多小波与时频域重叠式变换图像压缩算法研究
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摘要
目前基于小波变换(DWT)的压缩方法是图像压缩的主流方法,但是小波变换作为一种全局的变换方法,存在着存储开销大、计算量高等特征,不能满足便携式设备以及星载压缩等环境下的应用要求。叠式变换(LT)兼有余弦变换(DCT)实现简单、存储开销小和DWT的优点,文中通过分析已有的时域重叠(TLT)和频域重叠(FLT)叠式变换,提出一种同时进行时域和频域重叠的叠式变换算法(TFLT),并结合上下文熵编码,讨论时频域重叠式变换算法。实验结果表明,本文方法与JPEG2000相比,在保证恢复图像质量相同的前提下,过程的复杂性与存储量都有所改善,是一种低存储,低复杂度的高效方法。
由于多小波将光滑性、紧支性、对称性、正交性和更高阶的消失矩完美地结合在一起,它不但可以对信号提供一种更新的分析手段,而且对信号的逼近性质更好,重构信号在边界位置的性能也更完善。本文结合EBCOT的良好性能和多小波变换系数特性,提出一种结合滤波器和基于近似阶的预处理方法,并对多小波变换系数进行重新排列和量化处理,对EBCOT中位平面进行混合扫描方法相结合的压缩算法。实验结果表明该方法在一定程度上减少过程的复杂性,同时取得较好的压缩效果。
Nowadays compression method based upon wavelet transform has become the mainstream in image compressing field. But as we all know, wavelet transform can’t satisfy the requirement of portable devices and Space-Based compression for its drawback in large storing cost and high calculating complexity. Fortunately, Lapped Transform(LT), a classical transform arithmetic, possesses the DCT’s feature of simple realization and low storing cost, while maintaining DWT’s advantage. By analyzing its Time Lapped Transform(TLT) and Frequency Lapped Transform (FLT), this article brings forward a arithmetic which carries the temporal laps and frequent laps at the same time and discusses this time-frequency lapped method(TFLT) combining with context-based entropy coding. Experimental results implicate that this arithmetic is a low storage-cost and complicated method, for its better performance over JPEG2000 in both realization and storage requirement.
Owing to combination of smoothness, tight support, symmetry, orthogonality and higher order of vanish moments, Multi-wavelets supply us with a new signal analysis method , which can better approximate the signal and performance well on the edge in reconstruction. Combining the favorable capability of EBCOT and characteristic of Multi-wavelet’s coefficients, This article puts forward an integrated filter and pretreatment method based on approximated stairs. It processes the vector quantification of Multi-wavelet’s coefficients and carries out the mix-scan compression arithmetic towards bit planes of EBCOT. Experimental results show that this method reduces calculating complexity to some extent while obtaining favorable compressing effects.
由于多小波将光滑性、紧支性、对称性、正交性和更高阶的消失矩完美地结合在一起,它不但可以对信号提供一种更新的分析手段,而且对信号的逼近性质更好,重构信号在边界位置的性能也更完善。本文结合EBCOT的良好性能和多小波变换系数特性,提出一种结合滤波器和基于近似阶的预处理方法,并对多小波变换系数进行重新排列和量化处理,对EBCOT中位平面进行混合扫描方法相结合的压缩算法。实验结果表明该方法在一定程度上减少过程的复杂性,同时取得较好的压缩效果。
Nowadays compression method based upon wavelet transform has become the mainstream in image compressing field. But as we all know, wavelet transform can’t satisfy the requirement of portable devices and Space-Based compression for its drawback in large storing cost and high calculating complexity. Fortunately, Lapped Transform(LT), a classical transform arithmetic, possesses the DCT’s feature of simple realization and low storing cost, while maintaining DWT’s advantage. By analyzing its Time Lapped Transform(TLT) and Frequency Lapped Transform (FLT), this article brings forward a arithmetic which carries the temporal laps and frequent laps at the same time and discusses this time-frequency lapped method(TFLT) combining with context-based entropy coding. Experimental results implicate that this arithmetic is a low storage-cost and complicated method, for its better performance over JPEG2000 in both realization and storage requirement.
