You are apparently in the context of no-reference, reference-free or blind image quality assessment. The topic is quite active, and I am not sure people have already a complete framework for that. Multiple distortions may affect images: random noise, compression artifact, static blur, motion blur, etc. They require different metrics. Some references to standard with, and help you for more focused questions:

• No-Reference Image Quality Assessment in the Spatial Domain, 2012
• Making a “Completely Blind” Image Quality Analyzer, 2013
• No-reference image quality assessment based on spatial and spectral entropies, 2014  MDID: A multiply distorted image database for image quality assessment, 2017

The first three papers come from the same group, an hint that the paint is still wet.

You are apparently in the context of no-reference, reference-free or blind image quality assessment. The topic is quite active, and I am not sure people have already a completely accepted framework for that. Multiple distortions may affect images: random noise, compression artifact, static blur, motion blur, etc. They require different metrics (benchmark data here). Some references to start with, and help you for more focused questions:

• No-Reference Image Quality Assessment in the Spatial Domain, 2012
• Making a “Completely Blind” Image Quality Analyzer, 2013
• No-reference image quality assessment based on spatial and spectral entropies, 2014 
• MDID: A multiply distorted image database for image quality assessment, 2017

The first three papers come from the same group, an hint that the paint is still wet.