Deep learning (DL) models are capable of successfully exploiting latent representations in MR data and have become state-of-the-art for accelerated MRI reconstruction. However, undersampling the measurements in k-space as well as the over- or under-parameterized and non-transparent nature of DL make these models exposed to uncertainty. Consequently, uncertainty estimation has become a major issue in DL MRI reconstruction. To estimate uncertainty, Monte Carlo (MC) inference techniques have become a common practice where multiple reconstructions are utilized to compute the variance in reconstruction as a measurement of uncertainty. However, these methods demand high computational costs as they require multiple inferences through the DL model. To this end, we introduce a method to estimate uncertainty during MRI reconstruction using a pixel classification framework. The proposed method, PixCUE (stands for Pixel Classification Uncertainty Estimation) produces the reconstructed image along with an uncertainty map during a single forward pass through the DL model. We demonstrate that this approach generates uncertainty maps that highly correlate with the reconstruction errors with respect to various MR imaging sequences and under numerous adversarial conditions. We also show that the estimated uncertainties are correlated to that of the conventional MC method. We further provide an empirical relationship between the uncertainty estimations using PixCUE and well-established reconstruction metrics such as NMSE, PSNR, and SSIM. We conclude that PixCUE is capable of reliably estimating the uncertainty in MRI reconstruction with a minimum additional computational cost.

翻译：摘要：深度学习模型能够成功利用MR数据中的潜在表示，已成为加速MRI重建的最先进技术。然而，k空间测量欠采样以及深度学习模型过参数化或欠参数化且非透明的特性，使这些模型面临不确定性。因此，不确定性估计已成为深度学习MRI重建中的关键问题。为估计不确定性，蒙特卡洛推理技术成为一种常见做法，该类技术利用多次重建结果计算重建方差作为不确定性度量。然而，这些方法要求通过深度学习模型进行多次推理，计算成本高昂。为此，我们提出一种基于像素分类框架在MRI重建过程中估计不确定性的方法。所提出的方法PixCUE（像素分类不确定性估计的缩写）可在单次前向传播中同时生成重建图像及不确定性图。我们证明，该方法生成的不确定性图与不同MR成像序列及多种对抗条件下的重建误差高度相关。此外，我们表明估计的不确定性与传统蒙特卡洛方法的结果具有相关性，并进一步建立了PixCUE不确定性估计与NMSE、PSNR、SSIM等成熟重建指标之间的经验关系。我们得出结论：PixCUE能以极低的额外计算成本可靠估计MRI重建中的不确定性。