# Image Human Thorax Using Ultrasound Traveltime Tomography with Supervised Descent Method
## 1 Introduction  
Ultrasound imaging is widely used in industrial and biomedical imaging. Industrial imaging is important in nondestructive evaluation (NDE) [1]. It can be used to evaluate the health of material [2; 3; 4; 5]. The information of liquid flow can also be obtained by ultrasound imaging [6; 7; 8]. In the medical field, ultrasound imaging is widely used for its low-cost, portability, radiationless, and real-time compared with other imaging methods, such as computed tomography (CT) and magnetic resonance imaging (MRI). Ultrasound is applied to imaging heart [9; 10; 11], liver [12; 13], brain [14; 15; 16] and many other human parts [17]. In most cases, ultrasound imaging is realized by transmitting ultrasound at megahertz into the human body and analyzing the reflected signal. However, this workflow is hard to implement in thorax imaging, because complex reflection and refraction occur at the lung-pleura interface and among the millions of alveoli inside the lungs, resulting in both chaotic and low-energy reflected signal [18]. In addition, the high frequency will cause severe attenuation, resulting in the reflected signal's low signal-to-noise ratio (SNR). Current thorax imaging methods include X-ray [19], CT [20], MRI [21], and electrical impedance tomography (EIT) [22]. Microwave thorax imaging is still in the research stage [23]. These methods all have limitations. The radiation from CT and X-rays is harmful to human health. The equipment of MRI is not portable and its imaging quality is not that good because of the air in the lung. The resolution of EIT and microwave imaging is relatively low. Though the reflected signal can hardly be used for thorax imaging, it contains information about the thorax state. B-lines are suggested to originate as ring-down artifacts fromirregularities at the lung-pleura interface, which contains information inside the thorax and correlates with a variety of respiratory diseases [24]. However, the results obtained from B-lines remain qualitative, subjective, and suboptimal [25]. In addition, information in the frequency domain can be used to diagnose pulmonary fibrosis quantitatively [25]. Ultrasound can also be used to monitor the states of the respiratory system, see [26; 27; 28]. In addition to reflected signal, transmission signal can be applied to thorax examination. Transmission signal is the signal that propagates through the human thorax. Acoustic wave can permeate human thorax as long as the frequency is low enough. According to [PERSON] et al. [29], the propagation of acoustic wave in human thorax shows three distinct bands according to frequency. Sound of frequency around 1 kHz can propagate in human thorax at velocity of 30-50 m/s. At this band, the thorax model is established and verified by simulations and experiments, see [30; 31]. The feasibility of diagnosing pulmonary diseases using sound at this band is also researched, see [32; 33]. Sound of frequency between 1 and 10 kHz is hard to permeate thorax. Ultrasound with frequency between 10 kHz and 750 kHz can permeate human thorax at velocity of about 1500 m/s. An ultrasound at this band permits monitoring of the human respiratory system. The transmission ultrasound signal can be analyzed directly for diagnosing lung diseases, see [34; 35]. In addition, the transmission ultrasound signal can be used to conduct traveltime tomography. This method is successfully implemented on breast imaging, see [36; 37]. So far, to the best knowledge of the authors, traveltime tomography for thorax has not been well studied. Ultrasound traveltime tomography reconstructs the acoustic velocity distribution from the measured time of the signal traveling from transmitter to receiver. This method is widely used in geophysics. It is robust at low SNR situations [38; 39] and can mitigate the challenge aroused by the complexity of ultrasound propagation in complicated media [40; 41]. The acoustic velocity is sensitive to the contents of gas, liquid, and their distribution, because their acoustic velocity differs a lot.