Magnetic resonance (MR) images of higher quality is demanded for helping with more accurate and earlier diagnosis of different diseases. The overall quality of MR images is limited due to the existence of different degradation factors such as (1) MR aberrations due to intrinsic properties of the MR scanner, (2) magnetic field inhomogeneity, and (3) inherent MRI noise. Correcting each MRI degradation factor could be solely useful for the quality enhancement of MR imaging with a limited impact. Here, we propose a unified Bayesian based compensated MR imaging (CMRI) system which jointly corrects for the different aforementioned MR aberrations as well as MR noise and hence generates compensated MR (CMR) images with a higher quality. Testing the proposed CMRI system on both MR physical phantom as well as diffusion weighted and T2 weighted MR imaging data resulted in producing MR images with an overall higher quality that better represents different structures of tissue. The quantitative performance analysis shows a higher Signal to Noise (SNR) and Contrast to Noise (CNR) ratios as well as less Coefficient of Variation (CV) for reconstructed images using the proposed CMRI system compared to the Blind Deconvolution Compensation (BDC) method as state-of-the-art. As such, the proposed CMRI system has potential in improving MR image quality, which is important for accurate and consistent clinical interpretation.