Efficient Noise Calculation in Deep Learning-based MRI Reconstructions

2025-05-04

AI Summary

Deep learning–based reconstruction models for accelerated MRI lack a theoretically grounded, computationally feasible method to quantify voxel-wise uncertainty arising from acquisition noise propagation. Method: We propose a theoretically rigorous and memory-efficient variance estimation framework. Its core innovations are: (1) the first unbiased estimator that analytically computes the diagonal elements of the noise covariance matrix; and (2) a Jacobian sketching technique leveraging random projection and first-order approximation to circumvent the computational intractability of high-dimensional Jacobian evaluation. Results: Evaluated on knee and brain MRI datasets, our method achieves accuracy comparable to Monte Carlo simulation while reducing computational cost and memory footprint by over an order of magnitude. It demonstrates strong robustness across varying noise levels, acceleration factors, and undersampling patterns. This enables interpretable, fidelity-aware assessment for trustworthy AI-driven clinical MRI reconstruction.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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 approximates 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- 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. Our code will be made publicly available upon acceptance.

Problem

• Quantifying noise propagation in DL-based MRI reconstructions
• Overcoming computational challenges in voxel-wise variance calculation
• Providing efficient uncertainty analysis for accelerated MRI methods

Innovation

• Estimates voxel-wise variance via Jacobian sketching
• Reduces computational demands significantly
• Robust across varying noise levels