Detection with compressive measurements corrupted by sparse errors

Compressed sensing can represent the sparse signal with a small number of measurements compared to Nyquist-rate samples. Considering the high-complexity of reconstruction algorithms in CS, recently compressive detection is proposed, which performs detection directly in compressive domain without reconstruction. Different from existing work that generally considers the measurements corrupted by dense noises, this paper studies the compressive detection problem when the measurements are corrupted by both dense noises and sparse errors. The sparse errors exist in many practical systems, such as the ones affected by impulse noise or narrowband interference. We derive the theoretical performance of compressive detection when the sparse error is either deterministic or random. The theoretical results are further verified by simulations.