Implicit Neural Networks with Fourier-Feature Inputs for Free-breathing Cardiac MRI Reconstruction

TL;DR

The paper tackles real-time, free-breathing cardiac MRI reconstruction from under-sampled measurements by leveraging an untrained implicit neural network with Fourier-feature inputs to model the heart as a function of space and time. The proposed Fourier-feature MLP (FMLP) acts as a strong spatio-temporal prior and is fitted to measurements via a data-consistency loss, enabling controllable regularization without training data. Empirical results show FMLP achieving image quality on par with or slightly better than state-of-the-art untrained CNN methods (notably t-DIP) across diverse regimes, albeit with higher computational cost; it also outperforms recent implicit-representation baselines that operate in Fourier space. The approach does not require any biosensors or patient data, highlighting its potential applicability across clinical settings, with future work aimed at reducing compute (e.g., pre-training) and extending to 3D reconstructions.

Abstract

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.

Figures (21)

• Figure 1: The FMLPs' network consists of separate spatial and temporal Fourier-feature embeddings that are concatenated, followed by an MLP that outputs the complex image intensity at the specified coordinate.
• Figure 2: The SER within the first 4s of acquisition time improves with increasing the amount of measurement data beyond 4s. The reconstruction quality can be improved by training the FMLP on a longer acquisition time. The methods were evaluated on the low-resolution high-SNR dataset with the same configurations as in Figure \ref{['fig:fmlp-tdip-bh-10-225-imgs']} and $z_{\text{slack}} = 0.1, 0.2,$ and $0.4$ for $T=225$ (4s), $450$ (8s), and $900$ (16s), respectively.
• Figure 3: On the low-resolution high-SNR dataset, the image quality of the FMLP and the t-DIP are similar, whereby the FMLP recovers anatomic details such as the papillary muscles in the left ventricle (red arrow) more accurately. The reconstructions by the NIK and the KFMLP are distorted by aliasing-like artifacts and fine-structured noise such that anatomic details are not well recognizable. The models were trained on $T=225$ frames.
• Figure 4: For an isotropic slice thickness (low-resolution low-SNR dataset) the reconstruction quality of all methods degrades and new artifacts are introduced. The FMLP and the t-DIP achieve a similar image quality and outperform the NIK and the KFMLP. The models were trained on $T=225$ frames.
• Figure 5: On the high-resolution dataset, the FMLP and the t-DIP achieve a similar reconstruction quality and both methods suffer from similar artifacts. The quality of the NIK and the KFMLP is decreased substantially by noise-like artifacts, especially for the KFMLP. The models were trained on $T = 225$ frames.