Ultrasound computed tomography (USCT) has been developed for breast tumor screening. The sound-speed modal of USCT can provide quantitative sound-speed values to help tumor diagnosis. Time-of-flight (TOF) is the critical input in sound-speed reconstruction. However, we found that the missing data problem in the detected TOF causes artifacts on the reconstructed sound-speed images, which may affect the tumor identification. In this study, to address the missing TOF data problem, we first adopted the singular value threshold (SVT) algorithm to complete the TOF matrix. The threshold value in SVT is difficult to determine, so we proposed a selection strategy, that is, to enumerate the threshold values as the multiples of the maximum singular value of the incomplete matrix and then evaluate the image quality to select the proper threshold value. In the numerical breast phantom experiment, the artifacts are eliminated, and the accuracy is higher than the accuracy of the compared methods. In the in vivo experiment, we reconstructed the sound-speed image of the breast of a volunteer with invasive breast cancer, and the SVT algorithm improved the image sharpness. The completion of DTOF based on SVT gives better accuracy than the compared methods, but too large a threshold value decreases the accuracy. In the future, the selection method of the threshold value needs further research, and more USCT cases should be included in the experiments.
Citation: Xiaoyue Fang, Ran Zhou, Haitao Gan, Mingyue Ding, Ming Yuchi. Time-of-flight completion in ultrasound computed tomography based on the singular value threshold algorithm[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 10160-10175. doi: 10.3934/mbe.2022476
Ultrasound computed tomography (USCT) has been developed for breast tumor screening. The sound-speed modal of USCT can provide quantitative sound-speed values to help tumor diagnosis. Time-of-flight (TOF) is the critical input in sound-speed reconstruction. However, we found that the missing data problem in the detected TOF causes artifacts on the reconstructed sound-speed images, which may affect the tumor identification. In this study, to address the missing TOF data problem, we first adopted the singular value threshold (SVT) algorithm to complete the TOF matrix. The threshold value in SVT is difficult to determine, so we proposed a selection strategy, that is, to enumerate the threshold values as the multiples of the maximum singular value of the incomplete matrix and then evaluate the image quality to select the proper threshold value. In the numerical breast phantom experiment, the artifacts are eliminated, and the accuracy is higher than the accuracy of the compared methods. In the in vivo experiment, we reconstructed the sound-speed image of the breast of a volunteer with invasive breast cancer, and the SVT algorithm improved the image sharpness. The completion of DTOF based on SVT gives better accuracy than the compared methods, but too large a threshold value decreases the accuracy. In the future, the selection method of the threshold value needs further research, and more USCT cases should be included in the experiments.
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Xiaoyue Fang, Ran Zhou, Haitao Gan, Mingyue Ding, Ming Yuchi. Time-of-flight completion in ultrasound computed tomography based on the singular value threshold algorithm[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 10160-10175. doi: 10.3934/mbe.2022476
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