The detection bound of the probability of error in compressed sensing using Bayesian approach

• المؤلفون الرئيسيون: Cao, Jiuwen, Lin, Zhiping
• مؤلفون آخرون: School of Electrical and Electronic Engineering
• التنسيق: Conference or Workshop Item
• اللغة: English
• منشور في: 2013
• الموضوعات: DRNTU::Engineering::Electrical and electronic engineering
• الوصول للمادة أونلاين: https://hdl.handle.net/10356/103144; http://hdl.handle.net/10220/16909
• المؤسسة: Nanyang Technological University

In this paper, we consider the theoretical bound of the probability of error in compressed sensing (CS) with the Bayesian approach. In the detection problem, the signal is sparse and is reconstructed from a compressed measurement vector. Utilizing the oracle estimator in CS, we provide a theoretical bound of the probability of error when the noise in CS is white Gaussian noise (WGN). We show that without any additional information in CS, the probability of error obtained using the signal reconstructed by four recovery algorithms: the basis pursuit denoising (BPDN) algorithm, the Dantzig selector, the orthogonal matching pursuit (OMP) method and the compressive sampling matching pursuit (CoSaMP) algorithm is always larger than the derived theoretical bound. Simulation results demonstrate the effectiveness of our result.