# Quantitative Reconstruction of Absorption Coefficients for Photoacoustic Tomography
## 1 Introduction  
Photoacoustic tomography imaging is an emerging imaging modality that provides both structural and functional information of biological tissues with high contrast and excellent sensitivity [1; 2; 3; 4; 5; 6; 7; 8; 9]. It is a reliable avenue for detecting melanoma, subcutaneous blood vessels, prostate cancer and breast cancer [10; 11; 12; 13]. The high image contrast is provided by light-absorbing chromophores within the tissue, which may be natural endogenous molecules such as oxyhemoglobin, deoxyhemoglobin, melanin, or exogenous contrast agents such as dyes and nanoparticles [14]. Photoacoustic tomography imaging is based on the photoacoustic effect, which means the generation of acoustic waves by delivering short laser pulses into biological tissues. Some of the delivered energy will be absorbed and converted into heat, leading to transient thermoelastic expansion and thus wideband ultrasonic emission. The generated ultrasonic waves can be detected by acoustic sensors surrounding tissue surface, and then analyzed to reconstruct photoacoustic images [10]. In PA imaging [15; 16], the photoacoustic initial pressure distribution is proportional to the absorbed optical energy density, which is a product of both the optical absorption coefficient and thelocal light fluence. The photoacoustic image is a combination of optical absorption and light fluence and therefore it indirectly represents the structure and physiological information of biological tissues. However, the absorption coefficient distribution can reflect the spatial distribution of the absorbers in a direct way and explicitly without being affected by the change of light fluence. Quantitative PA imaging aims to accurately and quantitatively estimate the distribution of chromophores in tissue. In order to achieve quantitative reconstruction of tissue absorption coefficients, the influence of the depth-dependent attenuation of light fluence should be eliminated [16; 17; 18]. Although various algorithms have been developed for quantitative estimation of the absorption coefficient [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39], they all have limitations on account of being researched primarily for simple simulation. [PERSON] et al. have previously developed a simple iterative method for quantitative reconstruction based on light fluence, that is, the absorption coefficient was iteratively fit by using the measured initial pressure map. While the algorithm converges to an accurate estimate values of absorption coefficients, it only realizes the numerical simulation of the 2-dimensional model. In addition, [PERSON] et al. extended their previous work by using multiwavelength excitation and gradient-based optimization to estimate the chromophores distribution. Finally, [PERSON] et al. were able to demonstrate the model-based recovery of absorption coefficient and reduced scattering coefficient or spectrally derived chromophores from a 4 \(\times\) 8 mm rectangular region in a Quantitative Photoacoustic Tomography (qPAT) image [15; 16; 17; 18; 19]. Thesis work of [PERSON] on Monte Carlo for qPAT, which were demonstrated that that linear inversion is only applicable to certain illumination wavelength bands and limited depth, and the alternative approach used a novel Monte Carlo model of light transport to simplify the computation of functional gradients [20]. [PERSON] et al. proposed a quantitative reconstruction sparse representation method based on different spatial distribution characteristics of light fluence and absorption. Although this method does not need the parameter-based fluence distribution, it will generate errors under non-uniform boundary illumination [21; 22; 23]. [PERSON] et al. proposed a method for quantitative reconstruction with multiple optical sources under the circumstances of a spatial variation of the Gruneisen coefficient and ideal transducer bandwidth. Their latest research also liberalizes the bandwidth of the ideal sensor [24].