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I am analyzing the videos recorded by a surveillance camera and noticed that, in most scenes, there is a sort of "halo" around the right part of people passing by (also around the orange dumpster). Please see the picture below for an example. enter image description here

I am wondering whether this undesired effect has a name and whether it can be compensated. If so, how?

Although I have no experience in photography, I have some notions of mathematical signal processing. Can I expect that, once this aberration is compensated for, the quality and the sharpness of each frame will improve? I assume it is a sort of "systematic error" that, once recognized, can be "subtracted" so to have sharper images.

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You can't 'rescue' what has already been thrown away.

It looks like the sharpening/smoothing/HDR algorithm employed by the camera's software is trying to iron out every imperfection, to such a degree that the car park & back of the guy's jacket become almost perfectly smooth surfaces.
This halo effect is typical of 'cheap' HDR processing. It's an algorithm fail, at source.

The halo effect to the right is almost mirrored by an opposite effect to the left.

Zoom of woman's coat & immediate surroundings…

enter image description here

There's a halo both sides, slightly different, but equally 'un-fixable' There is nothing left in the image to extract the data from.
The only 'fix' would be to persuade the camera's software to not do that & see if better software could make a better guess [I'm being intentionally vague, because we can't really guess just how poor the original image is.]

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If there is a thick glass placed at an angle in front of the lens it will cause double image (same size and shifted to one side) because of glass producing an internal shifted reflection.

It can then become an edge outline if aggressive sharpening is applied.

I do not believe you can efficiently correct it without having access to raw footage.

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