We present a simple algorithm for robust and unsupervised peak detection by determining a noise threshold in isotopically resolved mass spectrometry data. Solving this problem will greatly reduce the subjective and time consuming manual picking of mass spectral peaks and so will prove beneficial in many research applications. The Autopiquer approach uses autocorrelation to test for the presence of (isotopic) structure in overlapping windows across the spectrum. Within each window, a noise threshold is optimized to remove the most unstructured data whilst keeping as much of the (isotopic) structure as possible. This algorithm has been successfully demonstrated for both peak detection and spectral compression on data from many different classes of mass spectrometer and for different sample types and this approach should also be extendible to other types of data that contain regularly spaced discrete peaks.