Waveform inversion with source encoding for breast sound speed reconstruction in ultrasound computed tomography

Abstract

Ultrasound computed tomography (USCT) holds great promise for improving the detection and management of breast cancer. Because they are based on the acoustic wave equation, waveform inversion-based reconstruction methods can produce images that possess improved spatial resolution properties over those produced by ray-based methods. However, waveform inversion methods are computationally demanding and have not been applied widely in USCT breast imaging. In this work, source encoding concepts are employed to develop an accelerated USCT reconstruction method that circumvents the large computational burden of conventional waveform inversion methods. This method, referred to as the waveform inversion with source encoding (WISE) method, encodes the measurement data using a random encoding vector and determines an estimate of the sound speed distribution by solving a stochastic optimization problem by use of a stochastic gradient descent algorithm. Both computer-simulation and experimental phantom studies are conducted to demonstrate the use of the WISE method. The results suggest that the WISE method maintains the high spatial resolution of waveform inversion methods while significantly reducing the computational burden.

3-D Nonlinear Acoustic Inverse Scattering: Algorithm and Quantitative Results

“…This results in a typical scan time of approximately 7 minutes per breast and approximately 35 minutes to reconstruct. Remarkably, even other 2D model inversions that incorporate diffraction (beyond the Born/Rytov approximation) and refraction, can take reportedly similar reconstruction times[4],[3]. …”

“…There has been extensive development of the 2D quantitative inverse scattering method over the past several decades[3],[4],[5],[6], as well as 3D methods that utilize methods of inversion that do not account for diffraction[7]. …”

Generation of anatomically realistic numerical phantoms for photoacoustic and ultrasonic breast imaging

“…Furthermore, the development and optimization of advanced reconstruction algorithms also require simulation studies. To date, numerical phantoms employed in many PACT and USCT simulation studies are either two-dimensional (2-D) 12,13 or three-dimensional (3-D) volumes comprised of only simple objects. 12,[14][15][16][17] These oversimplified phantoms do not reflect the complex anatomical structures within the breast, thus limiting the value of simulation studies in guiding realworld system design and algorithm development.…”

Improved misfit function for attenuation and speed reconstruction in ultrasound computed tomography

“…The basis of FWI methods were laid out by Tarantola 2 in the field of seismology, where he introduced the formalism of the minimization of the least squares functional comprised by the waveform differences between observed and simulated waveforms by iterative gradient methods. The reconstruction of SS maps with FWI has been widely studied and it has been quite demonstrated the robustness of the method to provide high-resolution SS images [3][4][5] . Nevertheless, with the current formulations, the reconstruction of the AA maps is more challenging than the reconstruction of SS maps.…”