[CCoE Notice] Thesis Defense: Implementing a new and rigorous technique for 1-D NMR Inversion: Slope of L-curve and Adaptive Pruning

[Grayson, Audrey A]

MASTER’S THESIS DEFENSE
Naveen Krishnaraj
Implementing a new and rigorous technique for 1-D NMR Inversion: Slope of L-curve and Adaptive Pruning

Date: Tuesday 1st August 2017
Location: ERP 9, Room 123
Time: 1:30 pm – 3:30pm

Committee Chair: Dr. Michael Myers
Committee Members:
Dr. Lori Hathon
Dr. Alon Arad

1-D NMR data inversion is the process of obtaining T2 amplitude distribution from the NMR spin echo trains. NMR inversion is an ill-posed problem, because of the noise in the data allows for many possible solutions. We solve for the amplitudes on an equally spaced logarithmic scale, representing typical pore system distribution. If we simply used a least square method on this problem the solution is highly unstable, so we adopted a technique called Tikhonov-Regularization to restrict the range of possible solutions.
A robust version of this algorithm was developed and detailed parametric studies was performed. Two different L-cure parametrizations, the slope of the L-curve method and adaptive pruning was implemented. We generated forward models for the T2 echo train, using an assumption of multiply peaked amplitude distributions and varying levels of Gaussian white noise.  The forward models were then inverted using the developed algorithm to examine how much of the original information was lost.  We conclude with a discussion of the limitations of NMR inversion and the relative merits of each L-curve parametrization.
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