In this paper, we focus on increasing the spectrum awareness of cognitive radio users through statistical processing of spectrum sensing data, obtained via wideband energy-detection-based sensing techniques. Based on observations over real spectrum power measurements, we advocate the existence of correlation properties in the sensed power of measured neighboring channels and propose an inference methodology for exploiting them towards acquiring a more accurate view of the underlying wireless environment. To highlight the benefits of the proposed correlation-based inference methodology on cognitive radio systems, we emphasize on enhancements of white space discovery and channel selection processes, while we thoroughly discuss the impact of our findings on existing relevant approaches. Based on a systematic wireless spectrum survey in the metropolitan area of Athens, Greece, we validate our proposed methodology and assess the achieved performance improvements through the obtained measurement data, confirming its potential value in future cognitive radio networks.