A Unified Model for Compressed Sensing MRI Across Undersampling Patterns

TL;DR

This work tackles the practical instability of MRI reconstructions when undersampling patterns and output resolutions vary, by introducing a unified, discretization-agnostic framework based on neural operators. The approach uses two operators, $\text{NO}_{\mathbf{k}}$ in k-space and $\text{NO}_{\mathbf{i}}$ in image space, implemented as DISCO-based UDNO blocks to learn priors across function spaces and to maintain a fixed kernel size across resolutions. It achieves robust performance across multiple undersampling patterns and rates, outperforms state-of-the-art CNN-based end-to-end VarNet and diffusion-based methods, and enables zero-shot super-resolution and extended field-of-view reconstructions while offering dramatically faster inference. The results imply a versatile, clinically adaptable MRI reconstruction method that reduces the need for multiple pattern/resolution-specific models and improves reconstruction fidelity and speed.

Abstract

Compressed Sensing MRI reconstructs images of the body's internal anatomy from undersampled measurements, thereby reducing scan time. Recently, deep learning has shown great potential for reconstructing high-fidelity images from highly undersampled measurements. However, one needs to train multiple models for different undersampling patterns and desired output image resolutions, since most networks operate on a fixed discretization. Such approaches are highly impractical in clinical settings, where undersampling patterns and image resolutions are frequently changed to accommodate different real-time imaging and diagnostic requirements. We propose a unified MRI reconstruction model robust to various measurement undersampling patterns and image resolutions. Our approach uses neural operators, a discretization-agnostic architecture applied in both image and measurement spaces, to capture local and global features. Empirically, our model improves SSIM by 11% and PSNR by 4 dB over a state-of-the-art CNN (End-to-End VarNet), with 600$\times$ faster inference than diffusion methods. The resolution-agnostic design also enables zero-shot super-resolution and extended field-of-view reconstruction, offering a versatile and efficient solution for clinical MR imaging. Our unified model offers a versatile solution for MRI, adapting seamlessly to various measurement undersampling and imaging resolutions, making it highly effective for flexible and reliable clinical imaging. Our code is available at https://armeet.ca/nomri.

Figures (12)

• Figure 1: (a) We propose a unified model for MRI reconstruction, called neural operator (NO), which works across various measurement undersampling patterns, overcoming the resolution dependency limit of CNN-based methods like e2evarnet that require a specific model for each pattern. (b) NO achieves consistent performance across undersampling patterns and outperforms CNN architectures such as e2evarnet (for 2$\times$ acceleration with one unrolled network cascade). (c) NO is resolution-agnostic. As image resolution increases, it maintains a consistent kernel size for alias-free rescaling, unlike CNNs with variable kernel sizes that risk aliasing. (d) NO enhances zero-shot super-resolution MRI reconstruction, outperforming CNNs e2evarnet.
• Figure 2: MRI reconstruction pipeline. NO learns data priors in function space with infinite resolution. Specifically we propose NOs in the $\mathbf{k}$ (frequency) space $\text{NO}_{\textbf{k}}$ ($\mathbf{k}$ space NO) and image space $\text{NO}_{\textbf{i}}$ (image space NO), which capture both global and local image features, due to the duality between physical and frequency space. $\mathcal{F}^{-1}$ refers to the inverse Fourier transform. We provide the framework design details in Section \ref{['sec:unrolled']} and NO design details in Section \ref{['sec:nodesign']}.
• Figure 3: Super resolution (denser discretization) in $\mathbf{k}$ space or image space increases the FOV or resolution of the reconstructed image. With denser discretization, NO maintains a resolution-agnostic kernel while CNN kernels become relatively smaller in size. Empirically our NO outperforms CNNs e2evarnet (Section \ref{['sec:superres']}).
• Figure 4: MRI reconstructions with different undersampling patterns of various methods: NO (ours), E2E-VN++, E2E-VN e2evarnet, L1-Wavelet (learning-free compressed sensing) cs_mri, and CSGM (diffusion) jalal2021robust. NO reconstructs high-fidelity images across various downsampling patterns. Zoom-in view in the lower right of each image. Row 1: 4$\times$ Equispaced undersampling. Row 2: 4$\times$ Gaussian 2d undersampling. Row 3: 4$\times$ Radial 2d undersampling.
• Figure 5: Zero-shot super-resolution results in both extended FOV ($\text{NO}_{\textbf{k}}$) and high-resolution image space ($\text{NO}_{\textbf{i}}$). (a) Zero-shot extended FOV reconstructions: Our NO model shows fewer artifacts and higher PSNR in the reconstructed brain slices compared to the CNN-based E2E-VN e2evarnet on $4\times$ Gaussian, despite neither model seeing data outside the initial $160 \times 160$ FOV during training. (b) Zero-shot super-resolution reconstructions in image space on $2\times$ radial: with input resolution increased to $640 \times 640$ through bilinear interpolation, our NO model preserves reconstruction quality, while E2E-VN e2evarnet produces visible artifacts.

Theorems & Definitions (2)

• Definition E.1: Group Convolution
• Definition E.2: DISCO Convolutions