Deep Network Regularization for Phase-Based Magnetic Resonance Electrical Properties Tomography With Stein's Unbiased Risk Estimator

Magnetic resonance imaging (MRI) can estimate tissue conductivity values using phase-based magnetic resonance electrical properties tomography (MR-EPT). However, this method is prone to noise amplification due to the Laplacian operator's sensitivity. To address this issue, we propose a novel unsupervised preprocessing denoiser for MRI transceive phase images. Our approach draws inspiration from the deep image prior (DIP) technique, utilizing the random initialization of a convolutional neural network (CNN) to enforce implicit regularization. Additionally, we incorporate Stein.s unbiased risk estimator (SURE) to optimize the network, which serves as an unbiased estimator of mean square error, thereby eliminating the need for labeled data. This modification mitigates the overfitting commonly associated with the DIP approach, enabling a fully unsupervised framework. Furthermore, we process real and imaginary images instead of phase images, aligning more closely with the theoretical basis of the risk estimator. Our generative model does not require pre-training or extensive training datasets, maintaining adaptability across different resolutions and signal-to-noise ratio levels. In our evaluations, the proposed method significantly reduced residual noise in phase maps, improving both quantitative and qualitative outcomes in phantom and simulated brain data. It also outperformed existing denoising techniques by reducing noise amplification and boundary errors. Applied to data from healthy volunteers and patients, our method yielded conductivity maps with reduced errors and values consistent with established literature. To our knowledge, this is the first blind, fully unsupervised approach capable of implementing a 2D phase-based MR-EPT reconstruction algorithm.