The unprocessed HST images presented here today are significantly better than images from ground-based telescopes. Image processing methods promise to generate images which are, for many purposes, even better than the raw images.
These computer algorithms remove the "halos" which can be seen around stars in the unprocessed images. The halos are not really present around the stars; rather, they are the result of the faulty focus of the HST for light which reflects off of the outer edge of the primary mirror. Every object in the images can be seen to have these fuzzy halos.
Fortunately, there is still enough light in the cores of the images that we can readily distinguish individual stars, even in very crowded regions such as the center of this star cluster. That is what makes these images much better than those taken with ground-based telescopes.
The tiny, bright cores also make it possible for us to improve the images using computer image restoration techniques. The basic idea is this: if we know that every star has a little halo, why not just measure the position and brightness of the stars and then subtract the halos from the images? Not only does this produce a cleaner image, but it also makes it easier to detect faint stars which are partially obscured by the haze from nearby, brighter stars.
There are a number of image restoration techniques which are applicable to HST images. A wide variety of different methods give very similar results to those shown in the images here. It is much harder to apply these techniques to images from ground-based telescopes because such images lack the well-defined cores of the HST images and because the atmospheric blurring changes continuously, making it impossible to determine a fixed stellar profile.
There are two factors which limit the accuracy with which we can remove stellar halos using these techniques. First, if we do not know exactly what the halo ought to look like, we cannot subtract it perfectly. This is the primary factor limiting the restored images shown today: our knowledge of the "point spread function" (the image we expect for a star) for this particular color at this particular HST focus setting is imperfect. With more observations we expect to characterize the halos much more accurately, which should allow significantly better restorations.
A more fundamental limit is set by the noise-in the images. Astronomers observe very faint stars by counting the individual particles of light, or photons, which are collected by the telescope. For the faintest stars only a few photons are counted, and there is consequently an inherent uncertainty in the brightness measured for those stars. This counting noise makes it impossible to subtract halos around even the brightest stars perfectly. In fact, even to detect the presence of faint stars amidst the glare created by many overlapping halos may be very difficult or impossible. This is the greatest loss to HST science as a result of the spherical aberration of the telescope mirror: the faintest objects simply cannot be seen through the haze of crowded fields.
On the other hand, these images demonstrate unequivocally that HST can still do excellent science and that HST's wide field, high resolution images, even without image processing, are unrivaled by ground-based telescopes. Furthermore, HST can produce these images in the far ultraviolet, which is absorbed by the atmosphere.