Yes. In general this is described by signal-to-noise ratio (SNR) and broader signal-detection/information theory, including Shannon’s work. As noise rises relative to the signal, it becomes harder to distinguish real image structure from randomness. The practical result is that fine detail and low-contrast edges disappear first, while strong, high-contrast edges remain recognizable longer.

A useful way to think about it is that increasing noise reduces the effective bandwidth of the image: less subtle spatial information can be detected, so the image appears softer or less detailed. This is why denoising can make previously hidden detail recognizable again—if the method suppresses noise without destroying the underlying signal.

The relationship is not perfectly linear or simple. In some cases, a small amount of noise can actually help edge detection, a phenomenon called stochastic resonance. That helps explain why a little noise can sometimes make an image appear more natural or even slightly more perceptible.

So the short answer is: yes, there is theory, and the key concepts are SNR, detectability, contrast, and bandwidth. Exact visibility thresholds depend on the viewer, the image content, viewing conditions, and the type of noise.