  Aiming at separating the cartoon and texture layers from an image,
cartoon-texture decomposition approaches resort to image priors to model
cartoon and texture respectively. In recent years, patch recurrence has emerged
as a powerful prior for image recovery. However, the existing strategies of
using patch recurrence are ineffective to cartoon-texture decomposition, as
both cartoon contours and texture patterns exhibit strong patch recurrence in
images. To address this issue, we introduce the isotropy prior of patch
recurrence, that the spatial configuration of similar patches in texture
exhibits the isotropic structure which is different from that in cartoon, to
model the texture component. Based on the isotropic patch recurrence, we
construct a nonlocal sparsification system which can effectively distinguish
well-patterned features from contour edges. Incorporating the constructed
nonlocal system into morphology component analysis, we develop an effective
method to both noiseless and noisy cartoon-texture decomposition. The
experimental results have demonstrated the superior performance of the proposed
method to the existing ones, as well as the effectiveness of the isotropic
patch recurrence prior.
