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Design Method of Two-Channel Biorthogonal Graph Filter Bank Based on Lifting Structure

A filter bank and design method technology, applied in the direction of instruments, calculations, special data processing applications, etc., can solve the problem of not being able to take into account the frequency characteristics of sub-band filters

Active Publication Date: 2018-04-24
GUILIN UNIV OF ELECTRONIC TECH
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Problems solved by technology

However, there is currently only one method for the design of this type of structure, but because this method is based on polynomial decomposition, the frequency characteristics of the sub-band filter cannot be considered in the design

Method used

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  • Design Method of Two-Channel Biorthogonal Graph Filter Bank Based on Lifting Structure
  • Design Method of Two-Channel Biorthogonal Graph Filter Bank Based on Lifting Structure
  • Design Method of Two-Channel Biorthogonal Graph Filter Bank Based on Lifting Structure

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Embodiment Construction

[0028] A method for designing a two-channel biorthogonal graph filter bank based on a lifting structure, comprising the steps of:

[0029] The first step: the structure of the two-channel graph filter bank is as follows figure 1 shown. Its analysis and synthesis subband filters are expressed as functions on the analysis and synthesis spectral kernels:

[0030]

[0031] In the formula, H i is the i-th analysis subband filter, G i is the i-th synthetic subband filter, is h i (λ) is the value of the i-th analysis subband filter spectrum kernel at the characteristic root λ, g i (λ) is the value of the i-th integrated subband filter spectrum kernel at the characteristic root λ, P λ is the orthogonal projection matrix corresponding to the characteristic root λ. λ is the characteristic root of the Laplacian matrix of graph G, and σ(G) is the set of characteristic roots of the Laplacian matrix of graph G. i is the serial number of the subband filter.

[0032] if h 1 (λ) = ...

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Abstract

The invention discloses a two-channel biorthogonal figure filter band design method based on a lifting structure. Based on the single-stage lifting structure, the frequency characteristic of an analysis and synthesis frequency spectrum kernel can be effectively controlled. The single-stage lifting structure is utilized, the analysis and synthesis frequency spectrum kernel is represented as a function related to two lifting filters, the reconstitution condition is automatically met, and therefore optimization of an analysis and synthesis sub-band filter is converted into optimization of the two lifting filters, that is, the frequency characteristics of the analysis and synthesis filters can be described as a function related to the lifting filters. Quadratic programming problem optimization with constraint is achieved to obtain the good frequency characteristic. According to the method, the good frequency characteristic is obtained on the premise of guaranteeing the complete reconstitution characteristic.

Description

technical field [0001] The invention relates to the field of multi-rate signal processing, in particular to a design method for a two-channel bi-orthogonal graph filter bank based on a lifting structure. Background technique [0002] A graph is a model that effectively describes irregular geometric structures. Social networks, wireless sensor networks, financial networks, etc. can be described by graphs. The nodes of the graph represent the location of the data, the size of the data can be represented by the signal of the graph nodes, and the connection between the nodes in the graph can represent different data nodes. connection between. However, in practical applications, the amount of graph data is very large, and the processing of the whole graph will bring huge computational complexity, which is often impossible to achieve. Therefore, the processing of graph signals becomes the key, especially the multi-resolution analysis of graph signals. [0003] At present, some s...

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F17/50
Inventor 蒋俊正周芳欧阳缮刘庆华谢跃雷程小磊江庆穆亚起郭云
Owner GUILIN UNIV OF ELECTRONIC TECH
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