  The reionization of the Universe, it is believed, occurred by the growth of
ionized regions (bubbles) in the neutral intergalactic medium (IGM). We study
the possibility of detecting these bubbles in radio-interferometric
observations of redshifted neutral hydrogen (HI) 21 cm radiation. The signal 1
mJy will be buried in noise and foregrounds, the latter being at least a few
orders of magnitude stronger than the signal. We develop a visibility based
formalism that uses a filter to optimally combine the entire signal from a
bubble while minimizing the noise and foreground contributions. This formalism
makes definite predictions on the ability to detect an ionized bubble or
conclusively rule out its presence in a radio- interferometric observation. We
make predictions for the currently functioning GMRT and a forthcoming
instrument, the MWA at a frequency of 150 MHz (corresponding to a redshift of
8.5). For both instruments, we show that a 3 sigma detection will be possible
for a bubble of comoving radius R_b > 40 Mpc (assuming it to be spherical) in
100 hrs of observation and R_b 22 Mpc in 1000 hrs of observation, provided the
bubble is at the center of the field of view. In both these cases the filter
effectively removes the expected foreground contribution so that it is below
the signal, and the system noise is the deciding criteria. We find that there
is a fundamental limitation on the smallest bubble that can be detected arising
from the statistical fluctuations in the HI distribution. Assuming that the HI
traces the dark matter we find that it will not be possible to detect bubbles
with R_b < 8 Mpc using the GMRT and R_b < 16 Mpc using the MWA, however large
be the integration time.
