一种加权正交匹配追踪的盲多带信号重建方法

为研究多带信号的时域采样点盲重建该多带信号,将信号在适当大的包含其所有频带的频率区间上离散,信号频域重建归结为稀疏信号恢复问题。基于压缩感知恢复所需采样点少且其恢复稀疏信号要求观测矩阵的限制等距常数足够小,提出了一种改善观测矩阵的条件数,从而改善其限制等距常数的加权方法,以及相应的加权正交匹配追踪的盲多带信号重建方法,该方法对一般的稀疏信号恢复也适用。模拟中,对适当大的频率区间,取满足重建误差范围的适当小的离散间隔。模拟结果验证了对盲多带信号重建和一般的稀疏信号的恢复,提出的方法比直接用正交匹配追踪算法在相同条件下有更高的有效重建率。

A reweighted orthogonal matching pursuit method for blind multiband signal reconstruction

Blind multiband signal reconstruction is the reconstruction of the multiband signal from sampling points in the time domain. The signal was discretized over an appropriately large frequency range containing all of its bands, and then signal reconstruction in frequency domain boils down to sparse signal recovery. Based on the fact that fewer sampling points were needed for compressed sensing recovery and the RIC (restricted isometry constant) of the observation matrix was required to be small enough to recover the sparse signal, a reweighted method was proposed to improve the condition number of the observation matrix so as to improve its RIC, as well as a corresponding reweighted OMP (orthogonal matching pursuit) scheme for blind multiband signal reconstruction. The proposed method was also applicable to the recovery of general sparse signals. In simulations, for an appropriately large frequency range, an appropriately small discrete interval satisfying the reconstruction error range was taken. The simulation results verify that for blind multiband signal reconstruction and the recovery of general sparse signals, the reweighted OMP scheme has a higher efficient reconstruction rate than the OMP algorithm directly used under the same conditions.