Is there any data or theory about human visual system to identify details under noise?

Question

For one clean image, one person can identify every details at first. Then white Gaussian noise is added to the image.
With low noise level, one person can still identify every details even though noise is present.
With a litter higher noise level, small details and low contrast edges will be not be identified.
With much higher noise level, only strong edges can be identified.
Is there any data or theory about relationship between noise level and characterization of identificable features in the image?

This figure is from one paper about video denoising.
The first image is from one noisy video. The other three are obtained by different video deniosing methods. The details above the soldier is not observable because the noise level is high. After video denoising applied, the noise level is reduced and the details can be identified. Is there any data or theory about relationship between noise level and characterization of identificable features in the image?

Answer 1

The relationship between signal and noise in the most general sense is full of math, and was fully developed by Claude Shannon, some 70 years ago.

In general, noise is characterized by a ratio between the signal, and the signal plus noise. As you surmise, as more noise is added, it becomes more difficult to detect the signal, but more importantly, the bandwidth that can be supported goes down. This means a noisy picture will look softer than one with much less noise.

It is not always a simple, linear equation. For example, adding small amounts of noise can actually increase detection of edges, through a process called stochastic resonance. This helps explain why photographs with a bit of noise added can look more "pleasing" than ones that are relatively noise-free.

So, there is no simple answer, but yes, there is a corpus of information knowledge theory that applies to photography. But it is complicated, and if you're looking for something simple, like "doubling the noise halves the image quality," you're going to be disappointed.