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Magnetic resonance imaging (MRI) is a medical technology that uses powerful magnets, radio waves, and a computer to produce images of the body’s internal organs. The patient should be quiet and motionless during the scanning period, as unavoidable movements, such as breathing and heart rate, cause motion artifacts in the image, which cause contrast instability and low-resolution MRI images. Imaging in the clinical setting is performed at low resolution because the scanning time for high-resolution MR imaging would be very long and cumbersome, and imaging is also very expensive. Learning-based image superresolution methods can reconstruct MR images with optimal quality and resolution. However, these methods have problems such as the inability to find the intrinsic relationship between low- and high-resolution image patches in the training dictionary, specification of the proper amount of error in the training and testing stage due to variability in MR image contrast, inability to reconstruct objects by smoothed edges, and use of the backpropagation method in updating their weight vectors. In this paper, we propose a new superresolution method according to competitive learning-based approaches to overcome the problems of previous superresolution methods, which do not have the problems and complexities of those methods. The proposed method includes self-organizing maps as a preprocessor, the nearest neighbor algorithm as a classifier, and a high-frequency filter as a high-frequency image detail extractor. We constructed a single external dictionary from a combination of low-resolution and high-resolution feature patches and trained our SOM network. Next, we reconstruct the high-resolution image by converting the low-resolution input image into feature patch vectors, and for each vector, we find all corresponding neurons in the network and retrieve all their training feature vectors. Next, we train the nearest neighbor algorithm with the recovered vectors plus the input vector and find the best similarity vector to the input vector. After finding all the best similarity vectors to the input vectors, we reconstruct our high superresolution image. The proposed image superresolution method in practical experiments was trained, tested, and evaluated by the Div2k dataset and compared with other traditional and state-of-the-art image enhancement methods on various datasets, such as SET5, SET14, BSDS100, and URBAN100, and presented better results with higher accuracy and quality than traditional and state-of-the-art methods, both visually compared to each other by human and computational benchmarks, such as the peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM), to compare image superresolution algorithms. This method is best for reconstructing high-resolution magnetic resonance images that require high-frequency details and sharp edges with a smooth slope of the imaging objects in their structures. The execution time of the proposed algorithm is slower than that of the other algorithms, so we use GPU hardware and parallel programming techniques to increase the algorithm speed.