Recently, the Magnetic Resonance Imaging (MRI) images have limited and unsatisfactory resolutions due to various constraints such as physical, technological and economic considerations. Super-resolution techniques can obtain high-resolution MRI images. The traditional methods obtained the resolution enhancement of brain MRI by interpolations, affecting the accuracy of the following diagnose process. The requirement for brain image quality is fast increasing. In this paper, we propose an image super-resolution (SR) method based on overcomplete dictionaries and inherent similarity of an image to recover the high-resolution (HR) image from a single low-resolution (LR) image. We explore the nonlocal similarity of the image to tentatively search for similar blocks in the whole image and present a joint reconstruction method based on compressive sensing (CS) and similarity constraints. The sparsity and self-similarity of the image blocks are taken as the constraints. The proposed method is summarized in the following steps. First, a dictionary classification method based on the measurement domain is presented. The image blocks are classified into smooth, texture and edge parts by analyzing their features in the measurement domain. Then, the corresponding dictionaries are trained using the classified image blocks. Equally important, in the reconstruction part, we use the CS reconstruction method to recover the HR brain MRI image, considering both nonlocal similarity and the sparsity of an image as the constraints. This method performs better both visually and quantitatively than some existing methods.
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