MR-STAT Reconstruction Code

This repository contains an implementation of the partially-matrix free, inexact Gauss-Newton algorithm that can be used for MR-STAT. It use a 2D numerical brain phantom to generate synthetic data from which it then estimates $T_1$, $T_2$ and proton density. It only supports Cartesian readout trajectories at the moment. The reconstruction makes use of BlochSimulators.jl and should be able to run on modern NVIDIA GPU hardware.

Warning:

• This codebase uses an older version of BlochSimulators (v0.2.7), make sure to instantiate the environment as defined in the manifest.
• This codebase assumes a CUDA device is available.

Structure:

• Only the main.jl needs be run. It loads external packages and several functions, assembles a FISP sequence, a Cartesian trajectory and a numerical phantom (including spatial coordinates and coil sensitivity profiles). It generates (noiseless) data. An MR-STAT reconstruction is then performed on the generated data.
• The objective function is defined in utils/objective.jl. This function is also used by the non-linear solver to calculate the gradient of the objective and the (Gauss-Newton approximation to) the Hessian.
• Bloch simulations (in case of FISP: EPG simulations) are performed using the BlochSimulators.jl package.
• Partial derivatives are calculated using a finite difference approach, see DerivativeOperations/simulate_derivatives.jl.
• The matrix-vector products with the Jacobian matrix and its adjoint are implemented in a partially matrix-free method, see DerivativeOperations/Jv.jl and DerivativeOperations/Jᴴv.jl.
• The non-linear solver (Trust Region Reflective with Gauss-Newton approximation to the Hessian) is contained in the TrustRegionReflective submodule.