# Implicit Neural Networks with Fourier-Feature Inputs for Free-breathing Cardiac MRI Reconstruction arXiv: https://arxiv.org/abs/2305.06822 ยท HTML: https://mlsanity.com/paper/2305.06822/ ## Key facts - Cited by 15 papers in the map (data through 14 Oct 2026). - Builds on 22 of its 46 references that are in the map. - First posted on arXiv 11 May 2023. ## Builds on (most cited first, 22 of 22) - [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014) - [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) - [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017) - [Fast Dynamic Radiance Fields with Time-Aware Neural Voxels](https://mlsanity.com/paper/2205.15285/) (2022) - [NeRF in the Dark: High Dynamic Range View Synthesis from Noisy Raw Images](https://mlsanity.com/paper/2111.13679/) (2021) - [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017) - [Tensor4D : Efficient Neural 4D Decomposition for High-fidelity Dynamic Reconstruction and Rendering](https://mlsanity.com/paper/2211.11610/) (2022) - [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021) - [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018) - [Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1712.01751/) (2017) - [Time-Dependent Deep Image Prior for Dynamic MRI](https://mlsanity.com/paper/1910.01684/) (2019) - [IREM: High-Resolution Magnetic Resonance (MR) Image Reconstruction via Implicit Neural Representation](https://mlsanity.com/paper/2106.15097/) (2021) - [Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators](https://mlsanity.com/paper/1910.14634/) (2019) - [Compressive sensing with un-trained neural networks: Gradient descent finds the smoothest approximation](https://mlsanity.com/paper/2005.03991/) (2020) - [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) - [Dynamic imaging using a deep generative SToRM (Gen-SToRM) model](https://mlsanity.com/paper/2102.00034/) (2021) - [Extreme MRI: Large-Scale Volumetric Dynamic Imaging from Continuous Non-Gated Acquisitions](https://mlsanity.com/paper/1909.13482/) (2019) - [Complementary Time-Frequency Domain Networks for Dynamic Parallel MR Image Reconstruction](https://mlsanity.com/paper/2012.11974/) (2020) - [Scale-Agnostic Super-Resolution in MRI using Feature-Based Coordinate Networks](https://mlsanity.com/paper/2210.08676/) (2022) ## Built on by (most cited first, 15 of 15) - [Unsupervised reconstruction of accelerated cardiac cine MRI using Neural Fields](https://mlsanity.com/paper/2307.14363/) (2023) - [INFusion: Diffusion Regularized Implicit Neural Representations for 2D and 3D accelerated MRI reconstruction](https://mlsanity.com/paper/2406.13895/) (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) - [Fully Unsupervised Dynamic MRI Reconstruction via Diffeo-Temporal Equivariance](https://mlsanity.com/paper/2410.08646/) (2024) - [RSR-NF: Neural Field Regularization by Static Restoration Priors for Dynamic Imaging](https://mlsanity.com/paper/2503.10015/) (2025) - [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) - [Self-supervised Deep Unrolled Model with Implicit Neural Representation Regularization for Accelerating MRI Reconstruction](https://mlsanity.com/paper/2510.06611/) (2025) - [Compressive Imaging Reconstruction via Tensor Decomposed Multi-Resolution Grid Encoding](https://mlsanity.com/paper/2507.07707/) (2025) - [MoE-dqINR: A Unified Mixture-of-Experts Implicit Neural Representation Framework for Scan-Specific Dynamic and Quantitative MRI Reconstruction](https://mlsanity.com/paper/2605.31302/) (2026) - [Piecewise Dynamic Diffusion Regularization for Reconstruction of Cardiac Cine MRI](https://mlsanity.com/paper/2607.03299/) (2026) - [Enhancing Implicit Neural Representations with Image Feature Embedding for Unsupervised Cardiac Cine MRI Reconstruction](https://mlsanity.com/paper/2607.04069/) (2026) ## Abstract (arXiv) Cardiac magnetic resonance imaging (MRI) requires reconstructing a real-time video of a beating heart from continuous highly under-sampled measurements. This task is challenging since the object to be reconstructed (the heart) is continuously changing during signal acquisition. In this paper, we propose a reconstruction approach based on representing the beating heart with an implicit neural network and fitting the network so that the representation of the heart is consistent with the measurements. The network in the form of a multi-layer perceptron with Fourier-feature inputs acts as an effective signal prior and enables adjusting the regularization strength in both the spatial and temporal dimensions of the signal. We study the proposed approach for 2D free-breathing cardiac real-time MRI in different operating regimes, i.e., for different image resolutions, slice thicknesses, and acquisition lengths. Our method achieves reconstruction quality on par with or slightly better than state-of-the-art untrained convolutional neural networks and superior image quality compared to a recent method that fits an implicit representation directly to Fourier-domain measurements. However, this comes at a relatively high computational cost. Our approach does not require any additional patient data or biosensors including electrocardiography, making it potentially applicable in a wide range of clinical scenarios.