In this dissertation, we investigate the signal recovery and detection task for compressive sensing and wireless spectrum sensing.First, we investigate the compressive sensing task for the difference frames of videos.Exploiting the clustered property, we design an effective structural aware reconstruction technique that is capable of eliminating isolated nonzero noisy pixels, and promoting undiscovered signal coefficients.Further, we develop a novel optimization based method for the compressive sensing of binary sparse signals. We formulate the reconstruction task as a least square minimization procedure, and propose a novel regularization term based on the weighted sum of ell_1 norm and ell_infty norm.Moreover, we study the compressive sensing for asymmetrical signals.We devise an efficient algorithm that greatly improves the reconstruction quality of asymmetrical sparse signals.Further, we investigate sparse reconstruction of clustered sparse signals with asymmetrical features.We develop a powerful technique that is capable of taking inference of the signal, estimating the mixture density, and exploiting the clustered features.Finally, we investigate the spectrum sensing task for cognitive radio.We develop an eigenvalue based technique that notably improve the primary user detection performance under finite number of sensors and samples.Electrical Engineerin
