Bokeh preserves sharp edges; it just spreads them out. The circularly-symmetric boxcar filter of an ideal bokeh has a circularly-symmetric sinc frequency response in two-dimensional frequency space, and sinc’s falloff is pretty slow, just 6 dB per octave. So even a 32-pixel-wide bokeh is only attenuating single-pixel detail by about 30 dB.
(Of course, boosting single-pixel noise by 30 dB will add nontrivial graininess; that’s 5 bits of precision lost, after all. But some photos have that degree of precision.)
Indeed, as suggested in Starfield servo, under some circumstances such a bokeh can actually enhance sensor precision, and it might be preferable to use a large pinhole in front of a sensor rather than a lens on a camera, both because it gives you a more precise reading on the position of bright impulses in the visual field, and because it does a better job of taking advantage of the limited dynamic range of common image sensors. The principle is the same as how R’s default graphic for plotted points is a circle, not just a point, and in fact a disc in the center of the pinhole would probably work even better for extending the sensor dynamic range and precision. A more elaborate shadow mask such as a Hadamard matrix could improve this further.
Real camera bokehs tend to not be perfectly flat, even at small scales; although they don’t include Hadamard-matrix shadow masks, in addition to spherical aberrations, they do include tiny imperfections on the lens and lens filters that only add a tiny amount of stray light to a focused image, but are easily visible in unfocused images of (near) point source lights.
N.B.: This effect might be useful for getting lensless optical transmission microscopy out of commonplace digital cameras without taking the lenses off of them: put the slide reasonably close to the camera, illuminate with one or more out-of-focus point sources, ideally with some non-overlapping or mostly non-overlapping images on the focal plane.
These imperfections provide additional high-frequency information that could permit improved estimates of the unblurred image; moreover, in images that contain at least some bright points, they can provide much tighter estimates of the defocus of a particular region of the image. Also, if they are sufficiently strong, they can disambiguate behind-focal-plane defocus from in-front-of-focal-plane defocus. (Any kind of half-turn asymmetry in the bokeh can provide such disambiguation, including the common feature of approximate polygonality with an odd number of sides.)
Aside from the obvious approach of removing bokeh by applying Wiener filters selectively to parts of the image, it might be worthwhile to try not only convolution with an estimated bokeh shape but also morphological erosion with it, to identify candidate bright points — both to improve the estimate of bokeh shape and to measure the scale of the bokeh in different parts of the image.
Image-processing tricks on the bokeh are not limited to removing it and doing microscopy with it; you can also do camera identification (from the lens imperfections) and depth estimation. You might be able to correct chromatic aberration.
Bokeh can vary over the focal plane due to, for example, occlusion from a shroud extending in front of the lens. If this is recognizable it should be relatively easy to correct, but more general occlusion effects cannot be corrected in general — you might have a single light that’s half-covered by a finger halfway between the camera and the light, giving a sort of partially-eclipsed-moon bokeh not shared with much else in the scene.