Application of full waveform inversion algorithm in Laplace–Fourier domain for high-contrast ultrasonic bone quantitative imaging

Full waveform inversion (FWI) has been widely applied for the reconstruction of underground medium parameters in seismic communities and has made a great success. It is also a promising way to image hard tissues such as bones by ultrasonic FWI algorithm. However, the ultrasonic FWI methods for bone parameters imaging reported in literature so far are limited to the time domain and/or Fourier domain, and can only achieve quantitative imaging with acoustic velocity of bone less than 3000 m/s. Because the acoustic velocity of actual cortical bones can be as high as 4200 m/s, it is still a challenge for FWI to achieve higher parameter contrast bone imaging.Here, we proposed an ultrasonic FWI algorithm in Laplace-Fourier domain (LFDFWI) for high-contrast bone quantitative imaging. Compared to Time domain and Fourier domain, the LFDFWI algorithm is more appropriate for dealing with the presence of high contrast between bone tissues, reducing the possibility of inversion falling into a local minimum, and obtaining better inversion results. We adapted the seismic FWI algorithm to make it suitable for high-frequency ultrasonic sources and small-sized bone parameter imaging.We conducted a series of bone models to evaluate the effectiveness of the proposed algorithm, including four kinds of bone model derived from micro computed tomography (Micro-CT) image of rat. We evaluated the experimental results based on visual analysis, error analysis and structural similarity (SSIM). The numerical simulation results showed that, when acoustic approximation is used, the proposed method can obtain accurate high-contrast images of the velocity and density parameters of bone structure, the mean relative error (MRE) in the region of interest (ROI) were all less than 2%, and the SSIM is up to 98%; when the viscoelastic approximation is used, this method can also obtain the desired high-contrast bone parameter distribution, with MRE less than 4% and SSIM higher than 74%, both of which are better than FDFWI in Fourier domain (FDFWI).The results demonstrated that the proposed FWI algorithm can obtain high resolution bone parameter models close to the Micro-CT image, which proves its clinical application potential.