DFT调制方向滤波器组及其在图象去噪中的应用
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摘要
图像的方向信息的提取在图像处理中一直是很重要的环节,现有的各种方向提取方法虽然已经具有很好的方向提取特性,可是在设计难度和高低频划分等方面还是有着一些不足。本文研究了DFT调制方向滤波器组在图像噪声去除中的应用。通过对DFT调制滤波器组的二维扩展构造了对于方向具有选择性的滤波器组,在方向提取方面,相比于目前常见的方法有很多优点:有别于传统的可分的小波滤波器组,它消除了对角子带的方向交叉,并且可以提供更多的方向信息。同时,它也有别于传统的方向滤波器组,新的方向滤波器组在频率分割上具有更大的灵活性。进一步,提出的方向滤波器组被应用到图像去噪中,实验结果表明,使用新方向滤波器组的噪声去除算法能够明显改善噪声去除性能。
The description of directional information in image is always an important issue in image processing. There are many methods to extract the directional information of images. However, the underlying filter banks are often complicated in design and the frequency tiling suffers from some limitation in some extent. This paper proposes a new directional filter banks based on DFT modulated filter and applies the new directional filter banks in image denoising. The directional filter bank (DFB) based on 1-D DFT modulated filter is different from separable wavelet filter banks. It avoids the directional across in diagonal subbands and provides finer directional information than wavelet filter bank does. It is also different from the conventional DFBs and the new DFBs are more flexible in directional selectivity. Further, the proposed DFB is applied to image denoising and the experimental results show that the denoising algorithm using the new DFBs can significantly improve denoising performance.
The description of directional information in image is always an important issue in image processing. There are many methods to extract the directional information of images. However, the underlying filter banks are often complicated in design and the frequency tiling suffers from some limitation in some extent. This paper proposes a new directional filter banks based on DFT modulated filter and applies the new directional filter banks in image denoising. The directional filter bank (DFB) based on 1-D DFT modulated filter is different from separable wavelet filter banks. It avoids the directional across in diagonal subbands and provides finer directional information than wavelet filter bank does. It is also different from the conventional DFBs and the new DFBs are more flexible in directional selectivity. Further, the proposed DFB is applied to image denoising and the experimental results show that the denoising algorithm using the new DFBs can significantly improve denoising performance.
引文
[1]夏良正.数字图像处理(2),南京:东南大学出版社,1999:89-96.
[2]Minh.N.Do..Directional Multiresolution Image Representation.[EPFL Lausanne PhD Thesis].November 2001:13-41,36-48,67-90.
[3]M.Kivanc Mihcak,Igor Kozintsev,Kannan Ramchandran and Pierre Moulin,Low-complexity Image Denoising Based on Statistical Modeling of Wavelet Confidents.IEEE Signal Processing Letters,Vol.6,No.4 12,December 1999:300-303.
[4]P.P.Vaklyanathan,Multirate Systems and Filter Banks[A],Prentice-Hall,1993:545-659.
[5]J.Gerardo.Rosiles and Mark.J.T.Smith,"Texture Classification with a Biorthogonal Directional Filter Bank",IEEE International conference on Acoustics,Speech,and Signal Processing,2001.Vol.3,pp:1549-1552.
[6]J.Gerardo.Rosiles,Mark.J.T.Smith,"Image Denoising using Directional Filter Banks" International Conference on Image Processing,2000:292-295.
[7]Javier Portilla,Vasily Strela,Martin J.Wainwright,and Eero P.Simoncelli,"Image Denoising Using Scale Mixtures of Gaussians in the Wavelet Domain" IEEE Transcations on Image Processing,Vol.12,No.11,Nov 2003:1338-1351.
[8]S.Mallat,"A wavelet Tour of Signal Processing",2nd ed.New York Academic.1999.
[9]Martin.Vetterli,"Wavelet,approximation and compression" IEEE Signal Processing.Mag.,Vol.18,No.5,2001:59-73.
[10]Nick G.Kingsbury,"Complex wavelet for shift invariant analysis and filtering of signals," J.Appl.Comput.Harmon.Anal,Vol.10,No.3,May 2001:234-253.
[11]Ivan W.Selesick,Richard G.Baraniuk,and Nick G.Kingsbury,"The Dual-tree Complex Wavelet Transform",IEEE Signal Processing Mag.Nov.2005:319-322.
