###### Abstract  
The inaccuracy of inhomogeneous sound speed fields in photoacoustic imaging (PAI) can lead to the blurring and distortion of photoacoustic images. To solve this problem, conventional methods build speed models by using some a priori information or additional measuring equipment, which limits the application of PAI greatly. A data-driven speed field inversion method is proposed in this paper. It combines clustering with updates to the speed field. To reduce the complexity of the sound speed field model, the model is divided according to the similarity of the same tissue. The sound speed of the same tissue is regarded as a whole, which reduces the number of sound speed parameter solutions. Based on the simplified sound speed field model, the proposed method can adaptively adjust the step length of the sound speeds of various tissues by weight allocation. In this way, the updated amplitude of sound speeds of various tissues can be balanced and the accuracy of the sound speed field can be improved. A digital breast model is applied to verify the effectiveness of the proposed method. The results demonstrate that the method can build an appropriate speed field without additional information or equipment and improve the imaging performance of PAI. Keywords:photoacoustic imaging; inhomogeneous sound speed field; root mean square propagation algorithm; Gaussian mixture model +
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This assumption may lead to serious deviations in the time-of-flight (TOF) of photoacoustic signals [8; 9], which makes photoacoustic images blurred and distorted [10]. To avoid this situation, it is necessary to accurately estimate inhomogeneous sound speed fields in the process of image reconstruction. Due to the serious impact of the inaccuracy of sound speed fields on the performance of PAI, how to accurately estimate sound speed fields has become an urgent problem to be solved in PAI. Some researchers proposed the transformation of the problem of estimating sound speed fields into a data clustering problem, which directly obtains the regional distribution of each tissue through photoacoustic pressure data. [PERSON] et al. used K-means clustering to divide photoacoustic pressure data [11]. [PERSON] et al. extracted the sparse spectrum of photoacoustic pressure data by basis tracing and processed the data by using the clustering value of the sparse spectrum and the clustering boundary [12]. Two methods used different clustering algorithms to obtain regional information about each tissue. However, they all rely on clinical data for sound speed assignment when estimating inhomogeneous sound speed fields. In addition, other strategies have been proposed by several researchers to construct sound speed fields. [PERSON] et al. reported a joint reconstruction (JR) method based on an alternate optimization scheme, which can simultaneously obtain the sound speed distribution and absorbed light energy density of photoacoustic images [13]. Deep learning shows superior performance in improving imaging speed [14]. Some researchers also apply it to solve the problem of sound speed field estimation. [PERSON] et al. proposed a synchronous reconstruction network (SR-Net), which combines deep learning with a joint reconstruction algorithm. It can obtain a relatively accurate sound speed field [15]. [PERSON] et al. adopted a strategy combining multi-modal imaging techniques. They developed a hybrid photoacoustic-ultrasonic imaging system that uses ultrasonic tomography (USCT) equipment to obtain sound speed distribution [16]. The above three methods can obtain relatively accurate inhomogeneous sound speed fields. However, the JR algorithm and USCT enhanced reconstruction algorithm have high computational costs and system complexity. To sum up, the existing sound speed field estimation methods are still dependent on prior information and additional measurement equipment, and some methods with superior performance have high computational complexity. The limitations of these methods greatly limit the application of PAI.