  This paper introduces the synchrosqueezed curvelet transform as an optimal
tool for 2D mode decomposition of wavefronts or banded wave-like components.
The synchrosqueezed curvelet transform consists of a generalized curvelet
transform with application dependent geometric scaling parameters, and a
synchrosqueezing technique for a sharpened phase space representation. In the
case of a superposition of banded wave-like components with well-separated
wave-vectors, it is proved that the synchrosqueezed curvelet transform is
capable of recognizing each component and precisely estimating local
wave-vectors. A discrete analogue of the continuous transform and several
clustering models for decomposition are proposed in detail. Some numerical
examples with synthetic and real data are provided to demonstrate the above
properties of the proposed transform.
