Reconstruction of Convex Polynomial Diffusion MRI Models Using Semi-definite Programming

In this work we describe and perform the reconstruction of general polynomial diffusion MRI models, with the added constraint that the polynomials are convex. This is done by requiring the Hessian of the model to be sum-of-squares. The resulting optimization problem is shown to be solvable in a reasonable amount of time for the scale of data typical in clinical diffusion MRI acquisitions.

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