This paper proposes an extension of the log periodogram regression in perturbed long memory series that accounts for the added noise, also allowing for correlation between signal and noise, which represents a common situation in many economic and financial series. Consistency (for d < 1) and asymptotic normality (for d < 3/4) are shown with the same bandwidth restriction as required for the original log periodogram regression in a fully observable series, with the corresponding gain in asymptotic efficiency and faster convergence over competitors. Local Wald, Lagrange Multiplier and Hausman type tests of the hypothesis of no correlation between the latent signal and noise are also proposed.