Spectrum mapping has been increasingly important in various wireless communication applications, such as spectrum management, network planning, power control, dynamic spectrum access etc. In this letter, we consider the problem of time-varying spectrum situation map reconstruction using a small amount of sampled data. In contrast to traditional assumption that the statistical signal propagation model is known, we infer spatial propagation characteristics from the spectrum data. Then, a greedy optimization is applied to calculate the sampling locations with the reduced spatial spectrum situation basis representation, which also converts the original underdetermined problem of spectrum situation recovery into a least squares problem with spatial smoothness constraint, thus greatly reducing the matrix operations. Simulations confirm the superiority of our proposed algorithm in reconstruction performance and computational efficiency in online spectrum mapping tasks.