  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.
