We develop an image despeckling method that combines nonlocal self-similarity filters with machine learning, which makes use of convolutional neural network (CNN) denoisers. It consists of three major steps: block matching, CNN despeckling, and group shrinkage. Through the use of block matching, we can take advantage of the similarity across image patches as a regularizer to augment the performance of data-driven denoising using a pre-trained network. The outputs from the CNN denoiser and the group coordinates from block matching are further used to form 3D groups of similar patches, which are then filtered through a wavelet-domain shrinkage. The experimental results show that the proposed method achieves noticeable improvement compared with state-of-the-art speckle suppression techniques in both visual inspection and objective assessments.