## 3 Results and Discussions
### Training on the Entire Spectral Band  
In addition to the most sensitive spectral band, we also tested our network on the entire spectral band with the same data set as we used on the most sensitive spectral band and we assumed that using all frequency components could contribute to a smaller error since PA signal is broad-band signal. The lower spectral range of 0.5 to 10.5 MHz contains information of outlines of adipocytes in tissue samples. It shows the size of adipocyte group which consists of several adjacent adipocytes. Sizes of these adipocyte groups are relative to numbers and sizes of each individual adipocyte. Indicated by Equation (5), a lower frequency is correspondent to a larger size of adipocyte group which consists of more or larger adjacent adipocytes. Thus, the spectral bands in this range contribute to evaluation of average adipocyte size but with a larger MRE (more than 14%) as listed in Table 2. Higher frequency in spectral range of 10.5 to 24.5 MHz is correspondent to different adipocyte sizes estimated by Equation (5). A higher frequency is relative to a smaller adipocyte size. Therefore, different frequency components indicate adipocyte size distribution and combining spectral information of all frequency components may lead to a smaller error. To examine our hypothesis, our network was trained on the entire spectral band to obtain the error of combining all spectral components. Based on the normalized magnitude over a 0.05-MHz step in the range of 0.5 to 24.5 MHz, calculated when testing the network on different spectral bands, we calculated the sum of every six consecutive magnitude values and obtained the normalized magnitude over a 0.3-MHz step so that 80 input elements covered the entire spectral range of 0.5 to 24.5 MHz. Then, with normalized magnitude of the entire spectral band of 0.5 to 24.5 MHz with a 0.3-MHz step as the input and the correspondent average adipocyte size as the output, a network with the structure shown in Figure 5 was retrained 10 times. We performed the data augmentation for each retraining. The error distribution of all tested samples (330 samples) from the 10 retrainings is shown in Figure 7. As listed in Table 3, an average MAE of 394.19 \(\upmu\)m\({}^{2}\) and MRE of 9.30% was achieved, which is smaller than errors of using different spectral bands listed in Table 2. The result indicated that combining all frequency components could lead to more accurate evaluations. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Spectral Section** & **Error** & **Minimum** & **Maximum** & **Average** \\ \hline \multirow{2}{*}{Entire spectral band (0.5–24.5 MHz)} & MAE/\(\upmu\)m\({}^{2}\) & 326.76 & 455.84 & 394.19 \\  & MRE & 7.28\% & 10.94 \% & 9.30 \% \\ \hline \multirow{2}{*}{Most sensitive spectral band (12.5–16.5 MHz)} & MAE/\(\upmu\)m\({}^{2}\) & 463.61 & 609.06 & 548.37 \\  & MRE & 10.62\% & 14.90\% & 12.78\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean absolute errors (MAEs) and MREs of the test set in 10 retrainings using the most sensitive spectral band and entire band. Figure 7: Error distribution of all tested samples of 10 retrainings using the most sensitive spectral band (12.5–16.5 MHz) and the entire spectral band (0.5–24.5 MHz). (**a**) Absolute error distribution for all tested samples. Absolute errors are mainly within the range of 0 to 500 \(\upmu\)m\({}^{2}\) when training on the entire spectral band. The distribution of the relative errors is shown in (**b**). ### Training on the Entire Spectral Band  
We also compared the performance of the deep learning method with the conventional PASA method relying on linear fitting over the entire spectral band. This conventional method was used in a previous study to process the same data set from the human adipose tissue specimens [17]. With the power spectrum obtained from each tissue specimen over a spectral range of 0.5 to 24.5 MHz, a linear fit was produced which led to a quantified spectral parameter of _slope_.