Nuclear magnetic resonance T2 spectrum inversion method considering baseline shifting under low signal-to-noise ratio
A baseline offset and nuclear magnetic resonance technology, which is applied in electric/magnetic exploration, acoustic wave reradiation, radio wave measurement system, etc., can solve low signal to noise, unavoidable terminal non-zero phenomenon, and does not consider baseline offset, etc. question
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[0057] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.
[0058] 1. SVD filtering method
[0059] The present invention aims at data with a low signal-to-noise ratio, so it is first necessary to perform a filtering operation on the data to improve the signal-to-noise ratio of the data. For matrix H of order n×m n×m Do singular value decomposition, that is, there are n×n-dimensional orthogonal matrix U and m×m-dimensional orthogonal matrix V, and n×m-dimensional diagonal matrix S, so that:
[0060] h n×m =U n×n diag[ω 1 ,ω 2 ,…,ω k ,0,…,0]V m×m
[0061] In the formula, ω is the singular value of the matrix H. In general, the rank of a matrix without noise is small, while a matrix with noise is a full rank matrix. Due to the influence of noise, the singular values in the second half of the matrix will increase. The principle of SVD filtering is to set all the singular values after a certai...
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