  We consider the problem of detecting signals in the rank-one
signal-plus-noise data matrix models that generalize the spiked Wishart
matrices. We show that the principal component analysis can be improved by
pre-transforming the matrix entries if the noise is non-Gaussian. As an
intermediate step, we prove a sharp phase transition of the largest eigenvalues
of spiked rectangular matrices, which extends the Baik-Ben Arous-P\'ech\'e
(BBP) transition. We also propose a hypothesis test to detect the presence of
signal with low computational complexity, based on the linear spectral
statistics, which minimizes the sum of the Type-I and Type-II errors when the
noise is Gaussian.
