The limitation of resolution seriously affects the study of deep undercooling melt. Nowadays, the existing image super-resolution (SR) methods cannot restore the high-resolution (HR) image from a low-resolution (LR) image, and is not suitable for reconstructing the texture details of the deep undercooling melt. To solve these problems, we propose a method based on adaptive mixed sample and low-rank matrix decomposition optimization (AMS-LMDO) for single-image SR. Unlike other SR methods, we make a full use of the external and internal sample libraries to extract the complementary prior knowledge. Comparing with other individual sample libraries, the experimental results prove our method is more effective. Moreover, we also apply low-rank matrix decomposition to optimize reconstructed-HR image, which carried with sparse and uncorrelated errors and erroneous information. The simulation results show that compared with the current popular methods, the proposed method can not only restore the general images, but also recover the inherent high frequency details of the deep undercooling melt.