**3. Results**

To evaluate the performance of the reconstruction algorithms, we made a gel phantom with imaging target inside. The phantom was made by 3% Agar powder in water. Eight straight graphite pencil leads with a 0.5 mm diameter were placed co-centered in the same plane embedded in the gel. The size of the phantom was 30 × 30 mm (Figure 2b). The phantom was imaged using a single-transducer PACT system (Figure 2a). A Quanta-Ray PRO-Series Nd:YAG laser (Spectra-Physics Inc., Santa Clara, CA, USA) pumped a VersaScan V1.7 optical parametric oscillator (OPO) (Spectra-Physics Inc., USA), generating wavelengths in the range of 398–708 nm, with a pulse width of 7 ns and a repetition rate of 30 Hz. In this experiment, the illumination wavelength was 532 nm. A large graded index plastic optical fiber with a diameter of 10 mm and a numerical aperture of 0.55 was used on the top of the ring, 5 cm away from the sample, forming an uniform illumination. A cylindrically focused ultrasound transducer, V326-SU (Olympus Inc., Center Valley, PA, USA) with the element size of 0.375 inch, central frequency of 5 MHz and the focal length of 0.625 inch was positioned on a cylindrical construct. The position of the transducer was in the same plane as the pencil leads were. The diameter of the construct was 75 mm. The cylinder was rotated using a stepper motor (Applied Motion Products Inc., Watsonville, CA, USA) with a driver controlled by LabVIEW. The transducer was smoothly rotated around the phantom with the speed of 0.0125 round/s to collect the PA signal in 360 degrees. The data acquisition is performed using our FPGA based National Instrument (NI) system. Specification of the experiment is presented in Table 1. A photograph of the PAI system is shown in Figure 3. The system was placed on a 12 ft × 4 ft optical table (New Port, Inc., Irvine, CA, USA).

**Figure 2.** (**a**) Schematic of our PACT system; (**b**) gel phantom with eight 0.5 mm pencil leads.

**Figure 3.** Low-cost photoacoustic computed tomography (LC-PACT) system diagram comprised of an Nd:YAG 30Hz 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.

**Table 1.** Specification of the experimental setup presented in Figure 2.


For image reconstruction, we used a laptop with i7 core, 2.3 GHz CPU, and 8 GB Memory. Figure 4 demonstrates a set of results of different reconstruction algorithms on the phantom data acquired by our PACT system. They are C-scan images with their dimensions annotated in the right image. The reconstructed images with BP and CS with different sparsifying methods for different numbers of views (30, 60, 90, and 120) have been presented. As seen in the first column, BP generates images with a high level of artifacts and imaging noise. Even though increasing the number of angles improves the image quality with lower imaging noise and reconstruction artifacts, the images are still affected. The CS-based WT removes a considerable amount of artifacts presented in the BP image (initial image). However, it blurs the edges of the reconstructed image. Even for a low number of angles, the real structure of the imaging target is compromised. It can be seen that adding the TV sparsifying method to the WT sharpens the edges, especially for 90 and 120 angles. While improvement is obtained, it removes the artifacts in the image along with useful information, lowering the accuracy of the reconstructed image. Finally, the proposed method removes the artifacts effectively and more accurately by sharpening the edges while retaining the significant information in the image. It should be noted that, in all the reconstruction implementations, investigated in this study, the media is assumed

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 of sparse reconstruction with WT basis at the maximum possible number of views, i.e., 600, has been considered as the Gold standard image.

**Figure 5.** Results of reconstruction algorithms on the Shepp–Logan synthetic phantom for 60 view angles and different reconstruction algorithms.

**Figure 6.** Quantitative evaluation, (**a**) EPI and (**b**) PSNR, of the performance of four reconstruction algorithms with different number of view angles.

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.


**Table 2.** Execution time for different reconstruction algorithms with 120 view angles.
