Binary sparse signal recovery algorithms based on logic observation

Binary observation has been widely reported in the literature to localize or track moving objects due to its simple realization and good performance in improving energy efficiency. However, with the implementation of logic operators, the new observation models are out of the range of standard compressive sensing context, and thus lack of effective recovery algorithm. The purpose of this paper is to develop effective recovery algorithms and analyze their performance. Two kinds of recovery algorithms are developed and they are inspired from the matching pursuit method and Bayesian method, respectively. Theoretical conditions are also formulated to guarantee the successful recovery and the proposed algorithms are verified by a series of numerical experiments. Moreover, a construction method for the measurement matrix is also proposed, which is essential for model design. It is hoped that the proposed theories and algorithms can make contribution to the related applications of pattern recognition.