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arXiv · 1703.00303

Higher order analysis of the geometry of singularities using the Taylorlet transform

Thomas Fink
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Abstract

We consider an extension of the continuous shearlet transform which additionally uses higher order shears. This extension, called the Taylorlet transform, allows for a detection of the position, the orientation, the curvature and other higher order geometric information of singularities. Employing the novel vanishing moment conditions of higher order, $\int_\mathbb{R} g(t^k)t^m dt=0$, on the analyzing function, we can show that the Taylorlet transform exhibits different decay rates for decreasing scales depending on the choice of the higher order shearing variables. This enables a more robust detection of the geometric information of singularities. Furthermore, we present a construction that yields analyzing functions which fulfill vanishing moment conditions of different orders simultaneously.

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Thomas Fink. 2017-03-01. Higher order analysis of the geometry of singularities using the Taylorlet transform. https://arxiv.org/abs/1703.00303

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