Using Hart Smith’s, curvelet, and shearlet transforms, we investigate L functions with sufficiently smooth background and present here sufficient and necessary conditions, which include the special case with 1-dimensional singularity line. Specifically, we consider the situation where regularity on a line in a non-parallel direction is much lower than directional regularity along the line in a ...

In this paper we introduce a new localization framework for wavelet transforms, such as the 1D wavelet transform and the Shearlet transform. Our goal is to design nonadaptive window functions that promote sparsity in some sense. For that, we introduce a framework for analyzing localization aspects of window functions. Our localization theory diverges from the conventional theory in two ways. Fi...

Sobolev wavefront sets and 2-microlocal spaces play a key role in describing analyzing the singularities of distributions microlocal analysis solutions partial differential equations. Employing continuous shearlet transform to spaces, this paper we characterize sets, local Hölder distributions/functions. We then establish connections among through transform.

Microseismic noise suppression is widely used in the exploration of unconventional oil and gas resources. The effective microseismic downhole signals have extremely weak energy are contaminated by strong interference, making data processing interpretation difficult. need for high-frequency signal reservation presents a basic problem design methods. represent as continuous reflection event more ...

Abstract Coorbit theory is a powerful machinery that constructs family of Banach spaces, the so-called coorbit spaces , from well-behaved unitary representations locally compact groups. A core feature they can be discretized in way reflects geometry underlying group. Many established function such as modulation Besov Sobolev–Shubin and shearlet are examples spaces. The goal this survey to give ...