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Deep learning methods have become the state of the art for undersampled MR reconstruction. Particularly for cases where it is infeasible or impossible for ground truth, fully sampled data to be acquired, self-supervised machine learning methods for reconstruction are becoming increasingly used. However potential issues in the validation of such methods, as well as their generalizability, remain underexplored. In this paper, we investigate important aspects of the validation of self-supervised algorithms for reconstruction of undersampled MR images: quantitative evaluation of prospective reconstructions, potential differences between prospective and retrospective reconstructions, suitability of commonly used quantitative metrics, and generalizability. Two self-supervised algorithms based on self-supervised denoising and the deep image prior were investigated. These methods are compared to a least squares fitting and a compressed sensing reconstruction using in-vivo and phantom data. Their generalizability was tested with prospectively under-sampled data from experimental conditions different to the training. We show that prospective reconstructions can exhibit significant distortion relative to retrospective reconstructions/ground truth. Furthermore, pixel-wise quantitative metrics may not capture differences in perceptual quality accurately, in contrast to a perceptual metric. In addition, all methods showed potential for generalization; however, generalizability is more affected by changes in anatomy/contrast than other changes. We further showed that no-reference image metrics correspond well with human rating of image quality for studying …