Sharpening at that level is usually done with a deconvolution sharpener, such as the Smart Sharpen filter in Photoshop/Elements (or at higher radii, using a plugin like Topaz Labs InFocus). Unlike the usual sharpening tools like Unsharp Mask, which are just edge/contrast enhancers, deconvolution sharpeners attempt to compute what the data would have looked like with some amount of blur removed (that is, if the lens were perfect).
When you apply deconvolution sharpening at higher radii, you can extract detail from pictures that are badly out of focus or remove some amount of motion blur, usually at the expense of producing some ugly artifacts in parts of the picture that aren't the subject of interest (both bokeh regions and things that might have been in focus already will suffer).
When you use deconvolution sharpening at a low radius, especially under 1 pixel, it can largely overcome the effects of antialiasing (optical low pass) filters, Bayer-type colour filter arrays, and minor imperfections in the lens. It won't make things "pop" the way that unsharp masking will, since it's not so much about enhancing existing contrast as determining where the areas of contrast would have been in a more perfect optical and image recording system. You would still need to perform the same level of creative and output sharpening to get the "same" picture out of your workflow (for some value of "same"), but the final result can look like you've significantly upgraded your camera or lens.
(Higher radius deconvolution, at or just above one pixel — the sort of thing you might use a plugin for — works especially well for older cameras with less than 10MP resolution and the heavy AA filters of the period, as well as on moderately upscaled images, such as you get when you choose "the resolution higher than your camera actually provides" option in the Adobe Camera Raw or Lightroom output options.)