TITLE:
Study on Multi-Exponential Inversion Method for NMR Relaxation Signals with Tikhonov Segularization
AUTHORS:
Shanshan Chen, Hongzhi Wang, Xuelong Zhang
KEYWORDS:
NMR; Relaxometry; Inversion Relaxation; MATLAB
JOURNAL NAME:
Engineering,
Vol.5 No.10B,
October
23,
2013
ABSTRACT: The analysis of NMR
data in terms of inversion of relaxation distribution is hampered by the
ill-posed nature of the required solution about the Fredholm integral equation.
Naive approaches such as multi-exponential fitting or standard least-squares
algorithms are numerically unstable and often failed. This paper updates the
application of Tikhonov regularization to stabilize this numerical inversion problem and
demonstrates the method for automatically choosing the optimal value of the
regularization parameter. The approach is computationally efficient and easy to
implement using standard matrix algebra techniques, which is based on mathematical
ware MATLAB. Example analyses arepresented using both synthetic data and experimental
results of NMR studies on the liquid samples like as oils and yoghurt.