整型小波变换应用于医学图像压缩中的研究
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摘要
医学图像数字化步伐的加快使得PACS（影像存储与传输系统）的发展越来越引人注目。在PACS系统中需要提供较大容量的存储空间来保存海量的医学图像数据；在图像传输过程中，图像数据的大小也会影响到传输速度，因此如何解决PACS系统中这些医学图像的存储和传输问题就显得至关重要。解决这一问题的关键就在于：如何实现医学图像的有效压缩。
目前在PACS系统中较多采用的是JPEG图像压缩标准，该标准采用以离散余弦变换算法为主的区块编码方式,但有一定的局限性。随着基于小波理论的新一代的静态图像压缩标准JPEG2000的诞生及其广泛应用，我们关心的是能否把标准中的重要环节——小波变换应用到医学图像压缩领域，并取得良好的压缩效果。本论文研究了基于提升方案的整型小波变换应用于医学图像压缩，并取得了较好的压缩效果。论文的工作包括以下几个方面：一、采用“提升”算法，实现整型到整型的小波变换，大大降低了运算复杂度，解决了图像小波变换后滤波器系数为浮点数的问题，避免了对浮点数进行量化处理产生相应整数而引起的失真。论文选取CDF(2,2)小波基，取得了较好图像压缩效果；二、通过对小波系数的特点的研究，提出了将嵌入式零树编码和改进的游程编码相结合的方法，实现了小波系数的有效编码；三、采用改进的周期延拓法解决图像进行小波分解时出现的边界问题，并通过软件实现，取得较好的处理效果。
With the quick development of digitalized medical pictures, PACS is more and more noticeable. The memory space of large capacity is needed to store the mass medical picture datum, and the size of the picture data is one of the factors, which decides the transmission speed while the picture is transmitted. Thus it is important to solve the archiving and transmission problem of medical pictures in PACS. The key is how to realize the effective compression of the medical pictures.
The image compression standard in PACS now is the JPEG standard based on the DCT (Discrete Cosine Transform) algorithm, which can only be applied in the limited areas. With the birth and widely use of the JPEG2000, a new still image compression standard, we are interested in making full use of the wavelet transform in the medical image compression, which is the vital link in JPEG2000. The integer wavelet transform based on the Lifting Scheme for the medical picture compression is discussed in this paper. Firstly, the Lifting Scheme is adopted to realize the integer wavelet transform and reduce the operation complexity greatly. Secondly, on the basis of the research on the characteristics of the wavelet coefficients, the combination of the EZW (Embedded Zerotree wavelet) and advanced RLE (Run Length Encode) is presented to realize the efficient codes of the wavelet coefficients. Finally, the improved periodic extension algorithm is used to solve the boundary problem appeared in wavelet transform. The algorithm is realized by software and the good processing results are obtained.
目前在PACS系统中较多采用的是JPEG图像压缩标准，该标准采用以离散余弦变换算法为主的区块编码方式,但有一定的局限性。随着基于小波理论的新一代的静态图像压缩标准JPEG2000的诞生及其广泛应用，我们关心的是能否把标准中的重要环节——小波变换应用到医学图像压缩领域，并取得良好的压缩效果。本论文研究了基于提升方案的整型小波变换应用于医学图像压缩，并取得了较好的压缩效果。论文的工作包括以下几个方面：一、采用“提升”算法，实现整型到整型的小波变换，大大降低了运算复杂度，解决了图像小波变换后滤波器系数为浮点数的问题，避免了对浮点数进行量化处理产生相应整数而引起的失真。论文选取CDF(2,2)小波基，取得了较好图像压缩效果；二、通过对小波系数的特点的研究，提出了将嵌入式零树编码和改进的游程编码相结合的方法，实现了小波系数的有效编码；三、采用改进的周期延拓法解决图像进行小波分解时出现的边界问题，并通过软件实现，取得较好的处理效果。
With the quick development of digitalized medical pictures, PACS is more and more noticeable. The memory space of large capacity is needed to store the mass medical picture datum, and the size of the picture data is one of the factors, which decides the transmission speed while the picture is transmitted. Thus it is important to solve the archiving and transmission problem of medical pictures in PACS. The key is how to realize the effective compression of the medical pictures.
The image compression standard in PACS now is the JPEG standard based on the DCT (Discrete Cosine Transform) algorithm, which can only be applied in the limited areas. With the birth and widely use of the JPEG2000, a new still image compression standard, we are interested in making full use of the wavelet transform in the medical image compression, which is the vital link in JPEG2000. The integer wavelet transform based on the Lifting Scheme for the medical picture compression is discussed in this paper. Firstly, the Lifting Scheme is adopted to realize the integer wavelet transform and reduce the operation complexity greatly. Secondly, on the basis of the research on the characteristics of the wavelet coefficients, the combination of the EZW (Embedded Zerotree wavelet) and advanced RLE (Run Length Encode) is presented to realize the efficient codes of the wavelet coefficients. Finally, the improved periodic extension algorithm is used to solve the boundary problem appeared in wavelet transform. The algorithm is realized by software and the good processing results are obtained.
引文
[1] M.Unser. Approximation power of bi-orthogonal wavelet expansions. IEEE Trans. on signal Processing, 1996, Vol.44, pp.519-527.
