On Detection-Directed Estimation Approach On Detection-Directed Estimation Approach for Noisy Compressive Sensing

In this paper, we investigate a Bayesian sparse reconstruction algorithm called compressive sensing via Bayesian support detection (CS-BSD). This algorithm is quite robust against measurement noise and achieves the performance of an minimum mean square error (MMSE) estimator that has support knowledge beyond a certain SNR thredhold. The key idea behind CS-BSD is that reconstruction takes a detection-directed estimation structure consisting of two parts: support detection and signal value estimation. Belief propagation (BP) and a Bayesian hypothesis test perform support detection and an MMSE estimator finds the signal values belonging to the support set. CS-BSD converges faster than other BP-based algorithms and it can be converted to an parallel architecture to become much faster. Numerical results are provided to verify the superiority of CS-BSD, compared to recent algorithms.