Applying positivity constraints to q-space trajectory imaging: The QTI+ implementation

Diffusion MRI is a powerful technique sensitive to the microstructure of heterogeneous media. By relating the dMRI signal obtained via general gradient waveforms to the moments of an underlying diffusion tensor distribution, q-space trajectory imaging (QTI) provides several quantities indicative of the structural composition of the medium. Substantial improvements in the reliability of the produced estimates has been achieved via incorporating necessary positivity constraints in the estimation by employing Semidefinite Programming. Here we present the Matlab code implementing said constraints, provide a simple example showing the main functionalities of the package, and point to resources within the package that can be used to reproduce results recently published with this software. The block-based structure of our implementation allows the selection of steps to be performed, and facilitates the incorporation of new constraints in future releases.