1887

Abstract

Summary

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.

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/content/papers/10.3997/2214-4609.201900984
2019-06-03
2024-03-28
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References

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