TY - JOUR
T1 - Fast and robust rank-one matrix completion via maximum correntropy criterion and half-quadratic optimization
AU - Wang, Zhi-Yong
AU - So, Hing Cheung
AU - Liu, Zhaofeng
PY - 2022/9
Y1 - 2022/9
N2 - Matrix completion refers to seeking a low-rank matrix to match an incomplete matrix and fill its missing entries, and is an important topic because many real-world data can be modeled as low-rank matrices. Most existing schemes rely on ℓ2-norm minimization and hence are not robust to outliers. Even the ℓ1-norm based robust matrix completion algorithms proposed in the literature have poor recovery performance for large gross errors, and require knowing the matrix rank, which is difficult to accurately determine in practice. In this paper, we devise a robust and fast rank-one matrix completion algorithm via combining the maximum correntropy criterion (MCC) and half-quadratic (HQ) optimization theory. The MCC, i.e., minimizing the Welsch cost function, can resist the gross errors but it is non-convex. While HQ optimization can transform the Welsch cost function into a quadratic form, making the resultant optimization problem easy to solve. Furthermore, an adaptive kernel width strategy is derived and there are no tunable parameters except for the termination conditions in our algorithm. Computer simulations using synthetic data and experimental results of real-world images demonstrate that the developed method achieves accurate recovery performance and high computational efficiency.
AB - Matrix completion refers to seeking a low-rank matrix to match an incomplete matrix and fill its missing entries, and is an important topic because many real-world data can be modeled as low-rank matrices. Most existing schemes rely on ℓ2-norm minimization and hence are not robust to outliers. Even the ℓ1-norm based robust matrix completion algorithms proposed in the literature have poor recovery performance for large gross errors, and require knowing the matrix rank, which is difficult to accurately determine in practice. In this paper, we devise a robust and fast rank-one matrix completion algorithm via combining the maximum correntropy criterion (MCC) and half-quadratic (HQ) optimization theory. The MCC, i.e., minimizing the Welsch cost function, can resist the gross errors but it is non-convex. While HQ optimization can transform the Welsch cost function into a quadratic form, making the resultant optimization problem easy to solve. Furthermore, an adaptive kernel width strategy is derived and there are no tunable parameters except for the termination conditions in our algorithm. Computer simulations using synthetic data and experimental results of real-world images demonstrate that the developed method achieves accurate recovery performance and high computational efficiency.
KW - Adaptive kernel
KW - Half-quadratic optimization
KW - Maximum correntropy
KW - Rank-one
KW - Robust matrix completion
UR - http://www.scopus.com/inward/record.url?scp=85128332939&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85128332939&origin=recordpage
U2 - 10.1016/j.sigpro.2022.108580
DO - 10.1016/j.sigpro.2022.108580
M3 - RGC 21 - Publication in refereed journal
SN - 0165-1684
VL - 198
JO - Signal Processing
JF - Signal Processing
M1 - 108580
ER -