IEEE Trans Ultrason Ferroelectr Freq Control. 2017 May;64(5):811-825. doi: 10.1109/TUFFC.2017.2682061. Epub 2017 Mar 14.
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 has been 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 limitation can be overcome by replacing SGD with a structured optimization method, such as the regularized dual averaging method, that exploits knowledge of the composition of the cost function. In this paper, 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 nonsmooth regularization penalties to be naturally incorporated. The wave equation is solved by the 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 the use of SGD.
超声计算机断层扫描（USCT）在乳腺癌筛查中具有广阔的前景。基于波动方程反演的图像重建方法可以考虑更高阶的衍射效应，从而产生高分辨率的 USCT 图像，但计算量较大。最近，一种源编码技术与随机梯度下降（SGD）相结合，大大减少了图像重建时间。然而，该方法将随机数据保真项与确定性正则化项捆绑在一起。通过用结构优化方法（如正则化对偶平均方法）替代 SGD，可以克服这一限制，该方法利用了成本函数组成的知识。本文将对偶平均方法与源编码技术相结合，在保持源编码减少重建时间的同时，提高正则化的有效性。结果表明，每次迭代都可以分解为基于数据保真项的梯度下降步骤和对应正则化项的近端更新步骤。此外，正则化项从不显式地求导，允许自然地包含非光滑正则化惩罚项。利用时域方法求解波动方程。通过计算机模拟和实验研究验证了该方法的有效性。结果表明，对偶平均方法可以产生噪声更小、分辨率相当的图像，与使用 SGD 获得的图像相当。
