## 1 Introduction  
Photoacoustic (PA) tomography (PAT) is a noninvasive and nonionizing imaging technique that combines rich optical contrast and high ultrasonic resolution in deep tissue [1; 2; 3; 4]. During the PAT imaging process, the biological tissue is irradiated by a laser pulse, and then optical absorbers in the tissue absorb electromagnetic energy and generate ultrasound due to rapid thermoelastic expansion. The ultrasound signal is then detected by the ultrasound transducer array arranged outside the tissue. Finally, images with optical absorption contrasts are extracted from the detected PA signal using a reconstruction algorithm. PAT breaks through the optical diffraction limit and obtains images of tissue at depths of 5-6 cm with good acoustic spatial resolution. Therefore, PAT has application potential for high-quality in vivo vascular structure imaging [5], investigations of breast tumor tissue [6; 7; 8; 9], vasculature visualization [10; 11], small animal whole-body imaging [12; 13], osteoarthritis assessment [14; 15], drug delivery monitoring [16], and hemodynamic functional imaging [17].  
One promising application of PAT is high-resolution in vivo brain imaging, which is important in neurophysiology, neuropathology, and neurotherapy. In comparison with the often-used brain imaging modalities, including X-ray computerized tomography (CT) and magnetic resonance imaging (MRI), PAT is inexpensive and has good spatial resolution and temporal resolution [1; 2]. X-ray CT involves exposure to ionizing radiation, but PAT is nonionizing and safer. PAT can provide structural images as well as functional images of the brain.  
The classical image reconstruction algorithms used in PAT are usually based on the principle of coherent beamforming, which relies on an assumption of homogeneous media. In a scene with strong scattering, the coherence in signals is destroyed by the randomness of scattering, leading to a markedly decreased penetration depth and significant degradation in image quality [18]. This limitation hinders the application of PAT in a wider range of scenarios, such as transcranial PA brain imaging within the skull bone. The skull bone has much higher acoustic impedance than soft tissue. A severe acoustic impedance mismatch could cause amplitude and phase distortion, and decrease the resolution and contrast of the transcranial imaging, significantly reducing the brain image quality [19; 20; 21; 22]. Traditional approaches to overcome the limitation of acoustic scattering have mostly relied on a priori knowledge of the properties of tissue inhomogeneity or need to involve additional acoustic measurements, evidenced in the statistical reconstruction method [23], coherence factor optimization [24], and the interferometry method [25]. For a more general situation, a universal reconstruction algorithm with better performance is still required for acquiring high-quality images in scattering media.  
In this study, we created an image reconstruction method that combines a correlation matrix filter and a time reversal operator using an annular transducer array. After dividing the circular array into multiple sections, each sector array can be approximated as a linear array via phase and amplitude compensation. Then, using the correlation characteristics of the direct waves, a correlation full-matrix filter can be applied to separate the direct waves from the scattering waves [26; 27; 28; 29]. Finally, the imaging results of each section based on the time reversal method are superimposed to further improve the image quality. Both numerical simulation and phantom experiments were employed to validate the proposed method and examine its potential for extracting PA images inside a skull-like scattering layer.