PixCUE: Joint Uncertainty Estimation and Image Reconstruction in MRI using Deep Pixel Classification

Deep learning (DL) models are effective in leveraging latent representations from MR data, emerging as state-of-the-art solutions for accelerated MRI reconstruction. However, challenges arise due to the inherent uncertainties associated with undersampling in k-space, coupled with the over- or under-parameterized and opaque nature of DL models. Addressing uncertainty has thus become a critical issue in DL MRI reconstruction. Monte Carlo (MC) inference techniques are commonly employed to estimate uncertainty, involving multiple reconstructions of the same scan to compute variance as a measure of uncertainty. Nevertheless, these methods entail significant computational expenses, requiring multiple inferences through the DL model. In this context, we propose a novel approach to uncertainty estimation during MRI reconstruction using a pixel classification framework. Our method, PixCUE (Pixel Classification Uncertainty Estimation), generates both the reconstructed image and an uncertainty map in a single forward pass through the DL model. We validate the efficacy of this approach by demonstrating that PixCUE-generated uncertainty maps exhibit a strong correlation with reconstruction errors across various MR imaging sequences and under diverse adversarial conditions. We present an empirical relationship between uncertainty estimations using PixCUE and established reconstruction metrics such as NMSE, PSNR, and SSIM. Furthermore, we establish a correlation between the estimated uncertainties from PixCUE and the conventional MC method. Our findings affirm that PixCUE reliably estimates uncertainty in MRI reconstruction with minimal additional computational cost.