Synchrosqueezed Wave Packet Transform for 2D Mode Decomposition

This paper introduces the synchrosqueezed wave packet transform as a method for analyzing two-dimensional images. This transform is a combination of wave packet transforms of a certain geometric scaling, a reallocation technique for sharpening phase space representations, and clustering algorithms for modal decomposition. For a function that is a superposition of several wave-like components with a highly oscillatory pattern satisfying certain separation conditions, we prove that the synchrosqueezed wave packet transform identifies these components and estimates their local wavevectors. A discrete version of this transform is discussed in detail, and numerical results are given to demonstrate the properties of the proposed transform.

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