Photoacoustic imaging has great potential in the field of biomedical imaging because it is a beneficial combination of the high contrast of pure optical imaging and the high resolution of ultrasound imaging for deep-tissue. By acquiring the photoacoustic signals at multiple locations, we can obtain a two-dimensional or three-dimensional optical absorption distribution image of the biological tissue. However, it is difficult for actual photoacoustic imaging to acquire the photoacoustic signals with enough detector locations due to the constraints of hardware conditions and imaging time. In the case of insufficient signal sampling, the reconstruction quality of the photoacoustic image is seriously degraded, and a large number of artifacts appear consequently. To overcome this problem, we propose a reconstruction strategy which uses photoacoustic signals preprocessed by a recovered algorithm based on dictionary learning and sparse representation, and simulation experiments are carried out. The results show that by applying the proposed algorithm, a photoacoustic image can be reconstructed with less artifacts, clearer details and 8 dB peak signal-to-noise ratio improvement compared with images reconstructed without super-resolution reconstruction of photoacoustic signals. The simulation experiments with different signal-to-noise ratios verify that the proposed algorithm has good robustness.