As acoustic waves are affected by the channel characteristics, such as scattering and reverberation when propagating in water, sonar images often exhibit speckle noise which will cause visual quality of the image to decrease. Therefore, denoising is a crucial preprocessing technique in sonar image applications. However, speckle noise is mainly caused by the sediment echo signals which are related to the background of seafloor sediment and can be obtained by prior modeling. Although deep learning-based denoising algorithms represent a research hotspot now, they are not suitable for such applications due to the high calculation amount and the large requirement of original images considering that sonar is carried by Autonomous Underwater Vehicles (AUVs) for collecting sonar images and performing calculation. In contrast, dictionary learning-based denoising method is more suitable and easier to be modeled. Compared with deep learning, it can greatly reduce the calculation amount and is more easily integrated into AUV systems. In addition, dictionary learning method based on image sparse representation can effectively achieve image denoising similarly. In order to solve the above problems, we propose a new adaptive dictionary learning method based on multi-resolution characteristics, which combines K-SVD dictionary learning with wavelet transform. Our method has the characteristics of dictionary learning and inherits the features of wavelet analysis as well. Compared with several classical methods, the proposed method is better at speckle noise reduction and edge detail preservation. At the same time, the calculation time is greatly reduced and the efficiency is significantly improved.