Index signal de-noising method

Abstract

An index signal de-noising method relates to a signal de-noising method, and is easy to operate and exhibits excellent effects. The method includes the step of modeling index signals: filling the index signals in a Hankel matrix according to a set sequence, establishing a Hankel matrix low-rank reconstruction model, and solving the model to de-noise the signals. The method is fast in speed and high in precision, and parameters can be set on the basis of measured noise variances. During practical applications, the optimized model can be adopted to de-noise signals such as time-domain signals of nuclear magnetic resonance wave spectrums and signals that accord with the index characteristics, so the sampling time is reduced and the spectra resolution is increased. The index signal de-noising method, provided by the invention, exhibits excellent effects and is easy to operate.

Description

technical field [0001] The invention relates to a signal denoising method, in particular to an exponential signal denoising method. Background technique [0002] In many practical applications, such as nuclear magnetic resonance spectroscopy and radar target positioning, the target signal we are interested in can be modeled as a linear superposition of several spectral peaks in the frequency domain (relative to the time domain), and the acquired time domain (relative to the frequency domain) domain) signal can be expressed as a superposition of a series of exponential functions. Due to the limitations of hardware and physical conditions, the actual sampled data is often polluted by noise, so it is impossible to distinguish some small signals. For general signals, a signal with a higher signal-to-noise ratio is usually obtained by repeated sampling: multiple signals are obtained by repeated sampling, and then the signals are superimposed and averaged. For some special signa...

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Problems solved by technology

For some special signals, such as the time domain signal of NMR spectrum, Cadzow (Y.Y.LinandL.P.Hwang,"NMRSignalEnhancementBasedonMatrixPropertyMappings,"JournalofMagneticResonance, SeriesA, vol.103, pp.109-114, 1993.) proposed a typical denoising method, but this method cannot guarantee that the obtained solution is the global optimal solution

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