Alternating iteration-based two-channel approximate orthogonal graph filter bank coefficient optimization method

A filter bank, approximately orthogonal technology, applied in the field of graph signal processing, can solve the problem of reconstruction error difference, reconstruction error reduction, etc., to reduce the maximum reconstruction error value, good effect, guarantee the degree of freedom. Effect

Inactive Publication Date: 2021-07-09
HANGZHOU DIANZI UNIV
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Problems solved by technology

[0003] Jun-Zheng Jiang, Fang Zhou, Peng-Lang Shui [1] By listing the energy expressions of the pass band and stop band of the two low-pass filters, minimizing the energy sum, adding restrictions to the filter coefficients, and optimizing with the CVX function, a non-orthogonal image filter bank is designed separately

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  • Alternating iteration-based two-channel approximate orthogonal graph filter bank coefficient optimization method
  • Alternating iteration-based two-channel approximate orthogonal graph filter bank coefficient optimization method
  • Alternating iteration-based two-channel approximate orthogonal graph filter bank coefficient optimization method

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Embodiment 1

[0050] Step 1, the low-pass filter h in this embodiment 0 (x) highest order N 0 =5, high pass filter h 1 (x) highest order N 1 =4, low pass filter h 0 (x) passband cut-off frequency ω p =0.8, stop band cut-off frequency ω s = 1.2.

[0051] Step 2. According to the ideal reconstruction conditions of the graph filter bank and the actual reconstruction error E(x), calculate the maximum reconstruction error E for comparing the performance of the graph filter bank max :

[0052] E. max =|E(x)| max

[0053] E(x)=h 0 (x) g 0 (x)+h 0 (2-x)g 0 (2-x)-2

[0054] Step 3, using the CVX function to solve the optimization objective function based on the alternate iteration method, and obtain the optimized filter coefficients. The alternate iterative method is to first fix the low-pass filter h 0 Coefficient of (x), optimizing g 0 (x) coefficient; then fix the optimized g 0 (x) coefficient, and then optimize h 0 (x) coefficient.

[0055] Step 4, repeat step 3 for iterative...

Embodiment 2

[0059] In this embodiment, the low-pass filter h 0 (x) highest order N 0 =9, high-pass filter h 1 (x) highest order N 1 =8, Figure 5 , 6, 7, and 8 are the comparison charts of reconstruction error values ​​after 1, 10, 50, and 100 iteration optimizations and reconstruction error values ​​before iterations, respectively.

[0060] Table 2 shows the filter h obtained after 100 iterations 0 (x), h 1 (x) Coefficient C 0 、C 1 :

[0061]

[0062]

[0063] Table 2

Embodiment 3

[0065] In this embodiment, the low-pass filter h 0 (x) highest order N 0 = 15, high pass filter h 1 (x) highest order N 1 =14. Figure 9 It is a comparison chart of the reconstruction error value after 1 iteration optimization and the reconstruction error value before iteration, and Table 3 shows the filter h obtained after 1 iteration 0 (x), h 1 (x) Coefficient C 0 、C 1 :

[0066]

[0067] table 3

[0068] Table 4 uses Jun-Zheng Jiang in three embodiments [1] The maximum reconstruction error value comparison of the filter coefficient obtained by the design method and the filter coefficient obtained by using the method of the present invention:

[0069]

[0070] Table 4

[0071] It can be seen from Table 4 that, in the case of different filter orders, the maximum reconstruction error values ​​of the filter coefficients optimized by the method of the present invention are better than those obtained by the design method of Jun-Zheng Jiang.

[0072] [1] Jun-Zhen...

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Abstract

The invention discloses an alternating iteration-based two-channel approximate orthogonal graph filter bank coefficient optimization method. According to the method, aiming at the problem of minimizing and maximizing filter coefficients of a graph filter bank, an optimal graph filter bank coefficient is obtained by determining a reconstruction error value of the graph filter bank, alternately optimizing an obtained objective function, fixing one group of coefficients to optimize the other group, and fixing the optimized group of coefficients to optimize the non-optimized group of coefficients. According to the invention, the coefficients of each graph filter bank are optimized mainly, and meanwhile, the optimization independence among the coefficients is ensured only for an approximate orthogonal graph filter bank structure, so that the maximum reconstruction error value is reduced, and the expected optimization target is achieved. Compared with a traditional optimization method, independent optimization of coefficients in the optimization process and the degree of freedom of design are guaranteed. Reconstruction errors can be reduced in the high-order and low-order filter coefficient optimization process, and a good effect is achieved.

Description

technical field [0001] The invention belongs to the technical field of graph signal processing, in particular to a two-channel approximate orthogonal graph filter bank coefficient optimization method based on alternate iterations. Background technique [0002] Filter banks are widely used in communication, speech coding, audio coding and image signal processing, and the theory and design of M-channel uniform filter banks have been extensively studied. In these applications, it is often necessary to decompose the signal into a group of sub-band signals, each occupying a sub-band of the original signal frequency band, usually non-overlapping or overlapping appropriately, and it is necessary to design an analysis filter bank to achieve single input to multiple output; Sometimes it is necessary to resynthesize these sub-band signals into the required signal, and it is necessary to design a comprehensive filter bank to realize multiple input to single output. Therefore, to accom...

Claims

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Application Information

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IPC IPC(8): G06T5/20G06T5/10
CPCG06T5/10G06T5/20
Inventor 王浩欧毅李祥振严建阳
Owner HANGZHOU DIANZI UNIV
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