TY - JOUR
T1 - Low-Rank Matrix Completion with Poisson Observations via Nuclear Norm and Total Variation Constraints
AU - Qiu , Duo
AU - K. Ng , Michael
AU - Zhang , Xiongjun
JO - Journal of Computational Mathematics
VL - 6
SP - 1427
EP - 1451
PY - 2024
DA - 2024/11
SN - 42
DO - http://doi.org/10.4208/jcm.2309-m2023-0041
UR - https://global-sci.org/intro/article_detail/jcm/23503.html
KW - Low-rank matrix completion, Nuclear norm, Total variation, Poisson observations.
AB - <p style="text-align: justify;">In this paper, we study the low-rank matrix completion problem with Poisson observations, where only partial entries are available and the observations are in the presence
of Poisson noise. We propose a novel model composed of the Kullback-Leibler (KL) divergence by using the maximum likelihood estimation of Poisson noise, and total variation
(TV) and nuclear norm constraints. Here the nuclear norm and TV constraints are utilized to explore the approximate low-rankness and piecewise smoothness of the underlying
matrix, respectively. The advantage of these two constraints in the proposed model is that
the low-rankness and piecewise smoothness of the underlying matrix can be exploited simultaneously, and they can be regularized for many real-world image data. An upper error
bound of the estimator of the proposed model is established with high probability, which is
not larger than that of only TV or nuclear norm constraint. To the best of our knowledge,
this is the first work to utilize both low-rank and TV constraints with theoretical error
bounds for matrix completion under Poisson observations. Extensive numerical examples
on both synthetic data and real-world images are reported to corroborate the superiority
of the proposed approach.</p>