Owing to combination of smoothness, tight support, symmetry, orthogonality and higher order of vanish moments, Multi-wavelets supply us with a new signal analysis method , which can better approximate the signal and performance well on the edge in reconstruction. Combining the favorable capability of EBCOT and characteristic of Multi-wavelet’s coefficients, This article puts forward an integrated filter and pretreatment method based on approximated stairs. It processes the vector quantification of Multi-wavelet’s coefficients and carries out the mix-scan compression arithmetic towards bit planes of EBCOT. Experimental results show that this method reduces calculating complexity to some extent while obtaining favorable compressing effects.
引文
[1] 成礼智,王红霞,罗永 编著 小波的理论与应用 科学出版社 2004.09
[2] David Salomon 著 吴乐南等译 数据压缩原理与应用 电子工业出版社 2003.09
[3] 杨枝灵 王开 等编著 Visual C++数字图像获取 处理及实践应用 人民邮电出版社 2003.01
[4] David S.Taubman Michael W.Marcellin著 魏江力,柏正尧 等译 JPEG2000图像压缩基础、标准和实践 电子工业出版社 2004.04
[5] 田丽华 编著 编码理论 西安电子科技大学出版社 2003.08
[6] 陈武凡 主编 小波分析及其在图像处理中的应用 科学出版社 2002.04
[7] 曾怡达,刘志刚,钱清泉 CL多小波预处理方法在故障数据压缩中的应用 电网技术 第28卷第7期 2004年4月
[8] 石钧 多小波:理论和应用.信号处理,1999; (4): 329-334
[9] 黄卓君,马争鸣.CL多小波图象编码.中国图象图形学报,2001; (7);662- 668
[10] 王玲,宋国乡.多小波的预处理及其在图像压缩中的应用.电子学报,2001;(10) : 1418-1420
[11] 黄卓君,马争鸣.多小波图像编码.中国图象图形学报,2000;(4 ):3 10-317
[12] 谢荣生,徐耀群,郝燕玲,洪艳. 一种新的多小波零树图像编码方法.哈尔滨商业大学学报,2001;( 5):3 3-36
[13] 崔丽鸿,程正兴.多小波与平衡多小波的理论和设计.工程数学学报,2002;(18): 105-117
[14] 沈振武,付正刚 小波图像压缩的研究与发展 咸宁学院学报,Vol.23,No.3 Jun.2003
[15] Mallat S G. Multifrequency channel decompositions of images and wavelet nodels[J ] . IEEE Trans. on ASSP ,1989 ,37(12) :209122110.
[16] Antonini M.,Barlaud M.,Mathieu P.,and Daubechies I.,Image coding using the wavelet transform, IEEE Trans. On Image Processing,VOL.1,1992,pp.205-220.
[17] Coben A. and Daubechies I. Biorthogonal bases of compactly supported wavelets,Commu Pure Appl.Math.VOL.XLV,1992,pp.485-560.
[18] Coben A. and Daubechies I.Orthogonal bases of compactly supported wavelets III.Better frequency resolution,SIAM Math.Anal.,VOL.24,1993,pp.520-527.
[19] Chui C.K. and Lian J.A.,A Study of Orthonormal Multiwavelets, J.Appl.Number.Math,VOL.20,1996,pp.272-298.
[20] Daubechies I.,Ten lectures on wavelets,Philadelphia:SIAM,1992.
[21] Devore R.A.,Image compression through wavelet transform coding,IEEE Trans.Image Processing,VOL.5.1996,PP.719-745.
[22] Devore R.A.,Jawerth B. and Lucier P.J.,Image compression through wavelet tranform coding,IEEE Trans.Infor.Theory,VOL.38,1992,pp.719-746.
[23] Jiang Q.,On the design of multifilter banks and orthonormal multiwavelet bases,IEEE Trans.,Signal Processing,VOL.46,1998,pp.3292-3303.
[24] Lebrun J. and Vetterli,Balanced multiwavelet theory and design,IEEE Trans.Signal Processing,VOL.46.1998,PP.1119-1124.
