To enhance the resolution of SAR image,based on Markov model and Shearlet transform, a learning based super-resolution algorithm was proposed.The proposed method consisted of two stages of training stage and learning stage. In the training stage,firstly,Shearlet transform was performed to high-resolution and low-resolution images in the training set to obtain high-frequency and mid-frequency information of different directions. Then these high-frequency and mid-frequency information were divided into blocks. In the learning stage,Shearlet transform was performed to extract the mid-frequency information of a low-resolution image.Then,Markov network was adopted to model the super resolved high-resolution image with the blocks obtained in the training stage.Maximum A Posteriori （MAP）was used to estimate the high-frequency information of the low-resolution image in different directions.The estimated high-frequency information and the low-resolution image were transformed into super resolved high-resolution image through inverse Shearlet transformation.Experimental results on SAR images showed that the results of the algorithm have a good performance in terms of visual effects and root mean square error.
