In the process of spectrum sensing applied to wireless communications, it is possible to build interference maps based on acquired power spectral values. This allows the characterization of spectral occupation, which is crucial to take management spectrum decisions. However, the amount of information both in the space and frequency domains that needs to be processed generates an enormous amount of data with high transmission delays and high memory requirements. Meanwhile, compressive sensing is a technique that allows the reconstruction of sparse or compressible signals using fewer samples than those required by the Nyquist criterion. This paper presents a new model that uses compressed multispectral sampling for spectrum sensing. The aim is to reduce the number of data required for the storage and the subsequent construction of power spectral maps with geo-referenced information in different frequency bands. This model is based on architectures that use compressive sensing to analyze multispectral images. The operation of a centralized manager is presented in order to select the power data of different sensors by binary patterns. These sensors are located in different geographical positions. The centralized manager reconstructs a data cube with the transmitted power and frequency of operation of all the sensors based on the samples taken and applying multispectral sensing techniques. The results show that this multispectral data cube can be built with 50% of the samples generated by the devices, and the spectrum cartography information can be stored using only 6.25% of the original data.