## 5 Discussion  
In this study, we investigated a method for PA bone imaging through deep learning post-processing. In traditional PA imaging, Fourier-domain and time-domain algorithms are proposed for initial pressure reconstruction [82; 83; 84; 85]. Strict boundary conditions and the assumption of a constant SOS limit their applications in bone imaging [40]. In addition, most of the bone samples consist of cortical and trabecular bones. Considering the complex propagation of the PA signal in the cortical bone and trabecular bone, the PA signal of the cortical bone is difficult to be distinguished directly from the PA signal of trabecular bone. Therefore, in the PA imaging of bone, the complex propagation modes in cortical and trabecular bone will lead to PA images with low resolution if we use the traditional reconstruction method of PA imaging. Inspired by the performance boost of CNNs in medical imaging (i.e., low-dose CT [86] and magnetic resonance imaging (MRI) acceleration [87]), we adopted the method through combining CNN and direct PA reconstruction algorithms. As the existing PA imaging technology is unable to  
Figure 7: Wilcoxon test on (**a**) PSNR and (**b**) SSIM of four methods for test set. The mean value of each data is represented by the height of the bar. The error bar indicates the range of data. provide high-resolution reconstructed images for bone, binarized micro-CT images are utilized as labels. The TR method was employed to produce low-quality PA images as the input of CNN, and was implemented as a comparison. Although model-based approaches have been reported to restore the initial pressure of PA source more accurately, they are at the cost of computational time [65]. Results prove that the proposed method successfully removes artifacts and partly corrects calculation errors, and outputs PA images closed to original micro-CT scans, with an inner micro-structure well restored. This improved result illustrates the promising future of PA bone imaging, where bone micro-structure can be presented without the suffering of radiation from micro-CT. Besides the performance boost, it seems that the AB-U-Net effect of different bone samples changes. As seen in Figure 4, the reconstruction of sample 3 is much better than that of sample 2, as PSNR is 19.46 dB versus 14.10 dB and SSIM is 0.92 versus 0.79. Table 1 also reveals a fluctuation in reconstruction quality, either of TR or AB-U-Net. In order to explore what causes the fluctuations, main parameters of bone properties were calculated for bone samples from test set were using the CT analyzer software suite (CTAn, version1.14.4.1, Skyscan, Antwerp, Belgium). Result suggests that the structure model index (SMI) of bone samples has a direct influence on the reconstruction results. The SMI value is an important indicator for the trabecular micro-structure, describing the structure model of trabecular bones (0 for an ideal plate structure and 3 for an ideal cylindrical rod structure) [88]. Figure 8 showed the relationship between SMI and PSNR of PA reconstructed images by TR (Figure 8a) and AB-U-Net (Figure 8b). The PSNR of PA images by two methods yields significantly negative correlations with SMI (R\({}^{2}\) = 0.55, \(p\) < 0.001 and R\({}^{2}\) = 0.34, \(p\) < 0.001). The performance of reconstruction improved as the SMI of cancellous bone samples decreased. Bones with smaller SMI mean that its structure is a more regular plate-like, while bones with bigger SMI means relatively complicated rod-like trabecula. Trabecular micro-structure complexity increases the difficulty of reconstruction tasks. On the other hand, for AB-U-Net, its performance is related to the original TR reconstruction. The accuracy of feature recognition and the following restoration of CNN is also decreased in the more complex bone micro-structure. However, in comparison to Figure 8a,b, the correlation between AB-U-Net method and SMI decreases, indicating a mitigation of interference from trabecular micro-structure complexity.