The internal wave generated by the movement of the underwater body makes the water surface form weak infrared texture signals, which makes it possible to use infrared means for detection. However, the contrast of texture signals is very low, and it is mixed with the background clutter with large amplitude, which causes great difficulty in signal extraction. Based on the curvelet transform, the curvelet scale component and direction component are screened according to the contrast and frequency characteristics of weak textures, and a clearer texture extraction image is obtained by combining with the threshold optimization and the edge gradient operator. Compared with the results of the traditional curvelet transform, the information entropy and frequency concentration of the image are improved by 30% and 11%, respectively. When the contrast of the weak texture is greater than 5% and the deviation between the direction of the screening frequency and the direction of the weak texture frequency is less than 12°, the algorithm can clearly extract texture information.