## 1 Introduction  
In recent years, the high incidence of orthopedic diseases like osteoporosis (approximately 40% of women and 20% of men over the age of 50 years [1]), and the resulting high costs of the treatment make it increasingly essential to monitor bone quality [2]. Several techniques have been developed for bone assessment non-invasively. Dual-energy X-ray absorptiometry (DXA) is regarded as the gold standard for bone mineral density (BMD) measurement [3; 4]. BMD measurement reflects the mineral content in bone tissue, but it can only explain about 60-70% of bone strength changes [5; 6]. Other variances like trabecular micro-structure are reported to be important complements for bone evaluation [7]. Although computerized tomography (CT) can provide bone geometry with relatively high resolution, it is achieved at the cost of delivering a considerable radiation dose [8]. As a newly non-ionizing radiation modality, quantitative ultrasound (QUS) has the advantages of low cost, portability and accessibility [9; 10]. The speed of sound (SOS) and broadband ultrasound attenuation (BUA) are two important parameters. They are measured as the mean values of the ultrasonically interrogated bone tissue, which are highly related to bone quantity, but rarely provide information about bone micro-structure [6]. The QUS parameters based on ultrasonic backscattering are used to characterize bone densities and structure [11; 12; 13; 14; 15; 16]. Ultrasonic backscatter measurements could even reflect additional density and structural features unrelated to current BMD measurement [17; 16]. Moreover, new advances in ultrasound imaging enable the visualization of bone anatomy [18]. Photoacoustic (PA) imaging is a newly emerging noninvasive imaging method based on different optical absorption in biological tissues [19; 20; 21; 22]. It is based on optical excitation and ultrasonic detection. The acoustic waves are generated by irradiating a short pulse laser on biological tissue with thermoelastic expansion. Ultrasonic signals propagating through the tissue are recorded using ultrasonic transducers. With different reconstruction algorithms, the PA imaging is to restore initial pressure of the tissue from detected signals [23]. As an imaging mode with non-ionizing radiation, PA imaging poses no health hazard compared with other X-ray based imaging modalities. Combining the advantage of ultrasonically deep imaging depth and optically high contrast, PA imaging presents the spatial distribution of tissue with high image quality. It has played an important role in the clinical detection of tumors and vessels [24; 25; 26; 27; 28]. Recent studies also have investigated the possibility of PA technology in the application of measuring BMD, bone composition and structure [29; 30; 31; 32]. [PERSON] et al. demonstrated that the feasibility of PA imaging in human peripheral joints and the imaging depth is sufficient to penetrate through larger human joints [33]. [PERSON] et al. achieved the detection of bone mineralization or decollagization by combining PA and ultrasound imaging modalities [34]. Furthermore, the latest experiments by Merrill validated that the PA reconstructed image of ex vivo porcine bone is available through PA microscopy system [35]. For bone imaging, PA imaging shows its great potential and a promising prospect. Despite exciting progress in PA imaging, the image reconstruction for bone tissue is still a big challenge. Unlike the soft tissue, bone tissue is a complex porous material composed by trabeculae bone and bone marrow filled within the pores [36]. The porous bone tissue is a strongly scattering medium with heavy ultrasonic attenuation and phase distortions, making it difficult to image bone structure with high PA image quality [37]. Besides, the high heterogeneity of bone tissue would produce large variations in ultrasonic velocity. There is a large difference in SOS between the two components of bone tissue, i.e., a typical SOS is 1500 m/s and 4000 m/s for bone marrow and trabeculae, respectively [38; 39].