## 1 Introduction  
Photoacoustic imaging (PAI), also known as optoacoustic tomography, is a novel biomedical imaging technique. It uses laser as the energy source and detects the excited ultrasound signals. Therefore, it combines the advantages of both the ultrasound imaging and the optical imaging [1; 2; 3]. Firstly, PAI inherits the advantage of the optical imaging's high contrast [1]. Secondly, it breaks through the imaging depth limitation of the optical imaging and can acquire an image at higher imaging depth with ideal resolution [3]. Thirdly, PAI is also a noninvasive imaging technique that is harmless to the tissue as long as the energy of laser is controlled. Furthermore, because PAI reflects the light absorption distributions of the tissue, it can indicate such physiological parameters as hemoglobin concentration and blood oxygen saturation [4; 5; 6]. With all these above-mentioned advantages, PAI serves as a great tool in many fields of biomedical application, e.g., brain imaging [7; 8], blood vessel imaging [9], tumor detection [10] and molecular imaging [11]. Currently, there are two kinds of PAI: computed-tomography PAI [12; 13] and photoacoustic microscope [14; 15]. This paper focuses on the computed-tomography PAI. Under these circumstances,the tissue is irradiated by laser uniformly followed by photoacoustic signals generated through the photoacoustic effect [1; 2; 3] and then the photoacoustic signals are detected by a transducer array or by an ultrasound transducer scanning around the tissue. The collected signals contain the light absorption property information of the tissue. Therefore, the optical absorption distribution of the tissue can be reconstructed by a certain image reconstruction algorithm. In this process, the photoacoustic image reconstruction algorithms play a significant role in ensuring the quality of the reconstructed images. Since the initial study, many efforts have been made for the development of the photoacoustic image reconstruction algorithms. Analytical reconstruction algorithms are the first kind of photoacoustic image reconstruction algorithms [16; 17; 18; 19; 20]. In 1995, [PERSON] et al. proposed the first photoacoustic image reconstruction algorithm by using the inverse Radon transform [16]. After that, the filtered back-projection method (FBP) proposed by [PERSON] et al. was the most popular reconstruction algorithm for PAI [18; 21; 22; 23; 24]. [PERSON] et al. proposed a fast Fourier backprojection-based algorithm to solve the photoacoustic equation in frequency domain [17]. The deconvolution reconstruction algorithm proposed by [PERSON] et al. utilized the deconvolution-based method to improve the results of both full-view and limited-view scanning [20]. The advantage of the analytical reconstruction algorithms lies in its fastness and concision. However, they have poor accuracy and high dependence on data. To overcome the shortcomings of the analytical reconstruction algorithms, the iterative reconstruction algorithms which set up a forward model from the photoacoustic signals to the image have been applied into PAI and have obtained excellent results [25; 26]. This kind of reconstruction method is also called model-based photoacoustic [27]. [PERSON] et al. proposed an iterative reconstruction algorithm for optoacoustic imaging [26]. [PERSON] et al. incorporated the full-wave mode into the iterative reconstruction algorithm to effectively solve the problem caused by the inhomogeneities of the sound speed [25]. The compressed sensing theory was also applied in the photoacoustic image reconstruction algorithms [28; 29; 30; 31]. Among the iterative algorithms, total variation-based (TV) algorithms are reported to work best [32; 33; 34]. [PERSON] et al. proposed a gradient descent-based TV (TV-GD) algorithm which has greatly improved the reconstruction results, especially in sparse-view sampling [34]. [PERSON] et al. proposed a TV-based Bregman iteration to effectively solve the PAI sub-sampling problem [32].