  In this paper, we present an image separation method for separating images
into point- and curvelike parts by employing a combined dictionary consisting
of wavelets and compactly supported shearlets utilizing the fact that they
sparsely represent point and curvilinear singularities, respectively. Our
methodology is based on the very recently introduced mathematical theory of
geometric separation, which shows that highly precise separation of the
morphologically distinct features of points and curves can be achieved by
$\ell^1$ minimization. Finally, we present some experimental results showing
the effectiveness of our algorithm, in particular, the ability to accurately
separate points from curves even if the curvature is relatively large due to
the excellent localization property of compactly supported shearlets.
