Abstract #2610

QTI+: a constrained estimation framework for q-space trajectory imaging

Magnus Herberthson¹, Tom Dela Haije², Deneb Boito^3,4, Aasa Feragen⁵, Carl-Fredrik Westin⁶, and Evren Özarslan^3,4

¹Dept. of Mathematics, Linköping University, Linköping, Sweden, ²Dept.of Computer Science, University of Copenhagen, Copenhagen, Denmark, ³Dept. of Biomedical Engineering, Linköping University, Linköping, Sweden, ⁴Center for Medical Image Science and Visualization, Linköping University, Linköping, Sweden, ⁵Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark, ⁶Laboratory for Mathematics in Imaging, Department of Radiology, Brigham and Women’s Hospital, Harvard Medical School, Boston, Boston, MA, United States

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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