An Efficient Method for NMR Data Compression Based on Fast Singular Value Decomposition

To improve the processing speed of nuclear magnetic resonance (NMR) echo data, data compression is essential prior to NMR inversion due to the large amount of raw echo data acquired via NMR logging. In this letter, a fast singular value decomposition (FSVD) method is proposed to compress NMR data, which differs from the SVD method by developing a lower dimensional submatrix that can capture most action in the kernel matrix based on a random Hadamard matrix, and then decomposing the sub-matrix using SVD. The 2-D NMR relaxation data are taken as examples to evaluate the efficiency of the FSVD method. The inverted <inline-formula> <tex-math notation="LaTeX">$T_{1}$ </tex-math></inline-formula>–<inline-formula> <tex-math notation="LaTeX">$T_{2}$ </tex-math></inline-formula> spectra after FSVD compression are compared with spectra after SVD compression and spectra without compression through numerical simulation experiments. Results show that under the same conditions, the compression time is shorter for the FSVD method than for the SVD method, the inversion time is far shorter for compressed NMR data than for uncompressed NMR data, and the accuracy of the inverted <inline-formula> <tex-math notation="LaTeX">$T_{1}$ </tex-math></inline-formula>–<inline-formula> <tex-math notation="LaTeX">$T_{2}$ </tex-math></inline-formula> spectra after compression is close to that without compression. In addition, the effect of the Hadamard matrix on the accuracy and speed of the FSVD method is studied through 1000 random simulations. Findings show that the compression results of the FSVD method with different Hadamard matrices are close, indicating that the efficiency of this method is not affected by the Hadamard matrix.