Denoising Method for NMR Signals Based on Two Domain Sparse Representation

Nuclear magnetic resonance (NMR) spectroscopy is very useful in basic chemical and physiological research, including the analysis of organic compounds. However, NMR spectroscopy has a problem of low signal-to-noise ratio (SNR) of the observed signal, and it is expected that an effective denoising method will improve the efficiency of measurement and enable a wide range of applications to samples with large changes over time. We have proposed a denoising method based on the fact that NMR signals have sparsity in the frequency range, and that sparsity is not lost when N-order differences are taken. Although this method shows higher denoising performance than existing methods, it tends to suppress the value in the frequency band excepting the around peak too much because it focuses on the sparsity of the waveform. In this paper, we propose a method for estimating smooth waveforms by applying dictionary-based denoising in addition to the above-mentioned methods.The simulation results show high denoising performance.