  Many computer vision problems can be posed as learning a low-dimensional
subspace from high dimensional data. The low rank matrix factorization (LRMF)
represents a commonly utilized subspace learning strategy. Most of the current
LRMF techniques are constructed on the optimization problems using L1-norm and
L2-norm losses, which mainly deal with Laplacian and Gaussian noises,
respectively. To make LRMF capable of adapting more complex noise, this paper
proposes a new LRMF model by assuming noise as Mixture of Exponential Power
(MoEP) distributions and proposes a penalized MoEP (PMoEP) model by combining
the penalized likelihood method with MoEP distributions. Such setting
facilitates the learned LRMF model capable of automatically fitting the real
noise through MoEP distributions. Each component in this mixture is adapted
from a series of preliminary super- or sub-Gaussian candidates. Moreover, by
facilitating the local continuity of noise components, we embed Markov random
field into the PMoEP model and further propose the advanced PMoEP-MRF model. An
Expectation Maximization (EM) algorithm and a variational EM (VEM) algorithm
are also designed to infer the parameters involved in the proposed PMoEP and
the PMoEP-MRF model, respectively. The superseniority of our methods is
demonstrated by extensive experiments on synthetic data, face modeling,
hyperspectral image restoration and background subtraction.
