KEYWORDS: Breast imaging, Ultrasound tomography, Ultrasonography, Data modeling, Breast, Image filtering, Wave propagation, Data acquisition, Transducers, Signal attenuation, Image quality
Conventional ultrasonography reconstruction techniques, such as B-mode, are based on a simple wave propagation model derived from a high frequency approximation. Therefore, to minimize model mismatch, the central frequency of the input pulse is typically chosen between 3 and 15 megahertz. Despite the increase in theoretical resolution, operating at higher frequencies comes at the cost of lower signal-to-noise ratio. This ultimately degrades the image contrast and overall quality at higher imaging depths. To address this issue, we investigate a reflection imaging technique, known as reverse time migration, which uses a more accurate propagation model for reconstruction. We present preliminary simulation results as well as physical phantom image reconstructions obtained using data acquired with a breast imaging ultrasound tomography prototype. The original reconstructions are filtered to remove low-wavenumber artifacts that arise due to the inclusion of the direct arrivals. We demonstrate the advantage of using an accurate sound speed model in the reverse time migration process. We also explain how the increase in computational complexity can be mitigated using a frequency domain approach and a parallel computing platform.
Waveform tomography results are presented from 800 kHz ultrasound transmission scans of a breast phantom, and from an in vivo ultrasound breast scan: significant improvements are demonstrated in resolution over time-of-flight reconstructions. Quantitative reconstructions of both sound-speed and inelastic attenuation are recovered. The data were acquired in the Computed Ultrasound Risk Evaluation (CURE) system, comprising a 20 cm diameter solid-state ultrasound ring array with 256 active, non-beamforming transducers.
Waveform tomography is capable of resolving variations in acoustic properties at sub-wavelength scales. This was verified through comparison of the breast phantom reconstructions with x-ray CT results: the final images resolve variations in sound speed with a spatial resolution close to 2 mm.
Waveform tomography overcomes the resolution limit of time-of-flight methods caused by finite frequency (diffraction) effects. The method is a combination of time-of-flight tomography, and 2-D acoustic waveform inversion of the transmission arrivals in ultrasonic data. For selected frequency components of the waveforms, a finite-difference simulation of the visco-acoustic wave equation is used to compute synthetic data in the current model, and the data residuals are formed by subtraction. The residuals are used in an iterative, gradient-based scheme to update the sound-speed and attenuation model to produce a reduced misfit to the data. Computational efficiency is achieved through the use of time-reversal of the data residuals to construct the model updates. Lower frequencies are used first, to establish the long wavelength components of the image, and higher frequencies are introduced later to provide increased resolution.
We approach the seismic inverse problem by forward modelling through finite differences in the frequency domain. We simulate a 3D wave equation, but we reduce the problem to a superposition of 2D problems by a wavenumber transformation in the out-of-plane direction. This combined frequency-wavenumber formulation is utilized in a convergent iterative inversion algorithm suitable for application to real data without the need for ad-hoc preprocessing of the seismic amplitudes. Because our algorithm operates in the frequency domain, it is straightforward to solve for a complex velocity parameter, in order to invert for inelastic attenuation. We invert single frequency components of the wavefield data at a time. Where the data are wide band it is often helpful to initiate the procedure with a low frequency, and then to use a high frequency to obtain an optimal resolution. Because the source behavior is rarely known in practice we include this parameter in our inversions. Our tests with synthetic data encourage us to answer the question posed in the title of this paper in the affirmative.
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