
Bayesian Inference for NMR Spectroscopy with Applications to Chemical Quantification
Nuclear magnetic resonance (NMR) spectroscopy exploits the magnetic prop...
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Gaussian noise removal with exponential functions and spectral norm of weighted Hankel matrices
Exponential functions are powerful tools to model signals in various sce...
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Complex diffusionweighted image estimation via matrix recovery under general noise models
We propose a patchbased singular value shrinkage method for diffusion m...
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Nonlinear dance motion analysis and motion editing using HilbertHuang transform
Human motions (especially dance motions) are very noisy, and it is hard ...
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Magnetic Resonance Spectroscopy Quantification using Deep Learning
Magnetic resonance spectroscopy (MRS) is an important technique in biome...
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Theory inspired deep network for instantaneousfrequency extraction and signal components recovery from discrete blindsource data
This paper is concerned with the inverse problem of recovering the unkno...
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Revisit to the Inverse Exponential Radon Transform
This revisit gives a survey on the analytical methods for the inverse ex...
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Application of HilbertHuang decomposition to reduce noise and characterize for NMR FID signal of proton precession magnetometer
The parameters in a nuclear magnetic resonance (NMR) free induction decay (FID) signal contain information that is useful in magnetic field measurement, magnetic resonance sounding (MRS) and other related applications. A real time sampled FID signal is well modeled as a finite mixture of exponential sequences plus noise. We propose to use the HilbertHuang Transform (HHT) for noise reduction and characterization, where the generalized HilbertHuang represents a way to decompose a signal into socalled intrinsic mode function (IMF) along with a trend, and obtain instantaneous frequency data. Moreover, the HHT for an FID signal's feature analysis is applied for the first time. First, acquiring the actual untuned FID signal by a developed prototype of proton magnetometer, and then the empirical mode decomposition (EMD) is performed to decompose the noise and original FID. Finally, the HHT is applied to the obtained IMFs to extract the Hilbert energy spectrum, to indicate the energy distribution of the signal on the frequency axis. By theory analysis and the testing of an actual FID signal, the results show that, compared with general noise reduction methods such as auto correlation and singular value decomposition (SVD), combined with the proposed method can further suppress the interfered signals effectively, and can obtain different components of FID signal, which can use to identify the magnetic anomaly, the existence of groundwater etc. This is a very important property since it can be exploited to separate the FID signal from noise and to estimate exponential sequence parameters of FID signal.
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