一種設(shè)計(jì)M通道雙正交過(guò)采樣圖濾波器組的新算法

蔣俊正; 劉松遼; 歐陽(yáng)繕

doi:10.11999/JEIT170462

一種設(shè)計(jì)M通道雙正交過(guò)采樣圖濾波器組的新算法

doi: 10.11999/JEIT170462

基金項(xiàng)目:

國(guó)家自然科學(xué)基金(61261032, 61371186)，桂林電子科技大學(xué)研究生教育創(chuàng)新計(jì)劃項(xiàng)目(2017YJCX21)

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- 文章訪問(wèn)數(shù): 1205
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出版歷程
- 收稿日期: 2017-05-16
- 修回日期: 2017-08-14
- 刊出日期: 2017-12-19

A Novel Method for Designing M-channel BiorthogonalOversampled Graph Filter Banks

Funds:

The National Natural Science Foundation of China (61261032, 61371186), Innovation Project of GUET Graduate Education (2017YJCX21)

摘要

摘要: 針對(duì)現(xiàn)有的M通道過(guò)采樣圖濾波器組整體性能較差的問(wèn)題，該文提出一種過(guò)采樣圖濾波器組設(shè)計(jì)的新算法。在新算法中，分兩步來(lái)設(shè)計(jì)圖濾波器組。首先，從頻譜特性方面考慮來(lái)設(shè)計(jì)分析濾波器，以分析濾波器的通帶波紋和阻帶能量為目標(biāo)函數(shù)，以3 dB約束為約束條件，通過(guò)半正定規(guī)劃求解出頻譜選擇性較好的分析濾波器；然后，從完全重構(gòu)特性方面考慮來(lái)設(shè)計(jì)綜合濾波器，以綜合濾波器的阻帶能量為目標(biāo)函數(shù)，以完全重構(gòu)條件為約束函數(shù)。上述兩個(gè)約束優(yōu)化問(wèn)題都是半正定規(guī)劃問(wèn)題，都可有效地求解。新算法綜合考慮了濾波器組的重構(gòu)特性和頻率特性，因此可以設(shè)計(jì)得到整體性能良好的M通道雙正交過(guò)采樣的圖濾波器組。仿真對(duì)比表明，與已有的設(shè)計(jì)算法相比，新算法設(shè)計(jì)所得的圖濾波器組具備更小的重構(gòu)誤差。
- 圖濾波器組 /
- 過(guò)采樣 /
- 完全重構(gòu) /
- 半正定規(guī)劃
Abstract: This paper presents an efficient algorithm to design M-channel oversampled graph filter banks with better overall performance. In the new algorithm, a two-step scheme is exploited to tackle the design task. Firstly, for controlling the spectral selectivity, the analysis filter is designed by solving a constraint optimization problem that minimizes the passband ripple and stopband energy subject to 3 dB constraint; secondly, by taking the Perfect Reconstruction (PR) condition into account, the design problem of synthesis filters is formulated into an optimization problem that minimizes the stopband energy subject to PR constraint. Both the optimization problems are Semi-Definite Programming (SDP), which can be efficiently solved. Since the proposed method fully considerate the spectral characteristic and PR condition, M-channel biorthogonal oversampled graph filter banks with better performance can be obtained. Numerical examples and comparison show that compared with the existing methods, the proposed method can lead to graph filter banks with smaller reconstruction error.
- Graph filter bank /
- Oversampled /
- Perfect Reconstruction (PR) /
- Semi-Definite Programming (SDP)

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參考文獻(xiàn)(16)

NARANG S K, CHAO Y H, and ORTEGA A. Graph-wavelet filterbanks for edge-aware image processing[C]. Statistical Signal Processing Workshop, IEEE, Ann Arbor, MI, 2012: 141-144. doi: 10.1109/SSP.2012.6319643.

CROVELLA M and KOLACZYK E. Graph wavelets for spatial traffic analysis[C]. Joint Conference of the IEEE Computer and Communications, San Francisco, CA, USA, 2003: 1848-1857. doi: 10.1109/INFCOM.2003.1209207.

GIRVAN M and NEWMAN M E. Community structure in social and biological networks[J]. Proceedings of the National Academy of Sciences of the United States of America, 2002, 99(12): 7821-7826. doi: 10.1073/pnas.122653799.

SHEN G and ORTEGA A. Optimized distributed 2D transforms for irregularly sampled sensor network grids using wavelet lifting[C]. IEEE International Conference on Acoustics, Speech and Signal Processing, Las Vegas, NV, 2008: 2513-2516. doi: 10.1109/ICASSP.2008.4518159.

WANG W and RAMCHANDRAN K. Random multiresolution representations for arbitrary sensor network graphs[C]. IEEE International Conference on Acoustics, Speech and Signal Processing, Toulouse, 2006: IV161-IV164. doi: 10.1109/ICASSP.2006.1660930.

TAY D B H, TANAKA Y, and SAKIYAMA A. Near orthogonal oversampled graph filter banks[J]. IEEE Signal Processing Letters, 2016, 23(2): 277-281. doi: 10.1109/LSP. 2016.2514490.

TANAKA Y and SAKIYAMA A. M-channel oversampled graph filter banks[J]. IEEE Transactions on Signal Processing, 2014, 62(14): 3578-3590. doi: 10.1109/TSP.2014.2328983.

SAKIYAMA A and TANAKA Y. Oversampled graph Laplacian matrix for graph filter banks[J]. IEEE Transactions on Signal Processing, 2014, 62(24): 6425-6437. doi: 10.1109/ TSP.2014.2365761.

TAY D B H and LIN Z. Design of near orthogonal graph filter banks[J]. IEEE Signal Processing Letters, 2015, 22(6): 701-704. doi: 10.1109/LSP.2014.2368128.

NARANG S K and ORTEGA A. Perfect reconstruction two-channel wavelet filter banks for graph structured data[J]. IEEE Transactions on Signal Processing, 2012, 60(6): 2786-2799. doi: 10.1109/TSP.2012.2188718.

NARANG S K and ORTEGA A. Compact support biorthogonal wavelet filterbanks for arbitrary undirected graphs[J]. IEEE Transactions on Signal Processing, 2013, 61(19): 4673-4685. doi: 10.1109/TSP.2013.2273197.

JIANG J Z, ZHOU F, and SHUI P L. Optimization design of two-channel biorthogonal graph filter banks[J]. Circuits, Systems, and Signal Processing, 2016, 35(2): 685-692. doi: 10.1007/s00034-015-0073-x.

SAKIYAMA A and TANAKA Y. Oversampled graph Laplacian matrix for graph signals[C]. IEEE, Signal Processing Conference, Lisbon, Portugal, 2014: 2225-2229.

SAKIYAMA A and TANAKA Y. Edge-aware image graph expansion methods for oversampled graph Laplacian matrix[C]. IEEE International Conference on Image Processing, Paris, France, 2014: 2958-2962. doi: 10.1109/ ICIP.2014.7025598.

CHEN S, SANDRYHAILA A, MOURA J M F, et al. Signal denoising on graphs via graph filtering[C]. IEEE, Global Conference on Signal and Information Processing (GlobalSIP). Atlanta, GA, 2015: 872-876. doi: 10.1109/ GlobalSIP.2014. 7032244.

SHI X, FENG H, ZHAI M, et al. Infinite impulse response graph filters in wireless sensor networks[J]. IEEE Signal Processing Letters, 2015, 22(8): 1113-1117. doi: 10.1109/LSP. 2014.2387204.

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