[12]Robert H.Bamberger and Mark J.T.Smith "A Filter Bank for Directional Decomposition of Images:Theory and Design".IEEE Transaction on Signal Processing.Vol.40,No.4,Apirl 1992:882-893.
[13]Minh N.Do and Martin Vetterli," Contourlets." In Beyond Wavelets,G.V.Welland,Ed.Academic,Ch.4,2003:83-105.
[14]Minh N.Do and Martin Vetterli "the Contourlet Transform:An Efficient Directional Multiresolution Image Representation" IEEE Transaction on Image Processing, vol.14, No. 12, December 2005:2091-2106.
[15]Truong T. Nguyen and Soontorn Oraintara "A Directional Decomposition, Theory, Design and Implementation". In Proc. IEEE Int. Symp, circuits Systems (ISCAS) Vancouver, Canada, Vol.3, May 2004: 281-284.
[16]Truong T. Nguyen and Soontorn Oraintara, " Multiresolution Directional Filter Banks: Theory, Design and application " IEEE Trans. Signal Processing, Vol.53, No. 10, October 2005:3895-3905.
[17]Truong T. Nguyen and Soontorn Oraintara, "A Multiresolution Directional Filter Bank For Image Applications" in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, May 2004:37-40.
[18]Truong T. Nguyen and Soontorn Oraintara "Texture Classification Using Non-uniform Directional Filter bank"2004 IEEE 11th Digital signal Processing workshop & IEEE signal Processing Education Workshop.2004:147-150.
[19]Truong T. Nguyen and Soontorn Oraintara, "A class of directional filter banks ". in Proc. IEEE Int. Symp. Circuits systems May 2005:1110-1113.
[20]Sang-il Park, Mark J. T. Smith and Russell M. Mersereau. "Improved Structures of Maximally Decimated Directional Filter Banks for Spatial Image Analysis", IEEE Transaction on Image Processing, Vol. 13, No. 11, November 2004:1424-1431.
[21] Paul S. Hong and Mark J.T. Smith, An Octave-band Family of Non-Redundant Directional Filter banks. In Proc. IEEE Int. Conf. Acoustics, Speech, Signal. May. 2002:1165-1168.
[22] Matthew R. Wilbur, Timothy N. Davidson and James P. Reilly. Efficient Design of Over-sampled NPR GDFT Filter banks. IEEE TRANSCATIONS ON PROCESSING VOL. 52, No. 7. JULY 2004: 1947-1963.
[23] Peng-Lang Shui, Image Denoising Algorithm via Doubly Local Wiener Filtering with Directional Windows in Wavelet Domain, IEEE Signal Processing Letters. 12(10). 2005: 681-684.
[24]Sang-il. Park, Mark. J. T. Smith, Jun Jae Lee, Fingerprint enhancement based on the directional filter bank. In Proceedings. 2000 International Conference on Image Processing, Nagoya. Japan. January 2000:793-796.
[25]Sang-il. Park, Mark. J. T. Smith and Russell M. Mersereau. A New Directional Filter Bank For Image Analysis and Classification. In Proceedings of IEEE International Conference on Acoustics. Speed, and Signal Processing, March.2000: 1417-1420.
[26]C.-C.Tseng.Eigenvalues and eigenvectors of generalized DFT generalized DHT,DCT-Ⅳ and DST-Ⅳ matrices[J].IEEE Trans.Signal Processing,2002,50(4):866-877.
[27]J.M.de Haan,N.Gribe,I.Claesson,and S.Nordholm.Filter bank design for subband adaptive microphone arrays[J].IEEE Trans.on Speech Audio Processing,2003,11(1):14-23.
[28]H.H.Dam,S.Nordholm,A.Cantoni and J.M.de Haan.Iterative method for the design of DFT filter bank[J].IEEE Trans.on Circuits and Syst,2004,51(11):581-586.
[29]杨福生.小波变换的工程分析与应用.北京:科学出版社.1999:150-176.
[30]P-L Shui and Z.Bao.M-band compactly supported orthogonal symmetric interpolating scaling functions[J]IEEE Trans.Signal Processing,2001,49(8):1704-1713.
[31]章毓敏.数字信号处理.北京:清华大学出版社.2002:13-43.
[32]Marian Kazubek.Wavelet Domain Image Denoising by Thresholding and Wiener Filtering.IEEE Signal Processing Letters,Vol.10,No.11,November 2003:324-326.
