Machine Learning in QSM:   Inversion Using Multi-Resolution Decomposition and Convolutional Neural Networks.

One of the remaining translational challenges in QSM is the need for post-processing algorithms that are rapid, robust, and accurate. Here, we present an alternative formulation of the QSM inversion problem. The field-to-source inversion is divided into a multi-resolution decomposition, whereby each resolution stage is divided into small independent processing regions. The basic premise of this concept is the isolate local susceptibility fields and sources at varying levels of resolution. When the susceptibility problem is divided in this fashion, field-to-source inversions can occur in regions of very volumetric matrix sizes (with varying voxel sizes per inversion). After inverting each of the sub-volumes, a combination procedure is implemented to combine the volumes and the resolution layers. Due to the small size of the inversion volumes, the dimensionality of the problem lends itself to the use of convolutional neural network modeling and application.