Spectrum resources management of growing demands is a challenging problem and Cognitive Radio (CR) known to be capable of improving the spectrum utilization. Recently, Power Spectral Density (PSD) map is defined to enable the CR to reuse the frequency resources regarding to the area. For this reason, the sensed PSDs are collected by the distributed sensors in the area and fused by a Fusion Center (FC). But, for a given zone, the sensed PSDs by neighbor CR sensors may contain a shared common component for a while. This component can be exploited in the theory of the Distributed Source Coding (DSC) to make the sensors transmission data more compressed. However, uncertain channel fading and random shadowing would lead to varying signal strength at different CRs, even placed close to each other. Hence, existence of some perturbations in the transmission procedure yields to some imperfection in the reporting channel and as a result it degrades the performance remarkably. The main focus of this paper is to be able to reconstruct the PSDs of sensors \textit{robustly} based on the Distributed Compressive Sensing (DCS) when the data transmission is slightly imperfect. Simulation results verify the robustness of the proposed scheme.