[33]Minh N.Do and Martin Vetterli.Pyramidal Directional Filter Banks and Curvelets.IEEE International conference on Acoustics,Speech,and Signal Processing,2001:158-161.
[34]W.Y.Chan,N.F.Law and W.C.Siu,Multi-scale Feature Analysis Using Directional Filter Bank.ICICS-PCM 2003.15-18 December 2003:822-826.
[35]Rong Duan,Hong Man and Ling Chen.Rotation Invariant Texture Classification Based on A Directional Filter Bank.2004 IEEE International Conference on Multimedia and Expo(ICME):1291-1294.
[36]F.C.A.Fernandes,R.L.C.van Spaendonck,and C.S.Burrus,Multidimensional,mapping-based complex wavelet transforms,IEEE Trans.Image Processing,14(1),2005:110-124.
[37]D.D.-Y.,Po and M.N.Do,Directional multiscale modeling of images using the contourlet transforms,IEEE Trans.Image Processing,15(6),2006:1610-1620.
[38]R.Eslami and H.Radha,"Translation-invariant contourlet transform and its application to image denoising," IEEE Trans.Image Processing,15(11),2006:3362-3374.
[2]Minh.N.Do..Directional Multiresolution Image Representation.[EPFL Lausanne PhD Thesis].November 2001:13-41,36-48,67-90.
[3]M.Kivanc Mihcak,Igor Kozintsev,Kannan Ramchandran and Pierre Moulin,Low-complexity Image Denoising Based on Statistical Modeling of Wavelet Confidents.IEEE Signal Processing Letters,Vol.6,No.4 12,December 1999:300-303.
[4]P.P.Vaklyanathan,Multirate Systems and Filter Banks[A],Prentice-Hall,1993:545-659.
[5]J.Gerardo.Rosiles and Mark.J.T.Smith,"Texture Classification with a Biorthogonal Directional Filter Bank",IEEE International conference on Acoustics,Speech,and Signal Processing,2001.Vol.3,pp:1549-1552.
[6]J.Gerardo.Rosiles,Mark.J.T.Smith,"Image Denoising using Directional Filter Banks" International Conference on Image Processing,2000:292-295.
[7]Javier Portilla,Vasily Strela,Martin J.Wainwright,and Eero P.Simoncelli,"Image Denoising Using Scale Mixtures of Gaussians in the Wavelet Domain" IEEE Transcations on Image Processing,Vol.12,No.11,Nov 2003:1338-1351.
[8]S.Mallat,"A wavelet Tour of Signal Processing",2nd ed.New York Academic.1999.
[9]Martin.Vetterli,"Wavelet,approximation and compression" IEEE Signal Processing.Mag.,Vol.18,No.5,2001:59-73.
[10]Nick G.Kingsbury,"Complex wavelet for shift invariant analysis and filtering of signals," J.Appl.Comput.Harmon.Anal,Vol.10,No.3,May 2001:234-253.
[11]Ivan W.Selesick,Richard G.Baraniuk,and Nick G.Kingsbury,"The Dual-tree Complex Wavelet Transform",IEEE Signal Processing Mag.Nov.2005:319-322.
[12]Robert H.Bamberger and Mark J.T.Smith "A Filter Bank for Directional Decomposition of Images:Theory and Design".IEEE Transaction on Signal Processing.Vol.40,No.4,Apirl 1992:882-893.
[13]Minh N.Do and Martin Vetterli," Contourlets." In Beyond Wavelets,G.V.Welland,Ed.Academic,Ch.4,2003:83-105.
[14]Minh N.Do and Martin Vetterli "the Contourlet Transform:An Efficient Directional Multiresolution Image Representation" IEEE Transaction on Image Processing, vol.14, No. 12, December 2005:2091-2106.
[15]Truong T. Nguyen and Soontorn Oraintara "A Directional Decomposition, Theory, Design and Implementation". In Proc. IEEE Int. Symp, circuits Systems (ISCAS) Vancouver, Canada, Vol.3, May 2004: 281-284.
[16]Truong T. Nguyen and Soontorn Oraintara, " Multiresolution Directional Filter Banks: Theory, Design and application " IEEE Trans. Signal Processing, Vol.53, No. 10, October 2005:3895-3905.
[17]Truong T. Nguyen and Soontorn Oraintara, "A Multiresolution Directional Filter Bank For Image Applications" in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, May 2004:37-40.
