Matrix completion from quantized samples via generalized sparse Bayesian learning

The recovery of a low rank matrix from a subset of noisy low-precision quantized samples arises in various applications, such as collaborative filtering, intelligent recommendation and millimeter wave channel estimation with few bit analog-to-digital converters (ADCs). In this paper, a generalized sparse Bayesian learning algorithm (Gr-SBL) combined with expectation propagation (EP) is proposed to solve the matrix completion (MC), termed MC-Gr-SBL. The MC-Gr-SBL automatically estimates the rank, the factors and their covariance matrices, and the noise variance. In addition, MC-Gr-SBL is proposed to solve the two dimensional line spectral estimation problem by incorporating the MUSIC algorithm. Finally, numerical simulations and real data experiments are conducted to verify the effectiveness of the proposed algorithm.