Compressive measurements detection without reconstruction

In order to improve the computation speed, the topic of compressive sensing (CS) has been widely applied in signal processing domain. In this paper, we proposed a novel algorithm to study the problem of signal detection from the compressive measurements. The proposed method requires no signal reconstruction. When the signal is projected in the sparse domain, we can obtain the sparse vector firstly. Then, we design a new random measurement matrix from a joint random Gaussian matrix and dictionary basis matrix. The proposed detector processes the compressive measurements directly. The threshold is designed according to the different distribution of measurements. Finally, the detector achieves deciding on the presence/absence of the signal. Computer simulations show that the proposed detector can achieve detecting the compressed signal with a high probability whose performance is better than others compressive detection methods. The proposed algorithm can work in low signal-noise-ratio (SNR), which has good performance and well application.