A method and system for crosstalk-free source encoding for accelerating full waveform inversion and tomography

Background

Ultrasound tomography is a powerful imaging technique used in both medical diagnostics (such as breast cancer screening) and geophysical exploration (such as subsurface mapping). The method relies on transmitting ultrasound waves from multiple sources and recording the resulting wavefields at numerous receivers to reconstruct detailed images of internal structures. Achieving high-resolution, three-dimensional images requires modeling the full physics of wave propagation, which is computationally intensive, especially as the number of sources and receivers increases. The need for rapid, accurate, and scalable imaging solutions is growing, driven by clinical demands for real-time diagnostics and the geoscience industry’s pursuit of high-fidelity subsurface models.

Traditional approaches to ultrasound tomography and full waveform inversion (FWI) face significant challenges related to computational cost and data acquisition speed. In conventional workflows, each source must be activated separately, and the resulting wavefields are simulated or measured one at a time to avoid crosstalk—unwanted interference between signals from different sources. This sequential process means that the computational and experimental effort scales linearly with the number of sources, resulting in long acquisition times and prohibitive computational demands for large-scale 3D imaging. Attempts to accelerate the process by activating multiple sources simultaneously typically introduce crosstalk artifacts, which degrade image quality and complicate the inversion process. Furthermore, existing source encoding techniques often require complex decoding procedures and are sensitive to noise, incomplete data, and variability in source or receiver configurations, limiting their practical utility in both clinical and field settings.

Technology

This technology enables rapid and efficient ultrasound tomography by employing a crosstalk-free source encoding method, where each transducer is assigned a unique, orthogonal frequency. All sources can be activated simultaneously, and their combined signals are captured as a superposed wavefield. A processor then uses Fourier analysis to decode the individual contributions of each source, leveraging the mathematical orthogonality of the assigned frequencies. This approach allows for the computation of full waveform inversion (FWI) gradients using only two numerical simulations per iteration—one forward and one adjoint—regardless of the number of sources. The system supports both frequency-domain and time-domain implementations, can be applied to 2D or 3D imaging, and is compatible with a wide range of misfit functions, including waveform, phase, amplitude, and travel-time measurements. It is robust to noise, incomplete receiver coverage, and variable source/receiver configurations, and is implemented in open-source software frameworks for both medical and geophysical imaging.

What differentiates this solution is its ability to eliminate the traditional computational bottleneck associated with multi-source imaging. Conventional FWI methods require separate simulations for each source, leading to computational costs that scale linearly with the number of sources. By encoding each source with a unique frequency and decoding their contributions using the orthogonality of the Fourier basis, this method reduces the number of required simulations per iteration to just two, regardless of the source count. This results in dramatic speedups—often 20x to 1000x—making full-physics 3D imaging feasible on modest hardware, such as a single GPU. The technique is flexible, supporting both computational and experimental acceleration, and is validated across a range of applications from high-resolution breast imaging to seismic tomography. Its mathematical rigor, robustness to real-world imperfections, and scalability set it apart as a transformative solution for real-time or near-real-time 3D imaging in both medical and geoscientific domains.

Benefits

• Significantly accelerates full waveform inversion (FWI) by reducing required simulations per iteration to two, independent of the number of sources.
• Enables simultaneous activation of multiple ultrasound or seismic sources without crosstalk or signal interference.
• Supports high-resolution 3D imaging in medical and geophysical applications with practical runtimes on modest hardware (e.g., single GPUs).
• Robust to noise, incomplete receiver coverage, and variable source/receiver configurations.
• Compatible with a wide range of misfit functions, including waveform, phase, amplitude, double-difference, and travel-time measurements.
• Reduces experimental data acquisition time by allowing all transducers to fire simultaneously.
• Implements efficient decoding methods using Fourier orthogonality, either in frequency domain or via time-domain convolution, minimizing memory and I/O demands.
• Scalable to large-scale problems and adaptable to various wave physics models, including viscoacoustic and elastic media with attenuation and anisotropy.

Applications

• Real-time 3D breast ultrasound imaging
• Rapid seismic subsurface tomography
• Accelerated non-destructive material testing
• Industrial process monitoring with ultrasound
• Fast geophysical exploration surveys

Additional info

This methodology employs orthogonal frequency encoding to activate multiple ultrasound transducers simultaneously without signal interference. By assigning unique frequencies to each source, a processor decodes superposed wavefields using Fourier analysis. This streamlines full waveform inversion, requiring only two numerical simulations per iteration — one forward and one adjoint — regardless of source count. It enables rapid, high-resolution 3D imaging by eliminating the computational overhead associated with individual source processing.