How to analyze image quality?
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.