[25] H. S. Malvar. Lapped transforms for efficient transform/subband Transactions on Acoustics, Speech, and Signal Processing, pp. 969-978 1990 coding. IEEE,vol. 38, June
[26] H. S. Malvar. Biorthogonal and nonuniform lapped transforms for transform coding withreduced blocking and ringing artifacts. IEEE Trans. on Signal Processing, pp. 1043-1053,Apr. 1998
[27] T D Tran. M2channel linear phase perfect reconstruction filter bank with integer coefficients (invited paper) [A] . SPIE International Sym2 posiumon Optical Science ,Engineering ,and Instrumentation. Session :Wavelet Applications in Signal and Image Processing [C] . Denver ,July 1999.Available from http :/ / thanglong. ee. jhu. edu/ Tran/ Pub/ intfb.ps. gz.
[28] T D Tran. Fast multiplierless approximation of the DCT [A] . 33rd Annual Conference on Information Sciences and Systems [C] ,Baltimore ,MD ,1999 : 9932938. Available from http :/ / thanglong. ee. jhu. edu/Tran/ Pub/ intDCT. ps. gz.
[29] B.G.Lee. A new algorithm to compute the discrete Cosine transform. IEEE Transactions ASSP-32. 1984,(6)
[30] T D Tran. The binDCT: fast multiplierless approximation of the DCT. IEEE Signal Processing Letters. Jun 2000, 7(6): 141-144
[31] Selesnick I.W.,Multiwavelet bases with extra approximation properties,IEEE Trans.Signal Processing,VOL.46,1998,pp.2898-2908.
[32] Selesnick I.W.,Balanced multiwavelet bases based on symmetric FIR filters,IEEE Trans.Signal Processing,VOL.48,2000,pp.184-191.
[33] Strela V.,Multiwavelets:theory and application,Ph.D.thesis,MIT,1996.
[34] Shapiro J M. Embedded image coding using zerotrees of wavelet coefficients. IEEE Trans. Signal Processing, 1993,41(12):3445~3462.
[35] A.Said and W.A.Pearlman. Anew,fast,and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans.Circuits Syst.VideoTechnol,vol.6, pp.243-250,June 1996.
[36] A.Zandi,J.Allen,E.Schwartz,and M.Boliek, CREW:Compression with reversible embedded wavelets,IEEE Data Compression Conference, Snowbird,UT, pp.212-221, March 1995.
[37] D.Le Gall and A.Tabatabai,”Sub-band coding of digital images using symmetric short kernel filters and arithmetic coding techniques,”in Proc.IEEE
[38] L.D.Villasenor.,B.Belzer,and J.Liao,”Wavelet filter evaluation for image compression,”IEEE Trans.Image Processing,vol.4.pp.1053-1060,Aug.1995.
[39] A.Said and W.A.Pearman,”An image multiresolution representation for lossless and lossy compression,”IEEE Trans.Image Processing,vol,5, pp.1303-1310, Sept,1996.
[40] G.Srang and T.Nguyen,Wavelets and Filter Banks.WellesleynMA: Wellesley-Cambridge Press,1996.
[41] M.J.Gormish,E.L.Schwartz,A.F.Keith,M.P.Boliek,and A.Zandi,”Lossless and nearly lossless compression of high-quality images,”Proc.SPIE, vol.3025, pp.62-70,Mar.1997.
[42] M.Antonini,M.Barlaud ,P.Mathieu,and I.Daubechies,”Image coding using wavelet tranform,”IEEE Trans.Image Processing,vol.1, no.2,pp.205-220, Apr. 1992.
[43] Lewis A S , Knowles G. Image Compression Using the 2 - D Wavelet Transform [J ] . IEEE Transactions on Image Processing , 1992 , 1.
[44] Chui C K , Lian J A . A study of orthonormal multi-wavelets[J].Applied Numerical Mathematics,1996,20(3):273-298.
[45] Jiang Q T . Orthogonal multiwavelet with optimum time-frequency resolution[J].IEEE Trans on Signal Processing,1998,46(4):830-844.
