Nuclear magnetic resonance(NMR)image is often used in medical diagnosis.Andimage super-resolution(SR)is the important steps in the NMR image analysis,which is valuable for the computer-aided detection(CADe)and computer-aided diagnosis(CADx).However,NMR is subjected to the development of hardware,thusit highlights the role of image SR.The learning based SR approach for a single imagehas received a lot of attention recently wherein.However,traditional image SRmethod only applies to the ideal image,which does not apply to the NMR imageswith complicated imaging process.The influence of the noise of NMR images mustbe taken into consideration.Extreme learning machine(ELM)is particularly outstandingamong the learning methods which requires fewer optimization constraintsand results in simpler implementation,faster learning,and better generalization performance.Therefore,in this paper,we propose a super-resolution method for singleNMR image based on the ELM,named SMSR,which can reestablish the NMR imageby establishing relationships between image patches across scales of the inputsingle NMR image by the ELM.Firstly,as the approach aims to reduce the effectsof the noise of NMR image during the process of SR.Degenerate NMR image to thedown-scaled images array to simulate the interference of the real imaging processof MRI.Secondly,synthesize the down-scaled images to interpolated NMR imagearray using bicubic interpolation.After this,instead of working directly in pixels,sparse representations is used as the image features to feed into the ELM to learnthe models.By choosing the proper learning model,we can get the final SR NMRimage.Finally,brain NMR images are used for experiment,after a series of evaluation,the results demonstrated the proposed method had 5%increase on regionaluniform,and 2%increase on grey uniform than the methods based SVR with higherefficiency.Which shows that our proposed approach can fulfill the requirements ofreal-world applications.