.08616/) (2019)
- [Time-Dependent Deep Image Prior for Dynamic MRI](https://mlsanity.com/paper/1910.01684/) (2019)
- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [Spatiotemporal implicit neural representation for unsupervised dynamic MRI reconstruction](https://mlsanity.com/paper/2301.00127/) (2022)
- [Neural Implicit k-Space for Binning-free Non-Cartesian Cardiac MR Imaging](https://mlsanity.com/paper/2212.08479/) (2022)
- [Deep Low-rank plus Sparse Network for Dynamic MR Imaging](https://mlsanity.com/paper/2010.13677/) (2020)
- [DIMENSION: Dynamic MR Imaging with Both K-space and Spatial Prior Knowledge Obtained via Multi-Supervised Network Training](https://mlsanity.com/paper/1810.00302/) (2018)
- [Deep Learning for Retrospective Motion Correction in MRI: A Comprehensive Review](https://mlsanity.com/paper/2305.06739/) (2023)
- [Implicit Neural Networks with Fourier-Feature Inputs for Free-breathing Cardiac MRI Reconstruction](https://mlsanity.com/paper/2305.06822/) (2023)
- [ICoNIK: Generating Respiratory-Resolved Abdominal MR Reconstructions Using Neural Implicit Representations in k-Space](https://mlsanity.com/paper/2308.08830/) (2023)
- [Accelerated respiratory-resolved 4D-MRI with separable spatio-temporal neural networks](https://mlsanity.com/paper/2211.05678/) (2022)
- [Unsupervised reconstruction of accelerated cardiac cine MRI using Neural Fields](https://mlsanity.com/paper/2307.14363/) (2023)
- [Data-Consistent Non-Cartesian Deep Subspace Learning for Efficient Dynamic MR Image Reconstruction](https://mlsanity.com/paper/2205.01770/) (2022)
- [Self-Supervised k-Space Regularization for Motion-Resolved Abdominal MRI Using Neural Implicit k-Space Representation](https://mlsanity.com/paper/2404.08350/) (2024)
- [Implicit Representation of GRAPPA Kernels for Fast MRI Reconstruction](https://mlsanity.com/paper/2310.10823/) (2023)

## Built on by (most cited first, 4 of 4)

- [KP-INR: A Dual-Branch Implicit Neural Representation Model for Cardiac Cine MRI Reconstruction](https://mlsanity.com/paper/2508.12147/) (2025)
- [Accelerating Stroke MRI with Diffusion Probabilistic Models through Large-Scale Pre-training and Target-Specific Fine-Tuning](https://mlsanity.com/paper/2603.13007/) (2026)
- [Enhancing Implicit Neural Representations with Image Feature Embedding for Unsupervised Cardiac Cine MRI Reconstruction](https://mlsanity.com/paper/2607.04069/) (2026)
- [K-space Gaussian Representation for Parallel MRI](https://mlsanity.com/paper/2608.00075/) (2026)

## Abstract (arXiv)

Neural implicit k-space representations (NIK) have shown promising results for dynamic magnetic resonance imaging (MRI) at high temporal resolutions. Yet, reducing acquisition time, and thereby available training data, results in severe performance drops due to overfitting. To address this, we introduce a novel self-supervised k-space loss function LPISCO, applicable for regularization of NIK-based reconstructions. The proposed loss function is based on the concept of parallel imaging-inspired self-consistency (PISCO), enforcing a consistent global k-space neighborhood relationship without requiring additional data. Quantitative and qualitative evaluations on static and dynamic MR reconstructions show that integrating PISCO significantly improves NIK representations. Particularly for high acceleration factors (R≥54), NIK with PISCO achieves superior spatio-temporal reconstruction quality compared to state-of-the-art methods. Furthermore, an extensive analysis of the loss assumptions and stability shows PISCO's potential as versatile self-supervised k-space loss function for further applications and architectures. Code is available at: https://github.com/compai-lab/2025-pisco-spieker