  Image structure-texture decomposition is a long-standing and fundamental
problem in both image processing and computer vision fields. In this paper, we
propose a generalized semi-sparse regularization framework for image structural
analysis and extraction, which allows us to decouple the underlying image
structures from complicated textural backgrounds. Combining with different
textural analysis models, such a regularization receives favorable properties
differing from many traditional methods. We demonstrate that it is not only
capable of preserving image structures without introducing notorious staircase
artifacts in polynomial-smoothing surfaces but is also applicable for
decomposing image textures with strong oscillatory patterns. Moreover, we also
introduce an efficient numerical solution based on an alternating direction
method of multipliers (ADMM) algorithm, which gives rise to a simple and
maneuverable way for image structure-texture decomposition. The versatility of
the proposed method is finally verified by a series of experimental results
with the capability of producing comparable or superior image decomposition
results against cutting-edge methods.
