An Exponential Signal Denoising Method Using Prior Information

Abstract

The invention provides an exponential signal denoising method achieved by means of prior information and relates to a denoising method for exponential signals.The prior exponential signals form a Hankel matrix according to a set sequence, the Hankel matrix is subjected to singular value decomposition, and a prior signal space and a prior singular value are obtained; then a Hankel matrix with the same size as the former Hankel matrix is established for the target exponential signals, and the matrix of the target signals is decomposed through the prior information space; after a weighted threshold is obtained from the prior singular value, a Hankel matrix of the denoised target signals is obtained from the singular value of the target exponential signals according to the weighted threshold; then the Hankel matrix of the target signals is solved, and finally the denoised signals are obtained.Through the prior information of the reference signals, the speed is high, the effect is good, and operation is easy.Denoising of a magnetic resonance spectrum can be achieved for signals with exponential features such as time domain signals of the magnetic resonance spectrum through the method, and the purposes of shortening the sampling time and increasing the signal to noise ratio of the spectrum are achieved.

Description

technical field [0001] The invention relates to an exponential signal denoising method, in particular to an exponential signal denoising method utilizing prior information. Background technique [0002] In practical applications, data is often polluted by noise, making it difficult to distinguish weak effective signals. For general signals, the method of repeated acquisition is usually used to obtain a signal with a higher signal-to-noise ratio, but this will prolong the sampling time, especially in some large-scale acquisitions, which will take too long; and for some special signals, the signal characteristics can be used Use some better denoising method. For exponential signals, such as nuclear magnetic resonance spectrum, radar carrier signal, etc., the usually collected time domain (relative frequency domain) signal can be expressed as the superposition of a series of exponential functions, and this special signal can be modeled as domain) is a linear superposition of ...

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Problems solved by technology

A typical denoising method based on this characteristic is truncated singular value decomposition (G.Golub and W.Kahan, Calculating the singular values ​​and pseudoinverse of amatrix[J], J.Soc.Ind.Appl.Math.B, 1965 ,2(2):205–224), although the denoising effect of this method is better than that of repeated acquisition, but the denoising effect is limited

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