Third-Order Statistics Reconstruction From Compressive Measurements

Estimation of third-order statistics relies on the availability a huge amount data records, which can pose severe challenges collecting hardware in terms considerable storage costs, overwhelming energy consumption, and unaffordably high sampling rate especially when dealing with high-dimensional such as wideband signals. To overcome these challenges, this paper focuses reconstruction cumulants under compressive sensing framework. Specifically, derives transformed linear system that directly connects cross-cumulants measurements to desired statistics. We provide sufficient conditions for lossless via solving simple least-squares, along strongest achievable compression ratio. reduce computational burden, we also propose an approach recover diagonal cumulant slices from measurements, is useful are inference task at hand. All proposed techniques tested extensive simulations. The developed joint estimation able required rates significantly by exploiting structure resulting signal stationarity, even absence any sparsity constraints or cumulants.