A new construction of shearlets

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-09-30 DOI:10.1142/s0219025722500217

Pooran Ghaderihasab, Ahmad Ahmadi

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引用次数: 0

Abstract

In order to achieve optimally sparse approximations of signals exhibiting anisotropic singularities, the shearlet systems that are systems of functions generated by one generator with dilation, shear transformation and translation operators applied to it were introduced. In this paper, we will construct the shearlet systems that are not only Parseval frames for $L^{2} (ℝ^{2})$ but they are also obtained from an $A B$ -MRA associated with wavelet multiresolution, and by using this approach, we obtain the corresponding filters for these systems. For this purpose, the tensor product of the corresponding wavelet scaling function and a compact support bump function is used to construct the scaling function associated with the shearlet.

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shearlets的新结构

为了获得具有各向异性奇异性的信号的最优稀疏逼近，引入了shearlet系统，该系统是由一个发生器产生的函数系统，并对其应用了膨胀、剪切变换和平移算子。在本文中，我们将构造L2(∈2)的shearlet系统，它们不仅是Parseval帧，而且是由与小波多分辨率相关的AB-MRA获得的，并利用这种方法获得了这些系统的相应滤波器。为此，使用相应小波尺度函数与紧凑支撑凹凸函数的张量积来构造与shearlet相关的尺度函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Infinite Dimensional Analysis Quantum Probability and Related Topics 数学-统计学与概率论

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： In the past few years the fields of infinite dimensional analysis and quantum probability have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. The number of first-class papers in these fields has grown at the same rate. This is currently the only journal which is devoted to these fields. It constitutes an essential and central point of reference for the large number of mathematicians, mathematical physicists and other scientists who have been drawn into these areas. Both fields have strong interdisciplinary nature, with deep connection to, for example, classical probability, stochastic analysis, mathematical physics, operator algebras, irreversibility, ergodic theory and dynamical systems, quantum groups, classical and quantum stochastic geometry, quantum chaos, Dirichlet forms, harmonic analysis, quantum measurement, quantum computer, etc. The journal reflects this interdisciplinarity and welcomes high quality papers in all such related fields, particularly those which reveal connections with the main fields of this journal.