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Continuous curvelet transform. I: Resolution of the wavefront set. (English) Zbl 1086.42022
The authors introduce the continuous curvelet transform and study its applications to the analysis of singularities. Under admissibility conditions for two window functions, they give a reproducing formula similar to that for the continuous wavelet transform. Then they show how the decay of the continuous curvelet transform can be used to characterize singularities of functions in various forms: point singularity, linear singularity, polygonal singularity, curvilinear singularity, and in general the singular support.

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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