1. A method for recovering a sparse signal of a finite field, in which a sparse signal recovery device recovers a target signal of the finite field from a measurement signal of the finite field, to which a noise signal is added, the method comprising: updating discrete probability information of a target signal element of the finite field and discrete probability information of a measurement signal element of the finite field by exchanging the discrete probability information of the target signal element with the discrete probability information of the measurement signal element a predetermined number of times, wherein the target signal element and the measurement signal element are related to each other; calculating a final posteriori probability based on a priori probability of the target signal element and the discrete probability information of the measurement signal element, acquired as the exchange result; and recovering the target signal by performing maximum posteriori estimation to maximize the final posteriori probability.