convex_diffusion is a convex optimization framework for generating asymmetric diffusion encoding gradient waveforms for high-resolution magnetic resonance diffusion imaging. It solves a quadratic optimization problem with convex constraints using semidefinite programming yielding optimized asymmetric spin echo sequences with short echo times that are robust regarding concomitant field effects and motion. The framework is written in MATLAB R2017a.

Install from Github source:

git clone https://github.com/alen-mujkanovic/convex_diffusion.git
git clone https://github.com/yalmip/YALMIP

If you want to run the example, you require MATLAB 2017a and will also have to install:

• YALMIP by Johan Löberg: https://yalmip.github.io/

and a convex solver supported by YALMIP, such as

• CPLEX by IBM: https://www.ibm.com/products/ilog-cplex-optimization-studio/
• SeDuMi from Lehigh University: http://sedumi.ie.lehigh.edu/
• SDPT3: https:/github.com/sqlp/sdpt3/

Alternatively, the code can be easily modified to use:

• CVX by CVX Research: http://cvxr.com/cvx/

If you use convex_diffusion in your research, you can cite it as follows:

@misc{mujkanovic2018convexdiffusion,
    author = {Alen Mujkanović, Chris Nguyen, David Sosnovik, Sebastian Kozerke},
    title = {convex_diffusion},
    year = {2018},
    publisher = {GitHub},
    journal = {GitHub repository},
    howpublished = {\url{https://github.com/alen-mujkanovic/convex_diffusion}},
}

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