Compressive Detection of Random Signals from Sparsely Corrupted Measurements

Compressed sensing (CS) integrates sampling and compression into a single step to reduce the processed data amount. However, the CS reconstruction generally suffers from high complexity. To solve this problem, compressive signal processing (CSP) is recently proposed to implement some signal processing tasks directly in the compressive domain without reconstruction. Among various CSP techniques, compressive detection achieves the signal detection based on the CS measurements. This paper investigates the compressive detection problem of random signals when the measurements are corrupted. Different from the current studies that only consider the dense noise, our study considers both the dense noise and sparse error. The theoretical performance is derived, and simulations are provided to verify the derived theoretical results.