  Continuum fitting is an important aspect of Lyman-alpha forest science, since
errors in the estimated optical depths scale with the fractional continuum
error. However, traditional methods of estimating continua in noisy and
moderate-resolution spectra (S/N < 10 pixel^-1 and R ~ 2000, respectively, such
as SDSS) using power-law extrapolation or the mean spectrum, achieve no better
than ~ 10-15% RMS accuracy. To improve on this, we introduce mean-flux
regulated/principal component analysis (MF-PCA) continuum fitting. In this
technique, PCA fitting is carried out redwards of the quasar Lyman-alpha line
in order to provide a prediction for the shape of the Lyman-alpha forest
continuum. The slope and amplitude of this continuum prediction is then
corrected using external constraints for the Lyman-alpha forest mean-flux. From
tests on mock spectra, we find that MF-PCA reduces the errors to 8% RMS in S/N
~ 2 spectra, and < 5% RMS in spectra with S/N > 5. The residual Fourier power
in the continuum is decreased by a factor of a few in comparison with dividing
by the mean continuum, enabling Lyman-alpha flux power spectrum measurements to
be extended to ~2x larger scales. Using this new technique, we make available
continuum fits for 12,069 z>2.3 Lyman-alpha forest spectra from SDSS DR7 for
use by the community. This technique is also applicable to future releases of
the ongoing BOSS survey, which is obtaining spectra for ~ 150,000 Lyman-alpha
forest spectra at low signal-to-noise (S/N ~ 2).
