Method and apparatus for transmitting sparse signal, and method and apparatus for recovering sparse signal via belief propagation and Bayesian hypothesis test

Disclosed are a method and an apparatus for transmitting a sparse signal, and a method and an apparatus for recovering the sparse signal. The method for recovering a sparse signal by using a sparse signal recovering device that recovers a target signal from a received signal includes receiving a measurement signal with a noise signal from a sparse signal transmitting device which scans a target signal based on a measurement matrix, performing a mutual update procedure in which a likelihood probability is calculated by using a posterior probability of the target signal based on a relation between the target signal and the measurement signal, and the posterior probability is updated by using the likelihood probability, and recovering the target signal by performing maximum a posterior estimation for a final posterior probability output through the mutual update procedure.