Enforcing necessary non-negativity constraints for common diffusion MRI models using sum of squares programming
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Enforcing necessary non-negativity constraints for common diffusion MRI models using sum of squares programming. / Dela Haije, Tom; Ozarslan, Evren; Feragen, Aasa.
In: NeuroImage, Vol. 209, 116405, 2020.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Enforcing necessary non-negativity constraints for common diffusion MRI models using sum of squares programming
AU - Dela Haije, Tom
AU - Ozarslan, Evren
AU - Feragen, Aasa
PY - 2020
Y1 - 2020
N2 - In this work we investigate the use of sum of squares constraints for various diffusion-weighted MRI models, with a goal of enforcing strict, global non-negativity of the diffusion propagator. We formulate such constraints for the mean apparent propagator model and for spherical deconvolution, guaranteeing strict non-negativity of the corresponding diffusion propagators. For the cumulant expansion similar constraints cannot exist, and we instead derive a set of auxiliary constraints that are necessary but not sufficient to guarantee non-negativity. These constraints can all be verified and enforced at reasonable computational costs using semidefinite programming. By verifying our constraints on standard reconstructions of the different models, we show that currently used weak constraints are largely ineffective at ensuring non-negativity. We further show that if strict non-negativity is not enforced then estimated model parameters may suffer from significant errors, leading to serious inaccuracies in important derived quantities such as the main fiber orientations, mean kurtosis, etc. Finally, our experiments confirm that the observed constraint violations are mostly due to measurement noise, which is difficult to mitigate and suggests that properly constrained optimization should currently be considered the norm in many cases.
AB - In this work we investigate the use of sum of squares constraints for various diffusion-weighted MRI models, with a goal of enforcing strict, global non-negativity of the diffusion propagator. We formulate such constraints for the mean apparent propagator model and for spherical deconvolution, guaranteeing strict non-negativity of the corresponding diffusion propagators. For the cumulant expansion similar constraints cannot exist, and we instead derive a set of auxiliary constraints that are necessary but not sufficient to guarantee non-negativity. These constraints can all be verified and enforced at reasonable computational costs using semidefinite programming. By verifying our constraints on standard reconstructions of the different models, we show that currently used weak constraints are largely ineffective at ensuring non-negativity. We further show that if strict non-negativity is not enforced then estimated model parameters may suffer from significant errors, leading to serious inaccuracies in important derived quantities such as the main fiber orientations, mean kurtosis, etc. Finally, our experiments confirm that the observed constraint violations are mostly due to measurement noise, which is difficult to mitigate and suggests that properly constrained optimization should currently be considered the norm in many cases.
KW - Constrained optimization
KW - Cumulant expansion
KW - Diffusion MRI
KW - Diffusional kurtosis imaging
KW - Diffusion tensor imaging
KW - Mean apparent propagator
KW - Sampling scheme design
KW - Semidefinite programming
KW - Spherical deconvolution
KW - Sum of squares optimization
KW - Sum of squares polynomials
U2 - 10.1016/j.neuroimage.2019.116405
DO - 10.1016/j.neuroimage.2019.116405
M3 - Journal article
C2 - 31846758
VL - 209
JO - NeuroImage
JF - NeuroImage
SN - 1053-8119
M1 - 116405
ER -
ID: 238004573