Variational Inference based sparse representation model for lost spectrum recovery

Multi-band signal level fusion technology is capable of dealing with discontinuity of available bandwidth caused by frequency resources limitation and jamming signals. However, multi-band signal level fusion faces the challenge of lost spectrum recovery. Existing parametric modeling approaches for lost spectrum recovery suffer from high sidelobes in range profile. To address this issue, a variational inference algorithm is proposed. Specifically, the sparse representation model of multi-band echo is constructed based on geometrical theory of diffraction (GTD) model firstly. To drive the insignificant components to exact zero, a spike-and-slab prior, which is a mixture of a Gaussian distribution and a Dirac delta function, is imposed on the weight vector. Nonetheless, the hybrid mechanism of spike-and-slab prior leads to a posterior distribution that is analytically intractable. Consequently, variational inference is employed to approximate the true posterior with tractable distributions. Then the maximum a posteriori (MAP) estimate is re-calculated to finally recover the lost spectrum. Simulation results demonstrate that the proposed algorithm effectively recovers lost spectrum under diverse spectral loss patterns and scattering center distributions, confirming its generalizability. Compared with lost spectrum recovery approaches based on commonly used all-pole model and sparse Bayesian learning (SBL), the proposed algorithm achieves lower Integrated Sidelobe Ratio (ISLR) of the high-resolution range profile (HRRP) derived from reconstructed full-band echo while exhibiting enhanced robustness against noise interference.