SpiNet-QSM: Model-based Deep Learning with Schatten p‐norm regularization for Quantitative Susceptibility Mapping
SpiNet-QSM: Model-based Deep Learning with Schatten p‐norm regularization for Quantitative Susceptibility Mapping
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QSM Problem
QSM Problem
QSM provides information about the underlying magnetic susceptibility distribution of a sample from MRI phase measurements. It is useful in the clinical diagnosis of diseases like Demyelination, Calcification, and Parkinson’s disease.
The following mathematical relation represents the linear approximated equation for the QSM reconstruction :
For solving QSM problem, it is required peform dipole deconvolution with local field. It is very cruical step in the QSM solving. Unfortunately, this it is an illposed problem.
SpiNet-QSM
SpiNet-QSM
The proposed SpiNet-QSM is a model-based deep learning technique for solving the QSM problem. The proposed approach can enforce p-norm (0 < p ≤ 2) on trainable regularizer, where its norm parameter (p) is trainable (automatically chosen).
SpiNet-QSM has two parts: data consistency term and regularization term.
SpiNet-QSM mathematical formulation
SpiNet-QSM mathematical formulation
In this approach, QSM problem was formulated as the following optimization problem by enforcing p-norm at denoiser/regularization term.
In this equation, the norm parameter (p) of the regularization term and regularization parameter(𝜆) are learnable for the QSM problem.
Here, J(\chi) has been iteratively solved using the majorization-minimization approach. In the Majorization, the upper bound function F(\chi) for J(\chi) has been defined and in the minimization step F(\chi) was solved.
The following equations defining the majorization and minimization step at K-th iteration.
SpiNet-QSM Architecture
SpiNet-QSM Architecture
SpiNet-QSM as a unrolled architecture
SpiNet-QSM as a unrolled architecture
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