Microlocal filtering with multiwavelet frames

多小波帧的微局部滤波

• 批准号: 13640171
• 负责人: ASHINO Ryuichi
• 金额: $ 2.18万
• 依托单位: Osaka Kyoiku University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640171/
• 关键词: microlocal analysis; wavelet frame; multiwavelet; filter; time frequency analysis; wavelet analysis; image processing; フレーム; ウェーブレット

Our orthonormal multiwavelet bases, which can decompose functions in the Hilbert space L^2(R^n) microlocally, are shown to be a "stepwise" unconditional basis in L^p(R^n) (1<p<∞) and other related spaces. As part of the proof, an elementary proof of the L^p(R^n) version of the sampling theorem with unconditional convergence is given. Finally, an application is given to the expression of some distributions as sums of boundary values of holomorphic functions.Orthogonal multiwavelets, whose Fourier transforms consist of characteristic functions of squares or sectors of annuli, are constructed in the Fourier domain and are shown to satisfy a multiresolution analysis with several choices of scaling functions. Redundant smooth tight wavelet frames are obtained and these nonorthogonal frame wavelets can be generated by two-scale equations from, a multiresolution analysis. Singularities can be localized in position and direction and the original images can be restored from the scarred images.

我们的正交多小波基可以微局部分解希尔伯特空间 L^2(R^n) 中的函数，被证明是 L^p(R^n) (1<p<∞) 中的“逐步”无条件基，并且作为证明的一部分，给出了无条件收敛的采样定理L^p(R^n)版本的基本证明。最后，给出了一些表达式的应用。分布为全纯函数的边界值之和。正交多小波，其傅里叶变换由正方形或圆环扇形的特征函数组成，在傅里叶域中构造，并被证明可以满足具有多种缩放函数选择的多分辨率分析。获得冗余平滑紧小波框架，并且这些非正交框架小波可以通过两尺度方程生成，多分辨率分析可以在位置和方向上定位奇异性以及原始的。可以从伤痕累累的图像中恢复图像。