Research On Parameter Extraction Method Of Full-wave Magnetic Resonance Sounding Signal Based On Total Least Squares

The technology of Magnetic Resonance Sounding(MRS)is a direct geophysical method of groundwater detection.Compared with other indirect measurement methods,MRS technology has the advantages of unique interpretation and quantified results.However,magnetic resonance signal is very weak,only nanofilt level,the collected signal is easy to be disturbed by the peak noise,power frequency harmonics and random noise in the environment.The extraction of characteristic parameters of magnetic resonance signal under the background of random noise has become a key problem in the application of magnetic resonance signal technology.How to extract the characteristic parameters of magnetic resonance signal submerged in random noise in subsequent data processing is an important research direction in the field of MRS denoising.Least Squares(LS)method is a way to find the optimal parameters of signal data by using the sum of Squares with minimum residuals.In the linear prediction equation,the disturbance is used to correct the noise in the constant vector.However,when there is noise in both the coefficient matrix and the constant matrix,the LS method will produce large variance.The Total Least Squares(TLS)method can solve the model parameters by considering the disturbance of the coefficient vector matrix and the constant vector matrix,which can overcome the influence of the disturbance changes on the data matrix itself.In view of the successful application experience of total least squares in digital signal processing,this paper presents a research on the parameter extraction method of full-wave magnetic resonance signal based on total least squares under the background of random noise.First,this paper on the basis of introducing the principle of magnetic resonance signal technology,instrument system,magnetic resonance signal characteristics and four characteristic parameters,analysis of the main noise affecting the magnetic resonance signal,and the basic principle of total least squares algorithm and steps are introduced in detail,through constructing linear prediction equation,performing the singular value decomposition of the augmented matrix,constructing the vandermonde matrix,and finding the general least-square solutions,the extraction of characteristic parameters of signal can be extracted from random noise well.The feasibility of applying the total least squares algorithm to magnetic resonance signal field is analyzed through formula derivation.Then,the parameter estimation experiment of periodic signal based on the total least squares algorithm was carried out.The selection of window length in the algorithm is also discussed which laid a foundation for the subsequent parameter extraction of MRS signal containing noise.Secondly,the simulation contrast least-square algorithm under random noise and total least squares algorithm respectively in different SNR,different larmor frequency,different relaxation time,different initial amplitude and different initial phase of the magnetic resonance signal parameters extraction performance at the same time,to analyze its change trend and the uncertainty.the simulation results show that: under the condition of same least-square algorithm parameters extraction error within 10%,and using total least squares algorithm parameters extraction error within 5%,verified the superiority of the proposed total least squares algorithm.Finally,In Changchun Culture Square,noise-containing signal acquisition and processing experiments were carried out to verify the magnetic resonance signal parameter extraction effect of the total least squares algorithm.The measured data are preprocessed to filter out the power frequency harmonics.then,using the general least squares algorithm for the rest of the noise signal parameter estimation,the measured data under different signal-to-noise ratio parameter extraction results show that the extract of nuclear magnetic resonance signal amplitude of the initial error are within10%.the uncertainty are within 5%.the error of the relaxation time and the uncertainty is within 5%,meeting the requirements of the subsequent inversion precision of nuclear magnetic resonance signal,further verifying the practicability of the total least squares algorithm.