Cumulant Slice Reconstruction From Compressive Measurements And Its Application To Line Spectrum Estimation

Higher-order statistics (HOS) estimation hinges on the availability of a huge amount of data records, which causes exceedingly high sampling rates and overwhelming energy consumption for the sampling devices, especially when dealing with wideband signals. To overcome these challenges, this paper develops a novel compressive cumulant slice sensing (CCSS) method that aims to efficiently reconstructing the 1-D diagonal slice of higher-order cumulants under the compressive sensing framework. It first parsimoniously collects data with a properly designed sampler based on the minimal sparse ruler principle, and then accurately reconstructs the 1-D diagonal cumulant slice from those compressive measurements. The reconstructed HOS can be useful in many signal processing tasks, which is illustrated through the task of line spectrum estimation with resilience to colored Gaussian noise at reduced sampling rates.