[46] Cotronei M,Montefusco L B,Puccio L.Multiwavelet analysis and signal processing[J].IEEE Trans on Circuits and Systems-II:Analog and Digital Signal Processing,1998,45(8):970-987.
[47] Goodman T N T,Lee S L.Wavelets of multiplicity[J].Trans American Mathematical Society,1994,342:307-324.
[48] Xia X G,Geronimo J S,Hardin D P et al.Design of prefilters for discrete multiwavelet transforms[J].IEEE Trans on Signal Processing,1996,44(1):25-34.
[49] Strela V,Heller P N, Topiwala Petal.The application of multiwavelet filter banks to image processing[J].IEEE Trans on Image Processing,1999,8(4):548-563.
[50] Tham J Y,Shen L X,Lee S Letal.A general approach for analysis and application discrete multiwavelet transforms[J] . IEEE Trans on Signal Processing,2000,48(2):457-464.
[51] Douglas P. Hardin1 and Jeffrey A. Marasovich Biorthogonal Multiwavelets on [-1, 1] Applied and Computational Harmonic Analysis 7, 34–53 (1999)
[52] David Taubman High Performance Scalable Image Compression with EBCOT IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 9, NO. 7, JULY 2000
[53] Vetterli M. and Herley C., Wavelets and filter banks: Theory and design, IEEE Trans. Acoust. Speech signal proc., 1992, Vol.40, No.9, pp. 2207-2232.
[54] Strela V and Heller P,N “The Application of Multiwavelet Transform to Image Coding”[J] IEEE.Trans.on Image Processing, 2000, Vol.9, No.2:270-273.
[55] Michael B.Martin and Amy E.Bell “New Image Compress Techniques using Multiwavelet and Multwavelet Packet”[J] IEEE.Trans.on Image Processing, 2001,Vol.10 No.4:500-503.
[56] David S.Taubman“High Performance Scalable Image Compression with EBCOT” [J] IEEE.Trans.on Image Processing, 2000, Vol.9, No.7:1158-1170.
[57] V. Strela and A. T. Walden, "Signal and Image Denoising via Wavelet Thresholding: Orthogonal and Biorthogonal, Scalar and Multiple Wavelet Transforms", Imperial College, Statistics Section, Technical Report TR-98-01 (1998).
[58] Attakitmongcol K,Hardin D P,Wikes D M.Multiwavelet Prefilters part II:optimal orthogonal prefilters[J]. IEEE Trans on Image Processing, 2001,10(10) :1476-1478
[2] David Salomon 著 吴乐南等译 数据压缩原理与应用 电子工业出版社 2003.09
[3] 杨枝灵 王开 等编著 Visual C++数字图像获取 处理及实践应用 人民邮电出版社 2003.01
[4] David S.Taubman Michael W.Marcellin著 魏江力,柏正尧 等译 JPEG2000图像压缩基础、标准和实践 电子工业出版社 2004.04
[5] 田丽华 编著 编码理论 西安电子科技大学出版社 2003.08
[6] 陈武凡 主编 小波分析及其在图像处理中的应用 科学出版社 2002.04
[7] 曾怡达,刘志刚,钱清泉 CL多小波预处理方法在故障数据压缩中的应用 电网技术 第28卷第7期 2004年4月
[8] 石钧 多小波:理论和应用.信号处理,1999; (4): 329-334
[9] 黄卓君,马争鸣.CL多小波图象编码.中国图象图形学报,2001; (7);662- 668
[10] 王玲,宋国乡.多小波的预处理及其在图像压缩中的应用.电子学报,2001;(10) : 1418-1420
[11] 黄卓君,马争鸣.多小波图像编码.中国图象图形学报,2000;(4 ):3 10-317
[12] 谢荣生,徐耀群,郝燕玲,洪艳. 一种新的多小波零树图像编码方法.哈尔滨商业大学学报,2001;( 5):3 3-36
[13] 崔丽鸿,程正兴.多小波与平衡多小波的理论和设计.工程数学学报,2002;(18): 105-117
[14] 沈振武,付正刚 小波图像压缩的研究与发展 咸宁学院学报,Vol.23,No.3 Jun.2003
[15] Mallat S G. Multifrequency channel decompositions of images and wavelet nodels[J ] . IEEE Trans. on ASSP ,1989 ,37(12) :209122110.
