A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from complex DWI

In this paper, we present a novel constrained variational principle for simultaneous smoothing and estimation of the diffusion tensor field from complex valued diffusion-weighted images (DWI). The constrained variational principle involves the minimization of a regularization term of L/sup p/ norms,...

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Bibliographic Details
Published in:IEEE transactions on medical imaging 2004-08, Vol.23 (8), p.930-939
Main Authors: Zhizhou Wang, Vemuri, B.C., Chen, Y., Mareci, T.H.
Format: Article
Language:English
Subjects:
Algorithms
Anatomy
Animals
Anisotropic magnetoresistance
Brain - anatomy & histology
Computer Simulation
Diffusion Magnetic Resonance Imaging - methods
Diffusion tensor imaging
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Imaging, Three-Dimensional - methods
Inequality
Information science
Information Storage and Retrieval - methods
Lagrangian functions
Least squares methods
Magnetic resonance imaging
Mathematical models
Nonlinear equations
Numerical Analysis, Computer-Assisted
Rats
Reproducibility of Results
Sensitivity and Specificity
Signal Processing, Computer-Assisted
Smoothing methods
Studies
Tensile stress
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Summary:In this paper, we present a novel constrained variational principle for simultaneous smoothing and estimation of the diffusion tensor field from complex valued diffusion-weighted images (DWI). The constrained variational principle involves the minimization of a regularization term of L/sup p/ norms, subject to a nonlinear inequality constraint on the data. The data term we employ is the original Stejskal-Tanner equation instead of the linearized version usually employed in literature. The complex valued nonlinear form leads to a more accurate (when compared to the linearized version) estimate of the tensor field. The inequality constraint requires that the nonlinear least squares data term be bounded from above by a known tolerance factor. Finally, in order to accommodate the positive definite constraint on the diffusion tensor, it is expressed in terms of Cholesky factors and estimated. The constrained variational principle is solved using the augmented Lagrangian technique in conjunction with the limited memory quasi-Newton method. Experiments with complex-valued synthetic and real data are shown to depict the performance of our tensor field estimation and smoothing algorithm.
ISSN:0278-0062
1558-254X
DOI:10.1109/TMI.2004.831218