Reconstruction of Q-ball images using a confidence-interval-based fidelity and an optimal transport-based (spatial) TV-regularizer. On the sphere, orientation distribution functions are regularized using spherical harmonics.

Abbreviations:

• bases: sh (spherical harmonics), srk (sparse reproducing kernels), n (none)
• fidelity: l (L2), w (Wasserstein), bnd (confidence intervals/bounds)
• regularizers: tvo (ODF pointwise), tvw (Wasserstein), tvc (coefficients)

Implemented models:

• n_w_tvw (SSVM)
• sh_w_tvw (modified SSVM)
• sh_l_tvc (Ouyang '14)
• sh_bndl1_tvc (modified Ouyang '14)
• sh_bndl2_tvc (modified Ouyang '14)
• sh_l_tvo
• sh_l_tvw (proposed)
• sh_bndl2_tvw (proposed)

Not yet implemented:

• sh_bndl1_tvw (proposed)
• srk_l_tvc
• srk_l_tvw

The recommended (and tested) setup is based on Ubuntu 16.04 with CUDA 8.0 or newer. In that case, the following lines will do:

sudo apt install -y python3 python3-venv python3.5-dev llvm-dev g++

# set up a virtual environment
python3 -m venv env
source ./env/bin/activate
pip install --upgrade pip
pip install wheel numpy
pip install -r requirements.0.txt
pip install -r requirements.1.txt

# install VTK 7.x with Python 3.x bindings
sudo add-apt-repository -y ppa:elvstone/vtk7
sudo apt update
sudo apt install -y vtk7
echo "/opt/VTK-7.0.0/lib/python3.5/site-packages" > env/lib/python3.5/site-packages/vtk7.pth

It is possible to run the code without CUDA using the solver parameter "use_gpu=False", but CUDA is recommended and enabled by default.

Optionally, parts of the code can be run using PyCVX which will profit a lot from using the (commercial) MOSEK solver:

# install mosek (you need a license!)
pip install git+https://github.com/MOSEK/Mosek.pip

Run the script demo.py without arguments to show available experiments and models:

python demo.py

After that, specify the experiment and model you want to test:

python demo.py cross sh_l_tvw

More options are documented when using

python demo.py cross sh_l_tvw --help

All logs, plots, parameters, results etc. are automatically stored in subdirectories of the results directory.

• The confidence-interval-based fidelity still has to be implemented.
• Evaluate results wrt. quality of fiber tractography (feasible?)