In photoacoustic (PA) reconstruction, spatial constraints or real-time system requirements often result to sparse PA sampling data. For sparse PA sensor data, the sparse spatial and dense temporal sampling often leads to poor signal continuity. To address the structural characteristics of sparse PA signals, a data interpolation algorithm based on extremum-guided interpolation is proposed. This algorithm is based on the continuity of the signal, and can complete the estimation of high sampling rate signals without complex mathematical calculations. PA signal data is interpolated and reconstructed, and the results are evaluated using image quality assessment methods. The simulation and experimental results show that the proposed method performs better than several typical algorithms, effectively restoring image details, suppressing the generation of artifacts and noise, and improving the quality of PA reconstruction under sparse sampling.