  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.
