Efficient Noise Calculation in Deep Learning-based MRI Reconstructions

Accelerated MRI reconstruction involves solving an ill-posed inverse problem where noise in acquired data propagates to the reconstructed images. Noise analyses are central to MRI reconstruction for providing an explicit measure of solution fidelity and for guiding the design and deployment of novel reconstruction methods. However, deep learning (DL)-based reconstruction methods have often overlooked noise propagation due to inherent analytical and computational challenges, despite its critical importance. This work proposes a theoretically grounded, memory-efficient technique to calculate voxel-wise variance for quantifying uncertainty due to acquisition noise in accelerated MRI reconstructions. Our approach is based on approximating the noise covariance using the DL network's Jacobian, which is intractable to calculate. To circumvent this, we derive an unbiased estimator for the diagonal of this covariance matrix—voxel-wise variance—, and introduce a Jacobian sketching technique to efficiently implement it. We evaluate our method on knee and brain MRI datasets for both data-driven and physics-driven networks trained in supervised and unsupervised manners. Compared to empirical references obtained via Monte-Carlo simulations, our technique achieves near-equivalent performance while reducing computational and memory demands by an order of magnitude or more. Furthermore, our method is robust across varying input noise levels, acceleration factors, and diverse undersampling schemes, highlighting its broad applicability. Our work reintroduces accurate and efficient noise analysis as a central tenet of reconstruction algorithms, holding promise to reshape how we evaluate and deploy DL-based MRI.

MRI scans allow doctors to look inside the body to diagnose medical conditions, but scans typically take a long time. Researchers developed methods using artificial intelligence (AI) to speed up MRI scans, but these advanced AI methods often don't clearly show how noise (unwanted random variations) affects the images they produce. Knowing precisely where and how much noise appears in MRI scans is essential, as noise can affect diagnosis and treatment decisions.In this work, we created a new approach to measure exactly how noise from faster scans spreads through AI-based MRI reconstructions. Our method efficiently estimates how much noise exists at each point (voxel) of an image, clearly indicating areas where the image might be less reliable. This helps radiologists trust AI-generated images by identifying uncertain regions. Our technique is accurate yet much faster and uses significantly less memory compared to previous methods. It works well with different body regions, different AI models, and various scan speeds, showing it can be broadly applied.Overall, our approach brings precise and efficient noise assessment back into modern MRI, enhancing the reliability of faster, AI-powered scans and supporting better medical decisions.