A cooperative approach to the sensing task of wireless cognitive radio (CR) networks is introduced based on a spatial model of the power spectrum density (PSD). The model entails a basis expansion of the PSD in frequency, weighted by unknown spatial functions that are estimated from CR measurements. A novel model estimator is developed using a least-squares (LS) criterion regularized with a smoothing penalty. The estimator yields a finitely-parameterized two-dimensional surface spanned by thin-plate splines, which approximates the distribution of power in space. An online PSD tracker is also developed for slowly time-varying power spectra. Different from existing approaches to interference spectrum cartography, the novel sensing scheme neither requires knowledge of second-order spatial statistics, nor it relies on stationarity assumptions.