非下采样图滤波器组的设计方法
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摘要
针对图滤波器组中难以准确定义一般图信号下采样运算的问题,提出了非下采样图滤波器组的设计方法。首先,采用样条滤波器作为分析滤波器组。然后,通过两种不同的方法设计综合滤波器组,其中,算法一利用顶点域的完全重构条件,构造出综合滤波器组;算法二从子带滤波器的频谱特性考虑,采用带约束优化算法设计综合滤波器组。两种方法可设计得到完全重构的两通道非下采样图滤波器组。最后,在两通道非下采样图滤波器组的基础上,采用级联的方式构造出具有多分辨分析特性的多通道非下采样图滤波器组。仿真结果表明,所提出的非下采样图滤波器组具备完全重构特性。并且,与已有的图滤波器组相比,设计所得的多通道非下采样图滤波器组具有更好的去噪性能。
In order to overcome the problem that it is difficult to accurately define the downsampling operation for a generalized graph signal in graph filter banks, this paper focuses on the design algorithm of nonsubsampled graph filter banks. Firstly, the spline filters are taken as the analysis filter banks. Then, two different methods are proposed to construct the synthesis filter banks.In the first algorithm, the synthesis filter banks can be constructed with the perfect reconstruction conditions in vertex domain. By taking into account the frequency of the subband filters in the second algorithm, the synthesis filter banks are designed by solving a constrained optimization problem involving the spectrum characteristics of the filters. The design methods can lead to two channel nonsubsampled graph filter banks with perfect reconstruction. Finally, taking the two channel nonsubsampled graph filter banks as a basic building block, multichannel nonsubsampled graph filter banks are constructed, which can realize multiresolution analysis of graph signal through cascading. Simulation results show that the designed nonsubsampled graph filter banks have perfect reconstruction property. Furthermore, the designed multichannel nonsubsampled graph filter banks have better denoising performance than the existing graph filter banks.
In order to overcome the problem that it is difficult to accurately define the downsampling operation for a generalized graph signal in graph filter banks, this paper focuses on the design algorithm of nonsubsampled graph filter banks. Firstly, the spline filters are taken as the analysis filter banks. Then, two different methods are proposed to construct the synthesis filter banks.In the first algorithm, the synthesis filter banks can be constructed with the perfect reconstruction conditions in vertex domain. By taking into account the frequency of the subband filters in the second algorithm, the synthesis filter banks are designed by solving a constrained optimization problem involving the spectrum characteristics of the filters. The design methods can lead to two channel nonsubsampled graph filter banks with perfect reconstruction. Finally, taking the two channel nonsubsampled graph filter banks as a basic building block, multichannel nonsubsampled graph filter banks are constructed, which can realize multiresolution analysis of graph signal through cascading. Simulation results show that the designed nonsubsampled graph filter banks have perfect reconstruction property. Furthermore, the designed multichannel nonsubsampled graph filter banks have better denoising performance than the existing graph filter banks.
引文
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[2]NARANG S K,CHAO Y H,ORTEGA A.Graph-wavelet filterbanks for edge-aware image processing[C].IEEEStatistical Signal Processing Workshop(SSP),Ann Arbor,MI,USA,2012:141-144.
[3]CHAO Y H,ORTEGA A,YEA S.Graph-based lifting transform for intra-predicted video coding[C].IEEE International Conference on Acoustics,Speech and Signal Process ing(ICASSP),Shanghai,China,2016:1140-1144.
[4]ONUKI M,ONO S,YAMAGISHI M,et al.Graph signal denoising via trilateral filter on graph spectral domain[J].IEEE Transactions on Signal and Information Processing Over Networks,2016,2(2):137-148.
[5]NARANG S K,ORTEGA A.Perfect reconstruction twochannel wavelet filter banks for graph structured data[J].IEEE Transactions on Signal Processing,2012,60(6):2786-2799.
[6]NARANG S K,ORTEGA A.Compact support biorthogonal wavelet filterbanks for arbitrary undirected graphs[J].IEEETransactions on Signal Processing,2013,61(19):4673-4685.
[7]JIANG J Z,ZHOU F,SHUI P L.Optimization design of two-channel biorthogonal graph filter banks[J].Circuits,Sys tems,and Signal Processing,2016,35(2):685-692.
[8]TANAKA Y,SAKIYAMA A.M-channel oversampled graph filter banks[J].IEEE Transactions on Signal Processing,2014,62(14):3578-3590.
[9]蒋俊正,刘松辽,欧阳缮.一种设计M通道双正交过采样图滤波器组的新算法[J].电子与信息学报,2017,39(12):2970-2975.
[10]EKAMBARAM V N,FANTI G C,AYAZIFAR B,et al.Spline-like wavelet filterbanks for multiresolution analysis of graph-structured data[J].IEEE Transactions on Signal and Information Processing Over Networks,2015,1(4):268-278.
[11]NGUYEN H Q,DO M N.Downsampling of signals on graphs via maximum spanning trees[J].IEEE Transactions on Signal Processing,2015,63(1):182-191.