# Neural Implicit k-Space for Binning-free Non-Cartesian Cardiac MR Imaging

arXiv: https://arxiv.org/abs/2212.08479 · HTML: https://mlsanity.com/paper/2212.08479/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 16 Dec 2022.

## Builds on (most cited first, 12 of 12)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [NeRF in the Dark: High Dynamic Range View Synthesis from Noisy Raw Images](https://mlsanity.com/paper/2111.13679/) (2021)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [NAF: Neural Attenuation Fields for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2209.14540/) (2022)
- [Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1712.01751/) (2017)
- [A Deep Cascade of Convolutional Neural Networks for MR Image Reconstruction](https://mlsanity.com/paper/1703.00555/) (2017)
- [Time-Dependent Deep Image Prior for Dynamic MRI](https://mlsanity.com/paper/1910.01684/) (2019)
- [Deep Low-rank plus Sparse Network for Dynamic MR Imaging](https://mlsanity.com/paper/2010.13677/) (2020)

## Built on by (most cited first, 30 of 35)

- [Spatiotemporal implicit neural representation for unsupervised dynamic MRI reconstruction](https://mlsanity.com/paper/2301.00127/) (2022)
- [Single-subject Multi-contrast MRI Super-resolution via Implicit Neural Representations](https://mlsanity.com/paper/2303.15065/) (2023)
- [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)
- [Global k-Space Interpolation for Dynamic MRI Reconstruction using Masked Image Modeling](https://mlsanity.com/paper/2307.12672/) (2023)
- [MedFuncta: A Unified Framework for Learning Efficient Medical Neural Fields](https://mlsanity.com/paper/2502.14401/) (2025)
- [INFusion: Diffusion Regularized Implicit Neural Representations for 2D and 3D accelerated MRI reconstruction](https://mlsanity.com/paper/2406.13895/) (2024)
- [IM-MoCo: Self-supervised MRI Motion Correction using Motion-Guided Implicit Neural Representations](https://mlsanity.com/paper/2407.02974/) (2024)
- [Moner: Motion Correction in Undersampled Radial MRI with Unsupervised Neural Representation](https://mlsanity.com/paper/2409.16921/) (2024)
- [Dynamic-Aware Spatio-temporal Representation Learning for Dynamic MRI Reconstruction](https://mlsanity.com/paper/2501.09049/) (2025)
- [PISCO: Self-Supervised k-Space Regularization for Improved Neural Implicit k-Space Representations of Dynamic MRI](https://mlsanity.com/paper/2501.09403/) (2025)
- [Neural Implicit Heart Coordinates: 3D cardiac shape reconstruction from sparse segmentations](https://mlsanity.com/paper/2512.19316/) (2025)
- [Gabor Primitives for Accelerated Cardiac Cine MRI Reconstruction](https://mlsanity.com/paper/2603.05681/) (2026)
- [Self-Supervised k-Space Regularization for Motion-Resolved Abdominal MRI Using Neural Implicit k-Space Representation](https://mlsanity.com/paper/2404.08350/) (2024)
- [RSR-NF: Neural Field Regularization by Static Restoration Priors for Dynamic Imaging](https://mlsanity.com/paper/2503.10015/) (2025)
- [Disentangled Learning Improves Implicit Neural Representations for Medical Reconstruction](https://mlsanity.com/paper/2605.04234/) (2026)
- [NeRF Solves Undersampled MRI Reconstruction](https://mlsanity.com/paper/2402.13226/) (2024)
- [Enhancing Dynamic CT Image Reconstruction with Neural Fields and Optical Flow](https://mlsanity.com/paper/2406.01299/) (2024)
- [Accelerating multiparametric quantitative MRI using self-supervised scan-specific implicit neural representation with model reinforcement](https://mlsanity.com/paper/2508.00891/) (2025)
- [KP-INR: A Dual-Branch Implicit Neural Representation Model for Cardiac Cine MRI Reconstruction](https://mlsanity.com/paper/2508.12147/) (2025)
- [Unsupervised Adaptive Implicit Neural Representation Learning for Scan-Specific MRI Reconstruction](https://mlsanity.com/paper/2312.00677/) (2023)
- [A Unified Deep Learning Framework for Motion Correction in Medical Imaging](https://mlsanity.com/paper/2409.14204/) (2024)
- [DDO-IN: Dual Domains Optimization for Implicit Neural Network to Eliminate Motion Artifact in Magnetic Resonance Imaging](https://mlsanity.com/paper/2503.08056/) (2025)
- [Motion-compensated cardiac MRI using low-rank diffeomorphic flow (DMoCo)](https://mlsanity.com/paper/2505.03149/) (2025)
- [Template-Guided Reconstruction of Pulmonary Segments with Neural Implicit Functions](https://mlsanity.com/paper/2505.08919/) (2025)
- [Compressive Imaging Reconstruction via Tensor Decomposed Multi-Resolution Grid Encoding](https://mlsanity.com/paper/2507.07707/) (2025)
- [Flow-Guided Implicit Neural Representation for Motion-Aware Dynamic MRI Reconstruction](https://mlsanity.com/paper/2511.16948/) (2025)
- [Texture-preserving implicit neural representation for Cone beam CT truncated reconstruction](https://mlsanity.com/paper/2606.06039/) (2026)
- [DD-INR: Dynamics-Driven Implicit Neural Representation for Accelerated Whole-Brain Functional MRI Reconstruction](https://mlsanity.com/paper/2606.10756/) (2026)

## Abstract (arXiv)

In this work, we propose a novel image reconstruction framework that directly learns a neural implicit representation in k-space for ECG-triggered non-Cartesian Cardiac Magnetic Resonance Imaging (CMR). While existing methods bin acquired data from neighboring time points to reconstruct one phase of the cardiac motion, our framework allows for a continuous, binning-free, and subject-specific k-space representation.We assign a unique coordinate that consists of time, coil index, and frequency domain location to each sampled k-space point. We then learn the subject-specific mapping from these unique coordinates to k-space intensities using a multi-layer perceptron with frequency domain regularization. During inference, we obtain a complete k-space for Cartesian coordinates and an arbitrary temporal resolution. A simple inverse Fourier transform recovers the image, eliminating the need for density compensation and costly non-uniform Fourier transforms for non-Cartesian data. This novel imaging framework was tested on 42 radially sampled datasets from 6 subjects. The proposed method outperforms other techniques qualitatively and quantitatively using data from four and one heartbeat(s) and 30 cardiac phases. Our results for one heartbeat reconstruction of 50 cardiac phases show improved artifact removal and spatio-temporal resolution, leveraging the potential for real-time CMR.