Deep-learning-based ultrasound sound-speed tomography reconstruction with Tikhonov pseudo-inverse priori Journal Article


Authors: Qu, X.; Ren, C.; Yan, G.; Zheng, D.; Tang, W.; Wang, S.; Lin, H.; Zhang, J.; Jiang, J.
Article Title: Deep-learning-based ultrasound sound-speed tomography reconstruction with Tikhonov pseudo-inverse priori
Abstract: Ultrasound sound-speed tomography (USST) is a promising technology for breast imaging and breast cancer detection. Its reconstruction is a complex non-linear mapping from the projection data to the sound-speed image (SSI). The traditional reconstruction methods include mainly the ray-based methods and the waveform-based methods. The ray-based methods with linear approximation have low computational cost but low reconstruction quality; the full wave–based methods with the complex non-linear model have high quality but high cost. To achieve both high quality and low cost, we introduced traditional linear approximation as prior knowledge into a deep neural network and treated the complex non-linear mapping of USST reconstruction as a combination of linear mapping and non-linear mapping. In the proposed method, the linear mapping was seamlessly implemented with a fully connected layer and initialized using the Tikhonov pseudo-inverse matrix. The non-linear mapping was implemented using a U-shape Net (U-Net). Furthermore, we proposed the Tikhonov U-shape net (TU-Net), in which the linear mapping was done before the non-linear mapping, and the U-shape Tikhonov net (UT-Net), in which the non-linear mapping was done before the linear mapping. Moreover, we conducted simulations and experiments for evaluation. In the numerical simulation, the root-mean-squared error was 6.49 and 4.29 m/s for the UT-Net and TU-Net, the peak signal-to-noise ratio was 49.01 and 52.90 dB, the structural similarity was 0.9436 and 0.9761 and the reconstruction time was 10.8 and 11.3 ms, respectively. In this study, the SSIs obtained with the proposed methods exhibited high sound-speed accuracy. Both the UT-Net and the TU-Net achieved high quality and low computational cost. © 2022 World Federation for Ultrasound in Medicine & Biology
Keywords: controlled study; signal noise ratio; tomography, x-ray computed; algorithms; ultrasound; simulation; algorithm; medical imaging; tomography; computer simulation; image processing, computer-assisted; image processing; image reconstruction; velocity; image segmentation; ultrasonics; signal to noise ratio; inverse problems; speed; mapping; complex networks; signal-to-noise ratio; human; article; mean square error; x-ray computed tomography; deep learning; deep neural networks; deep neural network; u-net; ultrasonic velocity measurement; sound-speed tomographies; ultrasound sound-speed tomography; tikhonov pseudo-inverse; linear mapping; nonlinear mappings; pseudo-inverses; tikhonov; u shape; u-shape net; root mean squared error
Journal Title: Ultrasound in Medicine and Biology
Volume: 48
Issue: 10
ISSN: 0301-5629
Publisher: Elsevier Inc.  
Date Published: 2022-10-01
Start Page: 2079
End Page: 2094
Language: English
DOI: 10.1016/j.ultrasmedbio.2022.05.033
PUBMED: 35922265
PROVIDER: scopus
DOI/URL:
Notes: Article -- Export Date: 3 October 2022 -- Source: Scopus
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  1. Jue Jiang
    50 Jiang