  In this article, we consider the stochastic Cahn--Hilliard equation driven by
multiplicative space-time white noise with diffusion coefficient of sublinear
growth. By introducing the spectral Galerkin method, we first obtain the
well-posedness of the approximated equation in finite dimension. Then with the
help of the semigroup theory and the factorization method, the approximation
processes is shown to possess many desirable properties. Further, we show that
the approximation process is strongly convergent in certain Banach space via
the interpolation inequality and variational approach. Finally, the global
existence and regularity estimate of the unique solution process are proven by
means of the strong convergence of the approximation process.
