  Detecting moving objects from ground-based videos is commonly achieved by
using background subtraction techniques. Low-rank matrix decomposition inspires
a set of state-of-the-art approaches for this task. It is integrated with
structured sparsity regularization to achieve background subtraction in the
developed method of Low-rank and Structured Sparse Decomposition (LSD).
However, when this method is applied to satellite videos where spatial
resolution is poor and targets' contrast to the background is low, its
performance is limited as the data no longer fits adequately either the
foreground structure or the background model. In this paper, we handle these
unexplained data explicitly and address the moving target detection from space
as one of the pioneer studies. We propose a technique by extending the
decomposition formulation with bounded errors, named Extended Low-rank and
Structured Sparse Decomposition (E-LSD). This formulation integrates low-rank
background, structured sparse foreground and their residuals in a matrix
decomposition problem. We provide an effective solution by introducing an
alternative treatment and adopting the direct extension of Alternating
Direction Method of Multipliers (ADMM). The proposed E-LSD was validated on two
satellite videos, and experimental results demonstrate the improvement in
background modeling with boosted moving object detection precision over
state-of-the-art methods.
