No-reference image quality assessment in magnetic resonance (MR) imaging is a challenging task due to the variable nature of these images and lack of standard quantification methods, which makes the interpretation to be almost always subjective. In this study, we propose an architecture where we: (i) extended the no-reference image quality assessment problem of MRI into a full-reference image quality assessment using unpaired generative adversarial network (GAN) and (ii) employed a weaklysupervised trained deep classifier to determine the quality of MR images by comparing each image with its synthetic higher quality reference image. Using this approach, we achieved 11.28% improvement in the accuracy of our MR image quality assessment algorithm on an independent data test with FPR in detecting low quality images, reduced from 13% to 9.6%.