[16] Antonini M.,Barlaud M.,Mathieu P.,and Daubechies I.,Image coding using the wavelet transform, IEEE Trans. On Image Processing,VOL.1,1992,pp.205-220.
[17] Coben A. and Daubechies I. Biorthogonal bases of compactly supported wavelets,Commu Pure Appl.Math.VOL.XLV,1992,pp.485-560.
[18] Coben A. and Daubechies I.Orthogonal bases of compactly supported wavelets III.Better frequency resolution,SIAM Math.Anal.,VOL.24,1993,pp.520-527.
[19] Chui C.K. and Lian J.A.,A Study of Orthonormal Multiwavelets, J.Appl.Number.Math,VOL.20,1996,pp.272-298.
[20] Daubechies I.,Ten lectures on wavelets,Philadelphia:SIAM,1992.
[21] Devore R.A.,Image compression through wavelet transform coding,IEEE Trans.Image Processing,VOL.5.1996,PP.719-745.
[22] Devore R.A.,Jawerth B. and Lucier P.J.,Image compression through wavelet tranform coding,IEEE Trans.Infor.Theory,VOL.38,1992,pp.719-746.
[23] Jiang Q.,On the design of multifilter banks and orthonormal multiwavelet bases,IEEE Trans.,Signal Processing,VOL.46,1998,pp.3292-3303.
[24] Lebrun J. and Vetterli,Balanced multiwavelet theory and design,IEEE Trans.Signal Processing,VOL.46.1998,PP.1119-1124.
[25] H. S. Malvar. Lapped transforms for efficient transform/subband Transactions on Acoustics, Speech, and Signal Processing, pp. 969-978 1990 coding. IEEE,vol. 38, June
[26] H. S. Malvar. Biorthogonal and nonuniform lapped transforms for transform coding withreduced blocking and ringing artifacts. IEEE Trans. on Signal Processing, pp. 1043-1053,Apr. 1998
[27] T D Tran. M2channel linear phase perfect reconstruction filter bank with integer coefficients (invited paper) [A] . SPIE International Sym2 posiumon Optical Science ,Engineering ,and Instrumentation. Session :Wavelet Applications in Signal and Image Processing [C] . Denver ,July 1999.Available from http :/ / thanglong. ee. jhu. edu/ Tran/ Pub/ intfb.ps. gz.
[28] T D Tran. Fast multiplierless approximation of the DCT [A] . 33rd Annual Conference on Information Sciences and Systems [C] ,Baltimore ,MD ,1999 : 9932938. Available from http :/ / thanglong. ee. jhu. edu/Tran/ Pub/ intDCT. ps. gz.
[29] B.G.Lee. A new algorithm to compute the discrete Cosine transform. IEEE Transactions ASSP-32. 1984,(6)
[30] T D Tran. The binDCT: fast multiplierless approximation of the DCT. IEEE Signal Processing Letters. Jun 2000, 7(6): 141-144
[31] Selesnick I.W.,Multiwavelet bases with extra approximation properties,IEEE Trans.Signal Processing,VOL.46,1998,pp.2898-2908.
[32] Selesnick I.W.,Balanced multiwavelet bases based on symmetric FIR filters,IEEE Trans.Signal Processing,VOL.48,2000,pp.184-191.
[33] Strela V.,Multiwavelets:theory and application,Ph.D.thesis,MIT,1996.
[34] Shapiro J M. Embedded image coding using zerotrees of wavelet coefficients. IEEE Trans. Signal Processing, 1993,41(12):3445~3462.
[35] A.Said and W.A.Pearlman. Anew,fast,and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans.Circuits Syst.VideoTechnol,vol.6, pp.243-250,June 1996.
[36] A.Zandi,J.Allen,E.Schwartz,and M.Boliek, CREW:Compression with reversible embedded wavelets,IEEE Data Compression Conference, Snowbird,UT, pp.212-221, March 1995.
