# Quantitative Reconstruction of Absorption Coefficients for Photoacoustic Tomography
## 3 Numerical Simulation
Here, we select 3 A-lines to visualize the iteration recovery of the absorption coefficient results. After 10 iterations, the value of the absorption coefficient was recovered quantitatively, and the accuracy reached 92.00% to 99.50%. Figure 4 excellently shows that the iterative method proposed in this paper quantitatively recovered the true absorption distribution for the complex tissue model. The results show that the proposed algorithm can effectively reduce or even eliminate the influence of light fluence on the measured absorption distribution. Figure 5 corresponds to the three A-lines (white dotted line) selected in Figure 4a, three profiles visualize the performance of the proposed quantitative recovery absorption coefficient method, which were the results of three iterations of 1, 5 and 10, respectively corresponding to the absorption distribution in Figure 4. Figure 5 shows that with the increase of iteration times, the absorption coefficient more obviously converges to the ground truth, which demonstrates the feasibility of the iterative algorithm proposed in this paper. Figure 4: Three iterations were selected to visualize the results of the recovered absorption coefficient distribution, which were the results of iterations 1, 5 and 10, respectively: **(a)** the No.1 iteration recovered result; **(b)** the No.5 iteration recovered result; **(c)** the normalized No.10 iteration recovered result. The axes z and x (left and bottom) illustrate the spatial scale, the unit is cm, whereas the color scale (right) represents the absorption coefficient value, the unit is cm\({}^{-1}\), the white dotted line represents the three A-lines selected. Figure 3: **(a)** The z-x section diagram of the tissue model, different objects are distinguished by different colors and shapes; **(b)** Pure background tissue fluence distribution. The axes z and x (left and bottom) illustrate the spatial scale, the unit is cm, whereas the color scale (right) unit is mJ/cm\({}^{2}\). Absorption energy distribution before iteration recovery and absorption coefficient distribution after iterative recovery are shown on a 3-D mesh in Figure 6a,b, respectively. As can be seen from the figure, before the quantitative recovery, it was hard to obtain the absorption distribution in deep tissue according to the graph of energy absorption deposition before the quantitative recovery. In contrast, the obtained absorption coefficient distribution was greatly improved after applying the quantitative iterative algorithm. The quantitative recovery algorithm has noticeable effect and iterative convergence, as shown in Figure 6. In addition, the results are listed in Table 2, including the raw data before and after the algorithm. By comparing the difference of the simulation results between the restored value and the real value, the proposed algorithm can obtain remarkably accurate quantitative absorption coefficients. Furthermore, we employ SSIM, RMSE, and PSNR as evaluation indicators to verify the reliability of the algorithm by comparing changes in various indicators before and after recovery [40; 41; 42]. In Table 2, we use SSIM as the local information evaluation index. SSIM1 represents the local corresponding area calculation result between the original data and the actual value before reconstruction, and SSIM2 represents the local corresponding area calculation result between the restored data and the actual value after reconstruction. The comparison proves that the proposed method makes the SSIM value totally enhanced. In particular, the degree of improvement in target2, target3- layer2-4, and target4, target5 in the deeper position is obviously advanced. Figure 5: Three A-line profiles were selected to visualize the performance of the proposed quantitative recovery absorption coefficient method, which were the results of three iterations of 1, 5 and 10, respectively corresponding to the absorption distribution in Figure 4. Each row represents the same A-line, each column represents the result of the same iteration.