Q-space trajectory imaging (QTI) provides a means to estimate the moments for a diffusion tensor distribution (DTD) characterizing the tissue. Commonly employed estimation methods do not typically yield mathematically acceptable estimates, namely that the tensor distribution consists of symmetric positive semidefinite tensors and that the second cumulant represents a covariance. We introduce the QTI+ framework, which utilizes semi-definite programming (SDP) to address this issue. Simulations using a DTD taking the form of a non-central Wishart distribution as well as real data show a marked improvement in the technique's robustness to noise compared to more common (unconstrained) estimation methods.
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