  The population of Low Surface Brightness (LSB) galaxies is crucial for
understanding the extremes of galaxy formation and evolution of the universe.
As LSB galaxies are mostly rich in gas (HI), the alpha.40-SDSS DR7 sample is
absolutely one of the best survey combinations to select a sample of them in
the local Universe. Since the sky backgrounds are systematically overestimated
for galaxy images by the SDSS photometric pipeline, particularly for luminous
galaxies or galaxies with extended low surface brightness outskirts, in this
paper, we above all estimated the sky backgrounds of SDSS images in the
alpha.40-SDSS DR7 sample, using a precise method of sky subtraction. Once
subtracting the sky background, we did surface photometry with the Kron
elliptical aperture and fitted geometric parameters with an exponential profile
model for each galaxy image. Basing on the photometric and geometric results,
we further calculated the B-band central surface brightness, mu_{0}(B), for
each galaxy and ultimately defined a sample of LSB galaxies consisting of 1129
galaxies with mu_{0}(B) > 22.5 mag arcsec^{-2} and the minor-to-major axis
ratio b/a > 0.3. This HI-selected LSB galaxy sample from the alpha.40-SDSS DR7
is a relatively unbiased sample of gas-rich and disk-dominated LSB galaxies,
which is complete both in HI observation and the optical magnitude within the
limit of SDSS DR7 photometric survey. We made analysis on optical and radio
21cm HI properties of this LSB galaxy sample. Additionally, we statistically
investigated the environment of our LSB galaxies, and found that up to 92% of
the total LSB galaxies have less than 8 neighbouring galaxies, which strongly
evidenced that LSB galaxies prefer to reside in the low-density environment.
