Numerical Study of Square Border Ultrasonic Transducer Element Arrays for Breast Imaging in Ultrasound Computed Tomography with Waveform Inversion Method

Ultrasound computed tomography (USCT) is a promising approach for early breast cancer screening. Existing studies that estimate breast images using Waveform inversion (WI) methods utilize a Circular ultrasonic transducer element array (CUTA) to collect the measurement data. However, very accurate transducer element positioning and directivity are required for signal calibration in the hardware system of these studies, thereby causing difficulties in hardware manufacturing. The purpose of this study is to estimate high-resolution USCT images using a WI method with a Square border ultrasonic transducer element array (SUTA), which reduces the difficulty of hardware manufacturing and creates accurate correspondence between the continuous and discrete forms of the transducer element positions. Therefore, in this study, an SUTA is adopted to collect the measurement data of breast imaging using the WI method. A penalized least-squares optimization problem is constructed to obtain the numerical solution of a sound speed distribution. Computer simulations are conducted to compare images reconstructed from the measurement data that are collected using an SUTA and a CUTA. The performance is evaluated using a numerical breast phantom. Results suggest that the biases of the images reconstructed are less than 1% with the evenly distributed SUTA and 1% with the CUTA, under a noise condition.