Radio maps have experienced their success in ap-plications of wireless communications for years by offeringmetrics of radio frequency (RF) information, e.g., power spectraldensity (PSD), within a geographical region of interest. Spectrumcartography technique constructs radio maps to expand theabilities of RF awareness. However, seldom of existing methodsaim at constructing radio maps by utilizing multiple domains in-formation. In this paper, a novel framework inspired by dynamiccompressed sensing (DCS) has been proposed firstly to solve thisproblem. This flexible framework first to apply joint group-Lassofor PSD map construction based on the different sparse patternsbetween space and frequency domains as well as innovativelyutilizes transmitters’ mobility patterns for support prediction ofDCS. Simulation experiments have been processed to assess theperformance of methods within the proposed framework andframework’s superiority has been proven.