In this paper, we have introduced an effective technique to remove the noise in the MRI and CT medical images during the process of acquisition, transmission, storage or compression. Removing these noise from medical images must be done without affecting relevant features of the image. Many techniques, such as genetic algorithm, Particle Swarm Optimization, Dynamic Multi-Swarm Particle Swarm Optimization and matching pursuit algorithm are used for denoising MRI and CT images. These techniques need more time to remove noise from medical images and find local point optimal. The proposed Differential Evolution based on Matching Pursuit (DE-MP) is used to detect best atom dictionary. The initial dictionary is created from an anisotropic atom. To evaluate the performance of the proposed techniques, the results of the proposed algorithm were compared with the other algorithm. The numerical results show that the performance of the proposed algorithm is more efficient and faster than other algorithms for medical images denoising.