Effective Denoising for Low-Field NMR Measurements Using Unsupervised Machine Learning

Low-field nuclear magnetic resonance (NMR) is a widely employed technique in geoscience. However, signal-to-noise ratio (SNR) is always an issue in low-field NMR measurement, which should be carefully addressed to ensure the accuracy of relaxation spectrum reconstruction for subsequent petrophysical interpretation and applications. This article presents a novel denoising method for low-field NMR measurements utilizing double-sparsity dictionary learning (DSDL), which is an unsupervised machine learning (ML) approach. The elaborate trained dictionary models could be directly implemented to denoise raw spin echoes with different SNRs. After denoising, digital phase-sensitive detection (DPSD) and phase rotation are conducted to obtain the multiexponential decay signals and fundamental noise signals for subsequent spectrum reconstruction. In this study, numerical simulations are mainly conducted. The preset $T_{2}$ spectrum models are built to derive raw spin echoes with different SNRs through forward modeling, and then are used to train the double-sparsity dictionary models. The dictionary models are trained on raw echo datasets with different Gaussian distributed noise and the same porosity, and tested on raw echo datasets with the same Gaussian noise and different porosities. The echo data before and after denosing are all inverted by using the singular value decomposition (SVD) method, which is a nonobjective inversion algorithm to avoid the parameter selection like the commonly used regularization inversion algorithm. All the inverted results are compared with the forwarding spectrum models. It is demonstrated that the DSDL method could effectively improve the quality of low-field NMR measurements, resulting in an accurate relaxation spectrum.