## 3 Results
### 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  
Figure 3: Simulative results. (**a**) The detected photoacoustic (PA) signals by a single transducer. (**b**) The detected PA signals by all transducers. (**c**) The image reconstructed by the delay and sum (DAS) beamforming method. (**d**) The image reconstructed by the proposed matrix filtering method.  
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\({}^{\circ}\). It is equivalent to an annular array with 180 elements.  
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 \({}^{\circ}\)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/m\({}^{3}\), 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.  
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  
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 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.  
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 effectively reduce the degradation of imaging quality caused by the beaker, and the experiments validated the performance of the proposed method.