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An Improved TSVD Based Linearized Bregman Iterative Algorithm for the Inversion of NMR T2 Spectrum
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, 81st EAGE Conference and Exhibition 2019, Jun 2019, Volume 2019, p.1 - 6
Abstract
The low field nuclear magnetic resonance technique has long been used to probe the pore size distribution and the fluid composition in geophysical prospecting and related fields. However, the inversion speed and the accuracy of the existed methods are still challenging due to the ill-posed nature of the first kind Fredholm integral equation of and the contamination of the noises. This paper introduces a novel algorithm to accelerate the convergence and inversion precision involving the empirical truncated singular value decompositions (TSVD) and the linearized Bregman iteration. We apply the L1 penalty term to construct the objective function and then solve the problem by the linearized Bregman iteration, aiming to reach fast convergence. To reduce the complexity of the computation, the empirical TSVD is proposed to compress the kernel matrix, as well as to get the appropriate truncated position. The presented method is validated through numerical simulations. The result indicates that the method is efficient, and can achieve favorable solutions for data with low signal to noise ratio.