Full waveform inversion using frequency shift envelope-based global correlation norm for ultrasound computed tomography

Many studies have been carried out on ultrasound computed tomography (USCT) for its ability to offer quantitative measurements of tissue sound speed. Full waveform inversion (FWI) is a technique for reconstructing high-resolution sound speed images by iteratively minimizing the difference between the observed ultrasound data and the synthetic data based on the waveform equation. However, FWI suffers from cycle-skipping, which usually causes FWI convergence at a local minimum. Cycle-skipping occurs when the phase difference between the observed data and the synthetic data exceeds half a cycle. The simplest way to avoid cycle-skipping is to use low-frequency information for reconstruction. Nevertheless, in imaging systems, the response bandwidth of the probe is limited, and reliable low-frequency information often exceeds the response band. Therefore, it is a challenge to perform FWI imaging and avoid cycle-skipping problems without low-frequency information. In this paper, we propose a frequency shift envelope-based global correlation norm (FSEGCN), where an artificial source wavelet with a lower frequency is adopted to calculate synthetic data. FSEGCN compared with FWI, envelope inversion (EI), global correlation norm (GCN), envelope-based global correlation norm (EGCN) through concentric circle phantom without low-frequency information. The experimental results demonstrated the capability of the proposed method to recover the sound speed close to the exact model in the absence of low-frequency information, whereas FWI, EI, GCN, and EGCN cannot. Experiments on phantoms of the human head and calf show that artificial source wavelets can reduce image artifacts and enhance reconstruction robustness, when original low-frequency information is absent.