A space-based method for the generation of a Schwartz function with infinitely many generalized vanishing moments with applications in image processing
Provides a theoretical tool for image processing to detect curvature and higher-order geometric information, but the impact is incremental as it extends existing shearlet-based methods.
The paper constructs a function with infinitely many generalized vanishing moments, enabling robust detection of higher-order geometric features (e.g., curvature) in singularities via the Taylorlet transform. The construction yields an explicit formula with connections to q-calculus and the Euler function.
In this article we construct a function with infinitely many vanishing (generalized) moments. This is motivated by an application to the Taylorlet transform which is based on the continuous shearlet transform. It can detect curvature and other higher order geometric information of singularities in addition to their position and the direction. For a robust detection of these features a function with higher order vanishing moments, $\int_\mathbb{R} g(x^k)x^m dx = 0$, is needed. We show that the presented construction produces an explicit formula of a function with infinitely many vanishing moments of arbitrary order and thus allows for a robust detection of certain geometric features. The construction has an inherent connection to q-calculus, the Euler function and the partition function.