In this letter, we investigate the problem of remote spectrum mapping with inaccessible areas, whose goal is to estimate the spatial power of the unreachable area with a small amount of sampled data in the reachable area. First, we establish a remote compressed spectrum mapping (RCSM) model considering the constraint of unreachable areas. Then, in contrast with traditional random or fixed sampling, we propose an optimization algorithm for sampling location selection within the accessible area, by directly optimizing from the perspective of matrix determination maximization. Its computational complexity is further reduced without loss of performance. Finally, we develop a spatial power estimation algorithm for inaccessible areas based on alternating direction method of multipliers. Numerical results verify the superiority of our RCSM algorithm in estimation performance and computational efficiency.