Compressed Blind Signal Reconstruction Model and Algorithm

The model of inherent connection between underdetermined blind signal separation and compressed sensing (CS) is analyzed first; then, the mathematical model of underdetermined blind signal reconstruction is built using CS. More specifically, the mixing matrix is estimated by exploiting the wavelet packet transform and k-means clustering methods up to permutation and scaling indeterminacy, and then, the measurement matrix and the measurement equation are obtained. To reconstruct the underdetermined sparse source signals, the proposed semi-blind compressed reconstruction algorithm is derived based on the blind signal reconstruction model and compressive sampling matching pursuit (CoSaMP) method. Our simulation results demonstrate that the proposed scheme is effective, irrespective of artificial data or real data. Moreover, the proposed scheme can be adjusted for different applications by modifying the mixing matrix estimation method and CoSaMP method with respect to the correspondence conditions.