Regularized Dual Averaging Image Reconstruction for Full-Wave Ultrasound Computed Tomography

Abstract

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.

Efficient Segmentation of a Breast in B-Mode Ultrasound Tomography Using Three-Dimensional GrabCut (GC3D)

“…Besides aforementioned challenges, one probable reason is that UST images are not publicly available, since UST imaging is an emerging modality. In such a situation, the major progress of UST image analysis is made by Delphinus Medical Technologies, Inc. [ 68 ] and the team from Karlsruhe Institute of Technology [ 69 ]. The manual segmentation of UST images has been currently preferred, particularly because the imaging system is being upgraded.…”

Zone-Shrinking Fresnel Zone Travel-Time Tomography for Sound Speed Reconstruction in Breast USCT

“…The reflected signals are used to generate the reflection image, also known as the B-mode image of the hand-held ultrasound, while the transmitted signals are utilized to reconstruct the sound speed (SS) image and attenuation image [ 5 , 6 , 7 , 8 ]. The SS image and attenuation image can provide quantitative information [ 9 , 10 ] for diagnosis, e.g., a breast tumor normally has higher SS and attenuation coefficient than normal tissues [ 11 , 12 , 13 , 14 ]. One commonly used SS image reconstruction method is travel-time tomography [ 14 , 15 , 16 , 17 ] that adopts the information of travel time.…”

“…One commonly used SS image reconstruction method is travel-time tomography [ 14 , 15 , 16 , 17 ] that adopts the information of travel time. Compared to waveform tomography [ 8 , 12 , 13 ] that adopts the information of waveform, travel-time tomography is more computationally efficient and more stable. Raypath travel-time tomography (RTT) assumes the wave propagates through a raypath based on the approximation of infinitely high wave frequency, which is sensitive to the noise in the detected travel time.…”

A Novel Dictionary-Based Image Reconstruction for Photoacoustic Computed Tomography

“…Several reconstruction algorithms have been designed for PACT, where a circular or linear array has been used for data acquisition [17][18][19]. Back-Projection (BP) and its derivations e.g., filtered back projection (FBP), could be considered as the most eminent PACT reconstruction algorithm due to their simple implementation [20].…”