Dynamic re-use of licensed bands under the hierarchical spectrum access paradigm calls for innovative network-level sensing algorithms for spectrum opportunity awareness in the frequency, time, and space dimensions. Toward this direction, the present paper develops a distributed spectrum sensing algorithm whereby cognitive radios (CRs) cooperate to localize active primary user (PU) transmitters, and estimate their transmit-power spectral densities. The sensing scheme relies on a parsimonious linear system model that accounts for two forms of sparsity: one due to the narrow-band nature of PU transmissions compared to the large swath of monitored frequencies; and another one emerging when employing a spatial grid of candidate PU locations. Capitalizing on this dual sparsity, and combining the merits of Lasso, group Lasso, and total least-squares (TLS), a group sparse (GS) TLS problem is formulated to obtain hierarchically-sparse model estimates, and cope with model uncertainty induced by channel randomness, and grid-induced model offsets. The GS-TLS problem is collaboratively solved by the CRs in a distributed fashion, using only local message exchanges among neighboring nodes. In spite of the non-convexity of the GS-TLS criterion, the novel distributed algorithm has guaranteed convergence to (at least) a locally optimal solution. The analytical findings are corroborated by numerical tests.