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A generalized version of the 2-microlocal frontier prescription. (arXiv:1810.07247v1 [math.CA])
来源于:arXiv
The characterization of local regularity is a fundamental issue in signal and
image processing, since it contains relevant information about the underlying
systems. The 2-microlocal frontier, a monotone concave downward curve in
$\mathbb {R}^2$, provides a complete and profound classification of pointwise
singularity.
In \cite{Meyer1998}, \cite{GuiJaffardLevy1998} and \cite{LevySeuret2004} the
authors show the following: given a monotone concave downward curve in the
plane it is possible to exhibit one function (or distribution) such that its
2-microlocal frontier al $x_0$ is the given curve.
In this work we are able to unify the previous results, by obtaining a large
class of functions (or distributions), that includes the three examples
mentioned above, for which the 2-microlocal frontier is the given curve. The
three examples above are in this class.
Further, if the curve is a line, we characterize all the functions whose
2-microlocal frontier at $x_0$ is the given line. 查看全文>>