Photoacoustic imaging (PAI) is a newly emerging bimodal imaging technology based on the photoacoustic effect; specifically, it uses sound waves caused by light absorption in a material to obtain 3D structure data noninvasively. PAI has attracted attention as a promising measurement technology for comprehensive clinical application and medical diagnosis. Because it requires exhaustively scanning an entire object and recording ultrasonic waves from various locations, it encounters two problems: a long imaging time and a huge data size. To reduce the imaging time, a common solution is to apply compressive sensing (CS) theory. CS can effectively accelerate the imaging process by reducing the number of measurements, but the data size is still large, and efficient compression of such incomplete data remains a problem. In this paper, we present the first attempt at direct compression of incomplete 3D PA observations, which simultaneously reduces the data acquisition time and alleviates the data size issue. Specifically, we first use a graph model to represent the incomplete observations. Then, we propose three coding modes and a reliability-aware rate-distortion optimization (RDO) to adaptively compress the data into sparse coefficients. Finally, we obtain a coded bit stream through entropy coding. We demonstrate the effectiveness of our proposed framework through both objective evaluation and subjective visual checking of real medical PA data captured from patients.