This paper presents a novel algorithm to estimate the power spectral density (PSD) of stationary broadband noise disturbances in audio recordings. The proposed algorithm estimates the noise PSD as the mean value of an exponential distribution which corresponds to the truncated periodogram coefficients of the disturbed audio signal. An evaluation with a large number of speech and music test signals shows that a high PSD estimation accuracy can be obtained for a wide range of signal-to-noise ratios, allowing for unsupervised operation and thus constituting an important part of a fully automatic broadband noise restoration system for audio archives.