Line spectral estimation: Generalized bilinear modeling and hybrid inference method

• Published in: Signal processing 2022-06, Vol.195, p.108479, Article 108479
• Main Authors: Li, Zhiyan, Zhang, Haochuan
• Format: Article
• Language: English
• Subjects: Belief propagation; Bilinear generalized approximate message passing; Expectation-maximization; Line spectral estimation; Multiple snapshots
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2022.108479

•New algorithm of hybrid inference for line spectral estimation in multi-snapshot context.•Computationally efficient, only cubic complexity per iteration.•Comprehensively effective, approaching the Cramer-Rao bound. This paper studies line spectral estimation, a classical signal processing problem, under the new assumption of lower-resolution quantization and multiple snapshots. We take a Bayesian standpoint to reformulate the problem as regression in the generalized bilinear model, where the two matrices to estimate are stochastic and structurally correlated. We then propose a hybrid inference method that matches the BiG-AMP [1, 2], a high efficient bilinear regressor, with belief propagation [3], the classical sum-product message passing algorithm. To estimate the model order, we further incorporate the hybrid method into the expectation-maximization [4] framework. The algorithm obtained is then verified via extensive Monte Carlo simulations, in which the proposed algorithm comprehensively outperforms the two state-of-the-art methods, MVALSE [5] and MVALSE-EP [6], while keeping its computational complexity at a relatively low level.