Noise Analysis in Physics-based Deep Unrolled Network Reconstructions

Motivation: Characterizing noise is crucial for MRI reconstruction to ensure accurate SNR and image quality. However, current deep learning-based methods often neglect noise propagation. Goal(s): Develop a tool to analyze noise propagation of physics-based deep unrolled network reconstructions without relying on computationally intensive Monte Carlo simulations. Approach: Express image covariance via neural network's Jacobian, imaging operator, and coil covariance. Introduce a memory-efficient iterative algorithm that computes variance maps, avoiding full Jacobian storage. Results: Our technique accurately computes noise variance maps for state-of-the-art unrolled MRI reconstruction techniques, closely matching Monte-Carlo simulation results. Extremely low SNR levels and high acceleration factors reduce variance estimation accuracy. Impact: A practical tool facilitates noise analysis in physics-based deep learning reconstructions, so that image SNR can be assessed more objectively between reconstructions and patient scans. This would encourage researchers to develop more robust and trustworthy algorithms.