Robust multi-coil MRI reconstruction via self-supervised denoising

Abstract

We study the effect of incorporating self-supervised denoising as a pre-processing step for training deep learning (DL) based reconstruction methods on data corrupted by Gaussian noise. K-space data employed for training are typically multi-coil and inherently noisy. Although DL-based reconstruction methods trained on fully sampled data can enable high reconstruction quality, obtaining large, noise-free datasets is impractical. We leverage Generalized Stein's Unbiased Risk Estimate (GSURE) for denoising. We evaluate two DL-based reconstruction methods: Diffusion Probabilistic Models (DPMs) and Model-Based Deep Learning (MoDL). We evaluate the impact of denoising on the performance of these DL-based methods in solving accelerated multi-coil magnetic resonance imaging (MRI) reconstruction. The experiments were carried out on T2-weighted brain and fat-suppressed proton-density knee scans. We observed that self-supervised denoising enhances the quality and efficiency of MRI reconstructions across various scenarios. Specifically, employing denoised images rather than noisy counterparts when training DL networks results in lower normalized root mean squared error (NRMSE), higher structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR) across different SNR levels, including 32dB, 22dB, and 12dB for T2-weighted brain data, and 24dB, 14dB, and 4dB for fat-suppressed knee data. Overall, we showed that denoising is an essential pre-processing technique capable of improving the efficacy of DL-based MRI reconstruction methods under diverse conditions. By refining the quality of input data, denoising enables training more effective DL networks, potentially bypassing the need for noise-free reference MRI scans.

Figures (13)

• Figure 1: FastMRI Pre-Processing and Deep Learning-Driven MRI Reconstruction Pipeline. a) The pre-processing begins with pre-whitening and normalization of the raw k-space data. The whitened and normalized adjoint $A^\mathrm{H}y$ of the k-space is passed through the denoiser network $g_{\phi}$, outputting the MMSE denoised sample $\tilde{x}_\textrm{MMSE}$. We show the magnitude of a sample from the fastMRI dataset before and after denoising, including a histogram of the extracted noise patch to show the distribution of real and imaginary noise components. b) The MMSE denoised data $\tilde{x}_\textrm{MMSE}$ are utilized for training deep learning networks using two methods: (1) Generative Models, and (2) End-to-End. Accelerated reconstruction is then performed utilizing: (1) Diffusion Posterior Sampling (DPS), and (2) MoDL Forward Pass.
• Figure 2: Unconditional T2-Weighted Brain images generated from EDM models trained on two datasets: a) Noisy (Naive-EDM), and b) GSURE denoised (GSURE-EDM). Across each column, we show prior samples across three different training SNR levels. Across each row, we show different realizations of images generated from the same distribution. We can observe that GSURE-EDM consistently generates qualitatively superior images, notably at lower SNR levels.
• Figure 3: Unconditional Fat-Suppressed Knee images generated from EDM models trained on two datasets: a) Noisy (Naive-EDM), and b) GSURE denoised (GSURE-EDM). Across each column, we show prior samples across three different training SNR levels. Across each row, we show different realizations of images generated from the same distribution. We can observe that GSURE-EDM consistently generates qualitatively superior images, notably at lower SNR levels.
• Figure 4: Conditional T2-Weighted Brain images with DPS as the reconstruction method, utilizing EDM models trained on two datasets: a) Noisy (Naive-DPS) and b) GSURE denoised (GSURE-DPS). Across columns, we show reconstructions across three training/inference SNR levels. In the first row, we show the reconstruction example with quantitative comparison metrics. In the second row, we show the difference between the reconstruction and fully sampled image at $2.5\times$ brightness. We can observe that GSURE-DPS consistently outperforms Naive-DPS, notably at lower SNR levels.
• Figure S1: Validation examples from the GSURE denoising experiment across T2-Weighted Brain and Fat-Suppressed Knee data at three SNR levels. Across each column under the appropriate anatomy, we show noisy input $A^\mathrm{H}y$ vs the output of the GSURE network $\tilde{x}_\textrm{MMSE} = g_{\phi}\left(\frac{A^\mathrm{H}y}{\sigma^2} \right)$. Across each row under the appropriate anatomy, we show the same validation example at different SNR levels, where row $1$ always shows data at the original native SNR (without additive noise). Overall, the experiment showcases the utility of GSURE denoising in improving the quality of training data, especially in low SNR cases.