  Image foreground extraction is a classical problem in image processing and
vision, with a large range of applications. In this dissertation, we focus on
the extraction of text and graphics in mixed-content images, and design novel
approaches for various aspects of this problem.
  We first propose a sparse decomposition framework, which models the
background by a subspace containing smooth basis vectors, and foreground as a
sparse and connected component. We then formulate an optimization framework to
solve this problem, by adding suitable regularizations to the cost function to
promote the desired characteristics of each component. We present two
techniques to solve the proposed optimization problem, one based on alternating
direction method of multipliers (ADMM), and the other one based on robust
regression. Promising results are obtained for screen content image
segmentation using the proposed algorithm.
  We then propose a robust subspace learning algorithm for the representation
of the background component using training images that could contain both
background and foreground components, as well as noise. With the learnt
subspace for the background, we can further improve the segmentation results,
compared to using a fixed subspace. Lastly, we investigate a different class of
signal/image decomposition problem, where only one signal component is active
at each signal element. In this case, besides estimating each component, we
need to find their supports, which can be specified by a binary mask. We
propose a mixed-integer programming problem, that jointly estimates the two
components and their supports through an alternating optimization scheme. We
show the application of this algorithm on various problems, including image
segmentation, video motion segmentation, and also separation of text from
textured images.
