  Ultrasound computed tomography (USCT) holds great promise 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 to greatly reduce image
reconstruction times. However, this method bundles the stochastic data fidelity
term with the deterministic regularization term. This limitation can be
overcome by replacing stochastic gradient descent (SGD) 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 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 method. 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.
