# A Novel Dictionary-Based Image Reconstruction for Photoacoustic Computed Tomography
## 3 Results

Table 1: Specification of the experimental setup presented in Figure 2.  
Figure 3: Low-cost photoacoustic computed tomography (LC-PACT) system diagram comprised of an Nd:YAG 30 Hz Spectra Physics laser, an optical parametric oscillator (OPO), a circular ring, a DC supply for the motor driver, an NI DAQ, an NI trigger, a servo motor, a motor gear, a three-axis translation stage for phantom, and a transducer-amplifier unit. to be acoustically homogeneous. It should be noted that some algorithms produce more artifacts and decrease the visibility of the details in reconstructed images. The contrast of the image concerned with the proposed method is not changed, but the amount of artifact is, leading to a better visibility. The simulation results performed on Shepp-Logan synthetic phantom with 60 view angles confirm the superiority of the proposed method to other reconstruction algorithms (see Figure 5). For evaluation of the edge preservation capability of the proposed algorithm, we used the edge preservation index (EPI) [40]. This metric indicates the edge preservation capability in horizontal and perpendicular directions, after applying filters such as the Laplacian operator on the image. The EPI values for different methods/angle views are reported in Figure 6a. Each experiment was repeated 10 times. The values of deviation are shown by error bars in this figure. The value of EPI changes from 0 to 1. A higher value suggests a better ability to preserve the edges. Statistical analysis shows that, for a number of view angles lower than 45, the proposed algorithm outperforms other methods. This indicates that, with lower data acquisition time (a lower number of angles), the proposed method provides a higher image quality, compared to other methods. In addition, Figure 6a shows that the proposed method provides better preserved edges for numbers of angles between 80 and 92. The PSNR is calculated for different methods/angle views, and the results are presented in Figure 6b. PSNR is calculated using the formula presented in [23]. To calculate the minimum square error (MSE), the result  
Figure 4: Results of reconstruction algorithms on the phantom data acquired from our PACT system. Different rows show different number of views, 30, 60, 90, and 120, and columns show different reconstruction methods, BP, sparse with basis WT, sparse with basis WT+TV, and sparse with the proposed sparsifying method. of sparse reconstruction with WT basis at the maximum possible number of views, i.e., 600, has been considered as the Gold standard image. From the quantitative assessment of the results presented in Figure 6b, it can be seen that, for all numbers of angles, the proposed method results in a higher PSNR. For instance, for 60 angles, BP, WT, WT+TV, and the proposed method lead to PSNR values of about 42.5 dB, 49.5 dB, 50.5 dB, and 54.2 dB, respectively. In other words, PSNR is improved by about 27%, 9%, and 7%, in comparison to BP, WT, and WT+TV, respectively. Considering all the quantitative evaluation, it can be concluded that our proposed algorithm works effectively with a limited number of view angles, outperforming other algorithms. We performed statistical analysis on the PSNR values using SPSS(r). At every view angle, the improvement obtained by the proposed method compared to other aforementioned methods was statistically significant (\(p\)-value \(<\) 0.001). Table 2 shows the execution time for BP, sparse reconstruction with basis WT, sparse reconstruction with bases WT+TV, and the proposed reconstruction algorithms. The proposed method provides a higher image quality at the expense of a higher processing time, compared to other algorithms. The higher processing time of the proposed algorithm is due to the fact that it should use all the information of the three used sparsifying functions in order to reconstruct a photoacoustic image with a higher image quality. In addition, the feature measurement of the proposed algorithm increases the processing time as well.