[37] D.Le Gall and A.Tabatabai,”Sub-band coding of digital images using symmetric short kernel filters and arithmetic coding techniques,”in Proc.IEEE
[38] L.D.Villasenor.,B.Belzer,and J.Liao,”Wavelet filter evaluation for image compression,”IEEE Trans.Image Processing,vol.4.pp.1053-1060,Aug.1995.
[39] A.Said and W.A.Pearman,”An image multiresolution representation for lossless and lossy compression,”IEEE Trans.Image Processing,vol,5, pp.1303-1310, Sept,1996.
[40] G.Srang and T.Nguyen,Wavelets and Filter Banks.WellesleynMA: Wellesley-Cambridge Press,1996.
[41] M.J.Gormish,E.L.Schwartz,A.F.Keith,M.P.Boliek,and A.Zandi,”Lossless and nearly lossless compression of high-quality images,”Proc.SPIE, vol.3025, pp.62-70,Mar.1997.
[42] M.Antonini,M.Barlaud ,P.Mathieu,and I.Daubechies,”Image coding using wavelet tranform,”IEEE Trans.Image Processing,vol.1, no.2,pp.205-220, Apr. 1992.
[43] Lewis A S , Knowles G. Image Compression Using the 2 - D Wavelet Transform [J ] . IEEE Transactions on Image Processing , 1992 , 1.
[44] Chui C K , Lian J A . A study of orthonormal multi-wavelets[J].Applied Numerical Mathematics,1996,20(3):273-298.
[45] Jiang Q T . Orthogonal multiwavelet with optimum time-frequency resolution[J].IEEE Trans on Signal Processing,1998,46(4):830-844.
[46] Cotronei M,Montefusco L B,Puccio L.Multiwavelet analysis and signal processing[J].IEEE Trans on Circuits and Systems-II:Analog and Digital Signal Processing,1998,45(8):970-987.
[47] Goodman T N T,Lee S L.Wavelets of multiplicity[J].Trans American Mathematical Society,1994,342:307-324.
[48] Xia X G,Geronimo J S,Hardin D P et al.Design of prefilters for discrete multiwavelet transforms[J].IEEE Trans on Signal Processing,1996,44(1):25-34.
[49] Strela V,Heller P N, Topiwala Petal.The application of multiwavelet filter banks to image processing[J].IEEE Trans on Image Processing,1999,8(4):548-563.
[50] Tham J Y,Shen L X,Lee S Letal.A general approach for analysis and application discrete multiwavelet transforms[J] . IEEE Trans on Signal Processing,2000,48(2):457-464.
[51] Douglas P. Hardin1 and Jeffrey A. Marasovich Biorthogonal Multiwavelets on [-1, 1] Applied and Computational Harmonic Analysis 7, 34–53 (1999)
[52] David Taubman High Performance Scalable Image Compression with EBCOT IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 9, NO. 7, JULY 2000
[53] Vetterli M. and Herley C., Wavelets and filter banks: Theory and design, IEEE Trans. Acoust. Speech signal proc., 1992, Vol.40, No.9, pp. 2207-2232.
[54] Strela V and Heller P,N “The Application of Multiwavelet Transform to Image Coding”[J] IEEE.Trans.on Image Processing, 2000, Vol.9, No.2:270-273.
[55] Michael B.Martin and Amy E.Bell “New Image Compress Techniques using Multiwavelet and Multwavelet Packet”[J] IEEE.Trans.on Image Processing, 2001,Vol.10 No.4:500-503.
[56] David S.Taubman“High Performance Scalable Image Compression with EBCOT” [J] IEEE.Trans.on Image Processing, 2000, Vol.9, No.7:1158-1170.
[57] V. Strela and A. T. Walden, "Signal and Image Denoising via Wavelet Thresholding: Orthogonal and Biorthogonal, Scalar and Multiple Wavelet Transforms", Imperial College, Statistics Section, Technical Report TR-98-01 (1998).
[58] Attakitmongcol K,Hardin D P,Wikes D M.Multiwavelet Prefilters part II:optimal orthogonal prefilters[J]. IEEE Trans on Image Processing, 2001,10(10) :1476-1478