Phase Correction-Adaptive Line Enhancement for Noise Reduction of Low-Field NMR
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Appl Magn Reson (2013) 44:1381–1391 DOI 10.1007/s00723-013-0486-2
Magnetic Resonance
Phase Correction-Adaptive Line Enhancement for Noise Reduction of Low-Field NMR Qingming Xie • Lizhi Xiao • Lijun Cheng Junfeng Liu • Hongying Li • Feng Deng
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Received: 9 May 2013 / Revised: 9 September 2013 / Published online: 2 November 2013 Ó The Author(s) 2013. This article is published with open access at Springerlink.com
Abstract The amplitude of low-field nuclear magnetic resonance (NMR) is weak, and the echo is buried in the noise. The reduction of noise is critical to accurately extract echo amplitude. Phase correction-adaptive line enhancement (PC-ALE) is proposed to noise suppression based on the principle of ALE and NMR spin-echo characteristics. The echo amplitude is calculated after two-stage processes; phase shift from time-delay and filter tap would be compensated effectively in frequency domain. Simulation and experiments show that PC-ALE has prominent performance on noise suppression, envelope recovery, as well as the correction of the phase shift. The amplitude from the method of sample average nearby the middle of the echo is more accurate than the maximum peak when the PC-ALE is applied to noise suppression of spin-echo.
1 Introduction Low-field nuclear magnetic resonance (NMR) is applied for NMR well logging, core analyses, fluid magnetic resonance imaging, etc. [1, 2]. Compared to mediumfield (0.500–1 T) and high-field (1.500–2 T) NMR [3], spin echo is easily Q. Xie (&) L. Cheng J. Liu H. Li Key Laboratory of Shale Gas Exploration, Ministry of Land and Resources, Chongqing Institute of Geology and Mineral Resources, 177-9 Yangtze River 2 Road, Yuzhong, Chongqing 400042, China e-mail: [email protected] Q. Xie L. Xiao L. Cheng J. Liu H. Li Chongqing Shale Gas Research Centre of State Key Laboratory of Petroleum Resource and Prospecting, Chongqing 400042, China L. Xiao F. Deng Key Laboratory of Earth Prospecting and Information Technology, China University of Petroleum, Beijing 102249, China
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contaminated by noise and the amplitude is weak. The reduction of noise is critical to accurately extract echo, the amplitude, and the phase information. Methods of noise suppression in low-field NMR are diverse, such as, finite impulse response (FIR) filter [4], wavelet transform [5–7], principal component analyses (PCA) [8, 9], etc. FIR filter (i.e., low-pass, band-pass, and high-pass) is generally based on a priori knowledge of the spin echo; the de-noising performance is awful if a priori knowledge is insufficient. The signal-to-noise ratio (SNR) is improved by accumulation [10]; however, the method requires a large amount of data acquisition and is a time-consuming procedure. Despite of the good performance on noise reduction, the wavelet transform and PCA are not suitable for the real-time process due to the computational complexity, and are adopted to post-processing of echo trains. An adaptive noise canceller (ANC) based on the adaptive algorithm is widely us
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