We analyze the detection and classification of singularities of functions @math , where @math and @math . It will be shown how the set @math can be extracted by a continuous shearlet transform associated with compactly supported shearlets. Furthermore, if @math is a @math dimensional piecewise smooth manifold with @math or @math , we will classify smooth and non-smooth components of @math . This improves previous results given for shearlet systems with a certain band-limited generator, since the estimates we derive are uniform. Moreover, we will show that our bounds are optimal. Along the way, we also obtain novel results on the characterization of wavefront sets in @math dimensions by compactly supported shearlets. Finally, geometric properties of @math such as curvature are described in terms of the continuous shearlet transform of @math .
Shearlet tight frames have been extensively studied in recent years due to their optimal approximation properties of cartoon-like images and their unified treatment of the continuum and digital settings. However, these studies only concerned shearlet tight frames generated by a band-limited shearlet, whereas for practical purposes compact support in spatial domain is crucial.