Sharpest Images With "Lucky" Telescope
Imaging with the shutter closed measures a different source of noise known as dark current (thermal noise of the ccd will cause a small number of free electrons rather than those freed by incoming photons). This noise is proportional to the length of the exposure, unlike readout noise which is a single constant factor.
As far as I know (I'm just a theorist), it is impossible to remove readout noise, since it is affected by the actual distribution of electrons on the ccd image. Someone who actually deals with astronomical imaging should feel free to correct me here.