How to analyze image quality? I have a few sequences of images, taken at fixed camera position, that address a moving object, which means the object moves towards the camera. But all the sequences of images are the cropped images of the object and all images are in the same size (grayscale images). From naked eyes, we can see the images that are closer to the camera are  better than the ones that taken at far distance. How can I show scientifically or show a proof that the images have varied quality? I also want to compare the quality between  sequences.
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.