Research Of Variable Density Frequency Full Wave Inversion And Application On Ultrasound Bone Quantitative Measure

Since Full Waveform Inversion(FWI)was proposed in the 1970 s,this inversion imaging algorithm for obtaining high-precision of underground structures has attracted extensive attention of researchers.Now full waveform inversion has been applied to other fields besides geological and mineral exploration,such as concrete engineering fracture detection,medical imaging and so on.Based on the application of full waveform inversion in bone mineral density measurement in medical field,this paper has carried out corresponding research.Because full waveform inversion of frequency domain has the advantage of high computational efficiency compared with time domain,considering the instantaneity of medical field,this paper chooses full waveform inversion of frequency domain as the foothold and extends it to bone quantitative measurement.Traditional full waveform inversion is of constant density,that is,only velocity parameters are inverted.Quantitative bone measurement needs to obtain the speed of sound wave propagation in bone and bone density,so when it is applied to quantitative bone measurement,this paper explores the full waveform inversion of variable density.In order to meet the requirement of bone mineral density measurement,the velocity and density parameters of the target are inverted simultaneously.The forward difference forms of variable density,including the difference forms with PML perfectly matched layer,the gradient forms and Hessian forms of velocity and density parameters at this time are studied.The structure of bone(surrounded by soft tissues which are similar to water,and in the middle are bones)leads to the difference of sound wave velocity and medium density.The initial model used in inversion is relatively simple,which results in the big difference between the initial model and the target model,and the serious cycle jump phenomenon,which makes the inversion easy to fall into local minima.In order to solve this problem,this paper introduces the laplace-fourier transform for inversion,which reduces the dependence on the initial model and enormously make the inversion effect better.Full waveform inversion in bone quantitative measurement is quite different from traditional geological prospecting,including:(1)the grid scale of bone quantitative measurement is smaller(millimeters),while the grid of geological prospecting is larger(tens of meters).(2)The frequency of seismic source is different.Because of its small scale,bone quantification needs to adopt higher frequency(hundreds of KHZ),and the geological exploration has more smaller frequency on source.Higher frequencies and smaller mesh sizes lead to more severe boundary reflection and nonlinearity.In this paper,a lot of exploratory experiments have been done to obtain the appropriate attenuation coefficient and the Hessian matrix equilibrium factor coefficient at this time.Because of the coupling effect between velocity and density in full waveform inversion,it is difficult to obtain density parameters because of the inversion defect of density parameter itself(different diffraction sensitivity at different angles).In this paper,we adopt the strategy of joint velocity-density inversion,i.e.first,we carry out a joint velocity-density inversion,and then use the obtained results to carry out a round of density inversion.Density results and velocity results of the previous round are used as initial models for joint inversion,and finally more accurate inversion results are obtained.Finally,the accurate density parameters and velocity parameters of common human bone structures are obtained,with an error of less than 5%.It shows that it is meaningful to introduce variable density full waveform inversion into bone quantitative measurement in this paper.