[Paper Review] Implicit Neural Networks with Fourier-Feature Inputs for Free-breathing Cardiac MRI Reconstruction

Johannes F. Kunz, Stefan Ruschke+1 more|arXiv (Cornell University)|May 11, 2023

Advanced MRI Techniques and Applications22 citations

TL;DR

The paper presents FMLP, an untrained implicit neural network using Fourier-feature inputs to reconstruct 2D free-breathing cardiac MRI from under-sampled data, achieving image quality on par with or better than state-of-the-art untrained CNN-based methods at higher computational cost.

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.

Motivation & Objective

• Motivate real-time cardiac MRI reconstruction without training data.
• Develop an implicit network with Fourier-feature inputs as a spatial-temporal prior for beating-heart imaging.
• Demonstrate data-consistent fitting to under-sampled measurements across different resolutions and slice thicknesses.
• Compare reconstruction quality and computational cost against untrained CNN-based approaches and Fourier-domain methods.

Proposed method

• Represent the beating heart as an implicit MLP with separate spatial and temporal Fourier-feature embeddings.
• Fit the network by minimizing data-consistency loss against measured k-space data across frames.
• Use a complex-valued output (real and imaginary parts) to model image intensity.
• Train with Adam on frames sampled randomly; query x_hat from the trained network for video outputs.
• Compare to baselines: neural implicit k-space (NIK), Fourier-feature MLP in k-space (KFMLP), and time-dependent DIP (t-DIP).
• Hyper-parameters tune coordinate scales for spatial (sx, sy) and temporal (st) features and random Gaussian embeddings.

Experimental results

Research questions

• RQ1 Can an untrained implicit network with Fourier-feature inputs provide high-quality 2D real-time cardiac MRI reconstructions from highly under-sampled data?
• RQ2 How does the FMLP compare to NIK, KFMLP, and t-DIP in terms of image quality and computational cost across different resolutions and acquisition lengths?
• RQ3 Does separate spatial and temporal Fourier-feature embedding improve reconstruction sharpness and detail over joint embeddings?
• RQ4 What is the impact of increased acquisition time on reconstruction quality for implicit representations?

Key findings

• FMLP achieves image quality on par with or slightly better than t-DIP across datasets, and outperforms NIK and KFMLP in SER metrics.
• SER improves for FMLP and t-DIP with longer acquisition times, while NIK and KFMLP show limited gains.
• On three operating regimes (low/high resolution, varying SNR), FMLP and t-DIP provide comparable quality; KFMLP underperforms.
• Compared to baselines, FMLP yields sharper, more faithful cardiac details (e.g., papillary muscles) with fewer aliasing/noise artifacts.
• FMLP requires higher computational cost due to evaluating the full coordinate grid; NIK/KFMLP train faster since they sample only measured coordinates.