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Spectral Mappings for Graph Wavelets
IEEE Transactions on Signal Processing ( IF 5.4 ) Pub Date : 2022-06-13 , DOI: 10.1109/tsp.2022.3182470
David B. Tay 1
Affiliation  

Graph wavelet filters can be used to construct dictionaries of atoms, and signals defined over graphs can be represented as linear combinations of these atoms. These representations can facilitate the development of various signal processing tasks, e.g. denoising or feature extraction. We present here a method to construct these filters, using mappings on simple prototype filters, that readily allows for spectral domain shaping. Two types of spectral maps will be developed in this work. The first type of maps sharpens (increase the frequency selectivity) of the prototype filter. The second type of maps is equivalent to upsampling in the spectral domain, and can be used to construct a’trous like transforms. The a’trous like transform allows for a tree-structured implementation, and is reminiscent of the classical a’trous (with-holes) wavelet transform. The resulting filters, constructed using these maps, are polynomial functions, and can therefore be implemented without the need for any approximation or eigendecomposition. Both non-redundant and redundant frames can be constructed with these filters. A variety of design examples will be presented to demonstrate the versatility of the proposed method. Applications of the filters to non-linear approximation and denoising will also be considered.

中文翻译:

图小波的频谱映射

图形小波滤波器可用于构建原子字典,并且在图形上定义的信号可以表示为这些原子的线性组合。这些表示可以促进各种信号处理任务的开发,例如去噪或特征提取。我们在这里提出了一种构建这些滤波器的方法,使用简单原型滤波器上的映射,很容易实现谱域整形。在这项工作中将开发两种类型的光谱图。第一种类型的映射锐化(增加频率选择性)原型滤波器。第二种映射相当于频谱域中的上采样,可用于构建类似 a'trous 的变换。类似 a'trous 的变换允许树结构的实现,并且让人想起经典的 a'trous (with-holes) 小波变换。使用这些映射构建的结果滤波器是多项式函数,因此可以在不需要任何近似或特征分解的情况下实现。非冗余和冗余帧都可以用这些过滤器构建。将提供各种设计示例来展示所提出方法的多功能性。还将考虑将滤波器应用于非线性逼近和去噪。将提供各种设计示例来展示所提出方法的多功能性。还将考虑将滤波器应用于非线性逼近和去噪。将提供各种设计示例来展示所提出方法的多功能性。还将考虑将滤波器应用于非线性逼近和去噪。
更新日期:2022-06-13
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