Effect for softening gradients, such as after increasing image detail?

[Asterra]

I think you know what I mean. Take a look at this sample image:



Specifically, how the shading gradually ramps up in brightness as it approaches the middle. It was rendered in 8-bit without dithering, and so suffers from an obvious contouring effect, despite taking more or less full advantage of what 8 bit has to offer. Th goal here is to end up with a replacement for this contoured shading that utilizes dithering to mask the limits of 8-bit color.


Here's the thing. I know I could get this done if I 1) masked off the parts I don't want to change, and then 2) applied a blur to the contoured component. I know. But I have hundreds of images that need to be processed in a similar way, so painstakingly masking every single one is quite simply off the table.

What I really need is some kind of filter that can intelligently identify this sort of low-bit-depth contouring artifact and transform it into a higher-detail gradient. So that I could for example convert the image to 16-bit, apply the effect, then downconvert it back with dithering, and get my result.

I feel like this is a common enough artifact that good solutions exist by now. I just don't know where I should be looking.

Thanks in advance.