Virtual ground is a name for a mid-rail reference potential (ground means
reference potential really).
Decoupling goes across the supply, but can here be from virtual ground to each
supply rail. Its purpose in analog circuits is to reduce noise on the supply rails
and reduce the likelyhood of unwanted feedback from amplifier output to inputs
via supply-voltage variation.
White noise is broad-band and reducing bandwidth (such as with a low pass filter)
will reduce noise power in proportion. Noise amplitude is proportional to the square
root of noise power, hence voltage noise is commonly measured in nV/root-Hz
Noise can also be picked up - here shielding of cables and rf-filtering is important.