WaveSep: A Flexible Wavelet-Based Approach for Source Separation in Susceptibility Imaging

The separation of signal contributions from paramagnetic and diamagnetic susceptibility sources in MRI has important implications for understanding the biological functions and health conditions of the brain. However, general and flexible deep-learning-based tools that can provide this information in humans in vivo are limited. For instance, the state-of-the-art deep-learning-based source separation method in quantitative susceptibility mapping (QSM) demands high-quality paramagnetic and diamagnetic maps for training and only allows phase measurement from a single head orientation as input. Furthermore, no method currently exists to separate these contributions when considering the susceptibility anisotropy as in the more challenging framework of susceptibility tensor imaging (STI). In this paper, we present a unified and flexible algorithm for source separation for both QSM and STI, dubbed WaveSep. Our method allows for an arbitrary number of input measurements at any head orientations for better estimation accuracy given multiple input measurements, does not require ground-truth paramagnetic and diamagnetic data for training, and is able to estimate the anisotropic second-order susceptibility tensors without requiring significant additional measurements. Our method first solves the dipole inversion problem by using state-of-the-art, off-the-shelf data-driven models based on learned proximal operators, and then separates the paramagnetic and diamagnetic sources using a Wavelet-based separation approach, without the need for retraining. Experimental results on both simulation and in-vivo human brain data demonstrate the superior performance of WaveSep for susceptibility source separation in QSM, and unprecedented separation results in STI. Code is available at https://github.com/ZhenghanFang/WaveSep.