Binary sparse signal recovery with binary matching pursuit*

In numerous applications from communications and signal processing, we often need to acquire a K-sparse binary signal from sparse noisy linear measurements. In this work, we first develop an algorithm called binary matching pursuit (BMP) to recover the K-sparse binary signal. According to whether the residual vector is explicitly formed or not at each iteration, we develop two implementations of BMP which are respectively called explicit BMP and implicit BMP. We then analyze their complexities and show that, compared to the batch-orthogonal matching pursuit (OMP), which is the fastest implementation of OMP, the improvements of the explicit and implicit BMP algorithms are respectively n/(2K) and K times when some quantities are pre-computed. Finally, we provide sharp sufficient conditions of stable recovery of the support of the sparse signal using mutual coherence and restricted isometry property of the sensing matrix. Simulation tests indicate that the implicit BMP algorithm is around or more than n/(2K) times faster than batch-OMP with around or more than 20% lower rates of missed detection and false alarm.