Low-rank matrix factorization is a kind of machine learning algorithm. In recent years, the algorithm has received
extensive attention in the problem of seismic data reconstruction. Much research related to model building and numerical
calculations has been published. However, the exact solution of low-rank matrix factorization requires the regularization parameters,
and the regularization parameters are directly related to the statistical parameters such as the mean and variance of the
decomposed seismic data. But these parameters cannot be obtained precisely because of missing data and random noise. In order
to solve this problem, this paper introduces the Bayesian probabilistic matrix factorization algorithm, which simulates the mean
and variance randomly and calculates the optimal reconstruction result by calculating the probability density function. Synthetic
seismic data and real seismic data tests indicate that the proposed method could improve the accuracy and stability of seismic
data reconstruction.
Key words：
data reconstruction; machine learning; low-rank matrix factorization; Bayes’s theorem; Markov chain Monte Carlo
