  The low-rank matrix completion (LRMC) technology has achieved remarkable
results in low-level visual tasks. There is an underlying assumption that the
real-world matrix data is low-rank in LRMC. However, the real matrix data does
not satisfy the strict low-rank property, which undoubtedly present serious
challenges for the above-mentioned matrix recovery methods. Fortunately, there
are feasible schemes that devise appropriate and effective priori
representations for describing the intrinsic information of real data. In this
paper, we firstly model the matrix data ${\bf{Y}}$ as the sum of a low-rank
approximation component $\bf{X}$ and an approximation error component
$\cal{E}$. This finer-grained data decomposition architecture enables each
component of information to be portrayed more precisely. Further, we design an
overlapping group error representation (OGER) function to characterize the
above error structure and propose a generalized low-rank matrix completion
model based on OGER. Specifically, the low-rank component describes the global
structure information of matrix data, while the OGER component not only
compensates for the approximation error between the low-rank component and the
real data but also better captures the local block sparsity information of
matrix data. Finally, we develop an alternating direction method of multipliers
(ADMM) that integrates the majorization-minimization (MM) algorithm, which
enables the efficient solution of the proposed model. And we analyze the
convergence of the algorithm in detail both theoretically and experimentally.
In addition, the results of numerical experiments demonstrate that the proposed
model outperforms existing competing models in performance.
