Full-Waveform Inversion With Low-frequency Extrapolation Based on Sparse Deconvolution for Ultrasound Computed Tomography

Objective: In ultrasound computed tomography (USCT), full-waveform inversion (FWI) is a promising algorithm for high-resolution sound-speed reconstruction. When implementing FWI in practical imaging systems, insufficient high-quality, low-frequency information often leads to cycle skipping, which subsequently degrades convergence and accuracy. To address this problem, this paper proposes a modified FWI algorithm. Methods: Our approach incorporated low-frequency extrapolation for seismic imaging applications, capitalizing on the inherent sparsity of time-domain impulse response functions. Through a deconvolution-based framework, we enabled robust impulse response function estimation that facilitated the spectral extension of band-limited measurements. The extrapolated low-frequency components, while representing an approximate recovery rather than exact reconstruction of unmeasured frequencies, demonstrated sufficient fidelity for practical implementation in multi-frequency inversion workflows. Results: Numerical and experimental studies have demonstrated the efficacy of extrapolated low-frequency components in mitigating cycle-skipping artifacts. Compared with conventional low-pass filtering, the proposed method reduced the sound-speed reconstruction root mean square error from 34.47 m/s to 6.47 m/s. Phantom experiments confirmed the robustness of our method, demonstrating root mean square error reduction from 16.57 m/s (standard filtering) to 5.98 m/s (our method). Conclusion: This work relaxes the restriction of FWI in transducer frequency, potentially making FWI more compatible with high-frequency imaging modalities.