*3.2. Experimental Study*

We also performed an experiment on a vessel shape source to validate the performance of the proposed method. A schematic diagram of the experimental system is provided in Figure 4a. A vessel-shaped source placed in the ROI was irradiated by a Q-switched Nd: YAG pulse laser with a

wavelength of 532 nm. The pulse width was about 8 ns. The ultrasonic waves were detected by a 5 MHz central frequency line focused ultrasonic transducer (V310-SM, PANAMETRICS-NDT) with a −6 dB bandwidth of 4.4 MHz, then amplified (SA-230F5, NF) and sampled (PCI-5105, NI) at a sampling rate of 60 Mhz. Under the control of a rotary stepper motor, the transducer scanned clockwise around the sample with a radius of 4.3 cm and a step of 2◦. It is equivalent to an annular array with 180 elements.

**Figure 4.** PA imaging of a vessel-shaped source experiment. (**a**) Schematic diagram of the PA imaging experimental setup. (**b**) Photo of the sample.

Figure 4b is a picture of the imaging sample. A vessel-shaped source made of hair was embedded in agar for fixing, with an agar to water ratio of about 1.2%, and the sound velocity was measured as 1,460 m/s at 25 °C. To mimic the effect of the skull on brain imaging, we placed the sample in a glass beaker. The glass has a thickness of about 1.0 mm, and the corresponding speed of sound and density were 2,730 m/s and 2,500 kg/m3, respectively. The acoustic impedance of the glass beaker was much higher than that of the agar and the surrounding water. It caused strong acoustic scattering of the PA waves, as would the skull. Serious acoustic impedance mismatch between the glass beaker and the surrounding media could result in a significant drop in image quality.

For comparison, the images recovered by the DAS method and the proposed method in the cases with and without the beaker are shown in Figure 5. Figure 5a,b show the imaging results of the DAS method and the proposed method without the beaker. In both cases, the pattern is clear enough that the shape of the source is distinguishable.

**Figure 5.** Reconstructed images of the vessel shape source in the ROI. Reconstructed image of the sample without the beaker (**a**) by the DAS beamforming method and (**b**) by the proposed matrix filtering method. Reconstructed image of the sample with the beaker (**c**) by the DAS beamforming method and (**d**) by the proposed matrix filtering method.

However, for the sample in a beaker, the image recovered by the DAS method (Figure 5c) shows low contrast and strong background noise. The shape of the source is hard to distinguish. In the imaging result produced by our proposed method, we obtained a clear pattern of the vessel shape source with high contrast, which is similar to the result in Figure 5b. We conclude that the proposed method can e ffectively reduce the degradation of imaging quality caused by the beaker, and the experiments validated the performance of the proposed method.

#### **4. Discussion and Conclusions**

In summary, we developed an image reconstruction method for PAT. This method combines a correlation matrix filter and a time reversal operator. We applied this method to reconstruct PA images inside a scattering layer. Both numerical simulation and phantom experiments were used to examine the performance of the proposed method. The simulation quantitively validated that the proposed imaging method provides higher imaging quality in complex scattering media compared with the classic beamforming method. The advantages are reflected in better a SNR and FWHM.

Though demonstrating potential in preclinical and clinical applications, PAT is still in its early age of development. Among the several limitations preventing PAT's application, the main one is the amplitude and phase distortion of the received signals caused by the randomly distributed scatterers. In this research, we proposed an image reconstruction method to reduce the negative e ffect of the scattering waves by separating the direct waves from the received signals. With the filtered signals, PA images can be optimized, especially the resolution and the contrast between the targets and the background. This work might be valuable for understanding the physics of the interaction of sound in the complex media. The proposed method may potentially be used for acquiring high-quality images of the brain through the skull.

In this study, the experiments were performed by a point-by-point scanning with a single ultrasound transducer. Point-by-point scanning is not fast enough to meet the imaging requirements in pre-clinical or clinical scenarios. This problem can be solved by using a circular ultrasound array, which is what we are preparing to study in our next work. Additionally, as future work, we will evaluate the proposed method in an in vivo study on a small animal.

**Author Contributions:** R.W. designed the simulations, employed the experiments, analyzed the results, and wrote the paper. Z.L. assisted in both the experiments employment and writing of the paper.

**Funding:** This research was funded by the National Key R&D Program of China (2016YFC0102300), National Natural Science Foundation of China (NSFC) (11834008, 11874217), Fundamental Research Funds for the Central Universities and Natural Science Foundation of Jiangsu Province (No. BK 20181077).

**Conflicts of Interest:** The authors declare no conflict of interest.
