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In this work, we introduce a novel approach for determining a joint sparsespectrum from several non-uniformly sampled data sets, where each data set isassumed to have its own, possibly disjoint, and only partially known, samplingtimes. The potential of the proposed approach is illustrated using a spectralestimation problem in paleoclimatology. In this problem, each data pointderives from a separate ice core measurement, resulting in that even though allmeasurements reflect the same periodicities, the sampling times and phasesdiffer among the data sets. In addition, sampling times are only approximatelyknown. The resulting joint estimate exploiting all available data is formulatedusing a sparse reconstruction framework allowing for a reliable and robustestimate of the underlying periodicities. The corresponding misspecifiedCram\'er-Rao lower bound, accounting for the expected sampling uncertainties,is derived and the proposed method is shown to attain the resulting bound whenthe signal to noise ratio is sufficiently high. The performance of the proposedmethod is illustrated as compared to other commonly used approaches using bothsimulated and measured ice core data sets.

Determining Joint Periodicities in Multi-time Data With Sampling Uncertainties