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Non-downsampled graph filter bank design method based on convex optimization

A filter bank, non-subsampling technology, applied in design optimization/simulation, instrumentation, calculation, etc., can solve the problem of difficult sampling operation of graph filter bank, and achieve the effect of good denoising performance

Active Publication Date: 2018-04-17
GUILIN UNIV OF ELECTRONIC TECH
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  • Description
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  • Application Information

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Problems solved by technology

[0005] What the present invention aims to solve is the problem that the current graph filter bank design method is difficult to accurately define the graph signal downsampling operation of a general graph, and provides a non-downsampled graph filter bank design method based on convex optimization

Method used

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  • Non-downsampled graph filter bank design method based on convex optimization
  • Non-downsampled graph filter bank design method based on convex optimization
  • Non-downsampled graph filter bank design method based on convex optimization

Examples

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example 1

[0073] The magnitude response of the two-channel non-subsampling filter bank obtained by the direct construction method in the present invention is as follows image 3 As shown in (a), the reconstruction error is zero and the resulting filter bank is fully reconstructed. The parameters of the two-channel non-subsampled filter bank in the optimal design method are set to: L h0 = 2, L h1 = 2, L g0 =5,L g1 =5,λ s0 = 1.5, λ s1 = 0.6, α = 1, β = 0.1, ε r =10- 14 , the resulting two-channel non-subsampling filter bank is approximately completely reconstructed, and the reconstruction error PE=9.0927×10- 14 , the reconstructed signal-to-noise ratio SNR=274.45dB, the amplitude response is as follows image 3 (b) shown. The experimental comparison shows that the non-subsampled image filter bank designed by the direct construction method has better reconstruction characteristics than the non-subsampled image filter bank designed by the optimal design method, and the synthetic fi...

example 2

[0075] Using the graph filter bank designed in Example 1, the Minnesota traffic graph is denoised using the hard threshold method. The input noise graph signal f n First perform normalized preprocessing f=D 12 f n , the output signal after denoising Reverse processing D is the degree matrix of the graph. In this paper, the two-channel non-subsampled graph filter bank processes the high-frequency subband coefficients f 1 , as in the existing ones, the hard threshold is τ=3σ, and σ is the noise standard deviation. The three-channel non-downsampled image filter bank processes different high-frequency sub-band coefficients with different hard thresholds, and processes the high-frequency sub-band coefficient f 01 , verified by experiments, the hard threshold is τ=1.2σ, ​​and the high-frequency sub-band coefficient f is processed 1 , the hard threshold takes τ=3σ. When σ=1 / 2, use existing method 1 (critically sampled biorthogonal graph filter bank) and existing method 2 (M ...

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Abstract

The present invention discloses a non-downsampled graph filter bank design method based on convex optimization. The direct construction method and the optimization method are used to design the non-downsampled graph filter bank; and at the same time, the spectral characteristics and completeness reconstruction condition of the graph filter bank are fully considered. In the denoising simulation experiment of the graph signal, compared with the prior art, the denoising performance of the non-downsampled graph filter bank designed by the method disclosed by the present invention is better.

Description

technical field [0001] The invention relates to the technical field of graph filter banks in the field of graph signal processing, in particular to a design method of a non-subsampling graph filter bank based on convex optimization. Background technique [0002] In domains such as networking, computer vision, and high-dimensional cloud data, graphs provide a flexible model to represent data. With the development of graph signal processing, more and more scholars are engaged in research work in the field of graph signal processing. Graph signal processing extends many concepts and theories in traditional signal processing to the graph structure, and derives important concepts such as graph Fourier transform. Graph signals can represent both small-scale data signals and large-scale data signals. Since large-scale graphs have a large number of nodes and edges, graph Fourier transform is a global transformation, which is not suitable for processing large-scale graph signals. T...

Claims

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Application Information

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IPC IPC(8): G06F17/50G06F17/14
CPCG06F17/148G06F30/20
Inventor 蒋俊正杨圣欧阳缮孙希延纪元法刘松辽杨玉琳曹想赵海兵杨杰
Owner GUILIN UNIV OF ELECTRONIC TECH
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