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Magnetoencephalography (MEG) is an advanced imaging technique used to measure the magnetic fields outside the human head produced by the electrical activity inside the brain. Various source localization methods in MEG require the knowledge of the underlying active sources, which are identified by a priori. Common methods used to estimate the number of sources include principal component analysis or information criterion methods, both of which make use of the eigenvalue distribution of the data, thus avoiding solving the time-consuming inverse problem. Unfortunately, all these methods are very sensitive to the signal-to-noise ratio (SNR), as examining the sample extreme eigenvalues does not necessarily reflect the perturbation of the population ones. To uncover the unknown sources from the very noisy MEG data, we introduce a framework, referred to as the intrinsic dimensionality (ID) of the optimal …