Ultrasound reflection imaging is a promising imaging modality for detecting small, early-stage breast cancers. Properly accounting for ultrasound scattering from heterogeneities within the breast is essential for high-resolution and high-quality ultrasound breast imaging. We develop a globally optimized Fourier finite-difference method for ultrasound reflectivity image reconstruction. It utilizes an optimized solution of acoustic-wave equation and a heterogeneous sound-speed distribution of the breast obtained from tomography to reconstruct ultrasound reflectivity images. The method contains a finite-difference term in addition to the split-step Fourier implementation, and minimizes ultrasound phase errors during wavefield inward continuation while maintaining the advantage of high computational efficiency. The accuracy analysis indicates that the optimized method is much more accurate than the split-step Fourier method. The computational efficiency of the optimized method is one to two orders of magnitude faster than time-reversal imaging using a finite-difference time-domain wave-equation scheme. Our new optimized method can accurately handle ultrasound scattering from breast heterogeneities during reflectivity image reconstruction. Our numerical imaging examples demonstrate that the optimized method has the potential to produce high-quality and high-resolution ultrasound reflectivity images in combination with a reliable ultrasound sound-speed tomography method.
Keywords: breast heterogeneities, finite difference method, Fourier method, image reconstruction, optimized, reflectivity, sound speed, ultrasound breast imaging, ultrasound scattering
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