Nonlinear waveform inversion by use of the regularized dual averaging method for ultrasound computed tomography

Ultrasound computed tomography (USCT) is a promising medical imaging modality that offers several novel tissue contrasts and holds great potential for breast cancer screening. Waveform inversion-based image reconstruction methods account for higher order diffraction effects and can produce high-resolution USCT images, but are computationally demanding. Recently, a source encoding technique was combined with stochastic gradient descent (SGD) to greatly reduce image reconstruction times. However, this method bundles the stochastic data fidelity term with the deterministic regularization term. This non-optimal approach can be overcome by replacing stochastic gradient descent with a structured optimization method, such as the regularized dual averaging (RDA) method, that exploits knowledge of the composition of the cost function. In this work, the dual averaging method is combined with source encoding techniques to improve the effectiveness of regularization while maintaining the reduced reconstruction times afforded by source encoding. It is demonstrated that, for a particular choice of regularization function, each iteration can be decomposed into a gradient descent step based on the data fidelity term and a proximal update step corresponding to the regularization term. Furthermore, the regularization term is never explicitly differentiated, allowing non-smooth regularization penalties to be naturally incorporated. The wave equation is solved by use of a time-domain k-space pseudo-spectral method, implemented on general-purpose graphics processing units. The effectiveness of this approach is demonstrated through computer simulation and experimental studies. The results suggest that the dual averaging method can produce images with less noise and comparable resolution to those obtained by use of stochastic gradient descent.