Time Versus Frequency Domain full Waveform Inversion for Ultrasound Imaging

With full waveform inversion (FWI) all available information enclosed in the recorded wavefield - including multiple scattering, dispersion, and diffraction - is used to obtain accurate images showing quantitative information of the tissue parameters. These non-linear inversion methods are implemented either in the time or in the frequency domain. Unfortunately, selecting which implementation should be used for a specific problem is not trivial. To ease the selection process, we compare the performance of one time-domain inversion (TDI) and one frequency-domain inversion (FDI) - also known as Contrast Source Inversion - to provide insights into the strengths and weaknesses of each FWI method. In this contribution, we investigate the effect of the (i) bandwidth, (ii) problem complexity, (iii) number of sources and receivers, and (iv) initial speed-of-sound model on the performance of each FWI method by comparing the resulting reconstructions. Both methods are tested for the same configuration: a 2-D tomographic scan of a cancerous breast model. To avoid an inverse crime, TDI is tested on synthetic data obtained using a frequency-domain forward solver and CSI on data from a time-domain forward solver.