This paper presents the development of novel models which can be potentially useful in determining the upper limit of image compression thresholds, to preserve diagnostically relevant information in compressed medical images. These models were developed by evolving the correlation between the theoretically computed objective (peak signal-to-noise ratio and structural similarity) and subjective mean opinion score (MOS) quality parameters. The developed models were validated by comparing the model generated MOS with the corresponding experimental MOS of six independent observers considering joint photographic experts group (JPEG), JPEG2000 and set partitioning in hierarchical trees (SPIHT) compressions of computed tomography (CT) scan images. It is found that the correlation between the model generated and experimental MOS and PRD are ≥0.87 and ≤13% respectively for the compression range 0.05–2.0 bits/pixel of the CT scan images. Therefore our models can be potentially useful for observer-independent MOS prediction and quality assessment of reconstructed medical images. In addition this also avoids the need for exhaustive and time-consuming experimental MOS and thus it can be more suitable for teleradiology applications.