[18]Truong T. Nguyen and Soontorn Oraintara "Texture Classification Using Non-uniform Directional Filter bank"2004 IEEE 11th Digital signal Processing workshop & IEEE signal Processing Education Workshop.2004:147-150.
[19]Truong T. Nguyen and Soontorn Oraintara, "A class of directional filter banks ". in Proc. IEEE Int. Symp. Circuits systems May 2005:1110-1113.
[20]Sang-il Park, Mark J. T. Smith and Russell M. Mersereau. "Improved Structures of Maximally Decimated Directional Filter Banks for Spatial Image Analysis", IEEE Transaction on Image Processing, Vol. 13, No. 11, November 2004:1424-1431.
[21] Paul S. Hong and Mark J.T. Smith, An Octave-band Family of Non-Redundant Directional Filter banks. In Proc. IEEE Int. Conf. Acoustics, Speech, Signal. May. 2002:1165-1168.
[22] Matthew R. Wilbur, Timothy N. Davidson and James P. Reilly. Efficient Design of Over-sampled NPR GDFT Filter banks. IEEE TRANSCATIONS ON PROCESSING VOL. 52, No. 7. JULY 2004: 1947-1963.
[23] Peng-Lang Shui, Image Denoising Algorithm via Doubly Local Wiener Filtering with Directional Windows in Wavelet Domain, IEEE Signal Processing Letters. 12(10). 2005: 681-684.
[24]Sang-il. Park, Mark. J. T. Smith, Jun Jae Lee, Fingerprint enhancement based on the directional filter bank. In Proceedings. 2000 International Conference on Image Processing, Nagoya. Japan. January 2000:793-796.
[25]Sang-il. Park, Mark. J. T. Smith and Russell M. Mersereau. A New Directional Filter Bank For Image Analysis and Classification. In Proceedings of IEEE International Conference on Acoustics. Speed, and Signal Processing, March.2000: 1417-1420.
[26]C.-C.Tseng.Eigenvalues and eigenvectors of generalized DFT generalized DHT,DCT-Ⅳ and DST-Ⅳ matrices[J].IEEE Trans.Signal Processing,2002,50(4):866-877.
[27]J.M.de Haan,N.Gribe,I.Claesson,and S.Nordholm.Filter bank design for subband adaptive microphone arrays[J].IEEE Trans.on Speech Audio Processing,2003,11(1):14-23.
[28]H.H.Dam,S.Nordholm,A.Cantoni and J.M.de Haan.Iterative method for the design of DFT filter bank[J].IEEE Trans.on Circuits and Syst,2004,51(11):581-586.
[29]杨福生.小波变换的工程分析与应用.北京:科学出版社.1999:150-176.
[30]P-L Shui and Z.Bao.M-band compactly supported orthogonal symmetric interpolating scaling functions[J]IEEE Trans.Signal Processing,2001,49(8):1704-1713.
[31]章毓敏.数字信号处理.北京:清华大学出版社.2002:13-43.
[32]Marian Kazubek.Wavelet Domain Image Denoising by Thresholding and Wiener Filtering.IEEE Signal Processing Letters,Vol.10,No.11,November 2003:324-326.
[33]Minh N.Do and Martin Vetterli.Pyramidal Directional Filter Banks and Curvelets.IEEE International conference on Acoustics,Speech,and Signal Processing,2001:158-161.
[34]W.Y.Chan,N.F.Law and W.C.Siu,Multi-scale Feature Analysis Using Directional Filter Bank.ICICS-PCM 2003.15-18 December 2003:822-826.
[35]Rong Duan,Hong Man and Ling Chen.Rotation Invariant Texture Classification Based on A Directional Filter Bank.2004 IEEE International Conference on Multimedia and Expo(ICME):1291-1294.
[36]F.C.A.Fernandes,R.L.C.van Spaendonck,and C.S.Burrus,Multidimensional,mapping-based complex wavelet transforms,IEEE Trans.Image Processing,14(1),2005:110-124.
[37]D.D.-Y.,Po and M.N.Do,Directional multiscale modeling of images using the contourlet transforms,IEEE Trans.Image Processing,15(6),2006:1610-1620.
[38]R.Eslami and H.Radha,"Translation-invariant contourlet transform and its application to image denoising," IEEE Trans.Image Processing,15(11),2006:3362-3374.