Um, the first point, in digital imaging, is that a pixel is not a little square. It's a sample. So it doesn't have any extension to blur. Any filtering invariably happens either at sampling or at reconstruction.
Of course sharpness is a function of resolution. I'm not sure it makes sense to talk about capacity, because typically the resolution of the image is non-negotiable. The number of bits needed to encode it is variable and depends on compression technique used.
So in general, Shannon-style channel thinking operates on a different layer from the sampling and reconstruction processes we are discussing here. It's more relevant to how discrete pixel values are coded, or more elaborate compression mechanisms which exploit coherence in the image.
https://graphics.stanford.edu/courses/cs248-04/ho6/
Of course sharpness is a function of resolution. I'm not sure it makes sense to talk about capacity, because typically the resolution of the image is non-negotiable. The number of bits needed to encode it is variable and depends on compression technique used.
So in general, Shannon-style channel thinking operates on a different layer from the sampling and reconstruction processes we are discussing here. It's more relevant to how discrete pixel values are coded, or more elaborate compression mechanisms which exploit coherence in the image.