[2] O.Rioul. Regular wavelets: a discrete-time approach. IEEE Trans. on Signal processing, 1993, Vol. 41, pp.3572-3579.
[3] M.Antonini, et. al.. Image coding using wavelet transform. IEEE Trans. Image Proc., 1992, Vol. 1, pp. 205-220.
[4] M.Vetterli, and C.Herley. Wavelets and filter banks: Theory and design. IEEE Trans. Acoust. Speech signal proc., 1992, Vol.40, No.9, pp. 2207-2232.
[5] A.Said, and W.A.Pearlman. A new fast and efficient image codec based on set partitioning in hierarchical trees. IEEE Trans. on Circuits and Systems for Video Technology, 1996, Vol. 6, pp. 243-250.
[6] I.Daubechies, And W.Sweldens. Factoring wavelet transforms into lifting steps. J. Fourier Anal. Appl., 1998, Vol. 4, No. 3, pp.247-269.
[7] W.Sweldens. The lifting scheme: A construction of second generation wavelets. SIAM J. Math. Anal., 1997.
[8] S.Mallat. A theory for multiresolution signal decomposition:the wavelet representation. IEEE Trans. Pattern Analysis and machine Intelligence, 1989, Vol. 11, pp. 674-693.
[9] J.Shapiro. Embedded image coding using zerotrees of wavelet coefficients. IEEE Trans. on Signal Processing, 1993, Vol. 41, pp. 3445-3462.
[10] A.R.Caldebank, I.Daubechies, W.Sweldens, and B.L.Yeo. Wavelet transform that map integers to integers. Appl. Comput. Harmo. Anal.,vol.5, pp.332-369,1998.
[11] F.Sheng, A.Bilgin, P.J.Sementilli, and M.W.Marcellin. Lossy and lossless image compression using reversible integer wavelet transforms. Processings 1998 International Conference on Image Processing. Los Alamitos, CA: IEEE Press, vol.3, pp.876-880.
[12] M.D.Adams and F.Kossentini. Reversible integer-to-integer wavelet transforms for image compression: Performance evaluation and analysis. IEEE Trans. Image Processing, 9(6), pp. 1010-1024,2000.
[13] J.Reichel, G.Menegaz, M.J.Nadenau, and M.Kunt. Integer Wavelet Transform for Embedded Lossy to Lossless Image Compression, IEEE Trans. Image Processing, 10(3), pp. 383-392, 2001.
[14] A. Zandi, J.D.Allen, E.L.Schwartz and M.Boliek. CREW: Compression with Reversible Embedded Wavelets. Processings. DCC 1995 Data Compression Conference, pp. 212-221.
[15]C.A.Christopoulos, T.Ebrahimi and A.N.Skodras.JPEG2000:The New Still Picture Compression Standard. http://www.eecs.harvard.edu/~michaelm/E126/jpegb.pdf
[16]David B.H.Tay. Rationalizing the Coefficients of Popular Biorthogonal Filters. IEEE Transactions on Circuits and Systems for Video Technology, Vol.10, No.6, September 2000, pp. 998-1005.
[17][美]崔锦泰著，程正兴译，小波分析导论，西安：西安交通大学出版社，1995
[18]程正兴，小波分析算法与应用，西安：西安交通大学出版社，1998
[19]潘爱民，王国印，Visual c++技术内幕（第四版），清华大学出版社，2001
[20]胡广书，数字信号处理——理论、算法与实现，清华大学出版社，2002
[21]勒中鑫，数字图像信息处理，国防工业出版社，2003
[2] O.Rioul. Regular wavelets: a discrete-time approach. IEEE Trans. on Signal processing, 1993, Vol. 41, pp.3572-3579.
[3] M.Antonini, et. al.. Image coding using wavelet transform. IEEE Trans. Image Proc., 1992, Vol. 1, pp. 205-220.
[4] M.Vetterli, and C.Herley. Wavelets and filter banks: Theory and design. IEEE Trans. Acoust. Speech signal proc., 1992, Vol.40, No.9, pp. 2207-2232.
[5] A.Said, and W.A.Pearlman. A new fast and efficient image codec based on set partitioning in hierarchical trees. IEEE Trans. on Circuits and Systems for Video Technology, 1996, Vol. 6, pp. 243-250.
[6] I.Daubechies, And W.Sweldens. Factoring wavelet transforms into lifting steps. J. Fourier Anal. Appl., 1998, Vol. 4, No. 3, pp.247-269.
[7] W.Sweldens. The lifting scheme: A construction of second generation wavelets. SIAM J. Math. Anal., 1997.
[8] S.Mallat. A theory for multiresolution signal decomposition:the wavelet representation. IEEE Trans. Pattern Analysis and machine Intelligence, 1989, Vol. 11, pp. 674-693.
[9] J.Shapiro. Embedded image coding using zerotrees of wavelet coefficients. IEEE Trans. on Signal Processing, 1993, Vol. 41, pp. 3445-3462.
[10] A.R.Caldebank, I.Daubechies, W.Sweldens, and B.L.Yeo. Wavelet transform that map integers to integers. Appl. Comput. Harmo. Anal.,vol.5, pp.332-369,1998.
[11] F.Sheng, A.Bilgin, P.J.Sementilli, and M.W.Marcellin. Lossy and lossless image compression using reversible integer wavelet transforms. Processings 1998 International Conference on Image Processing. Los Alamitos, CA: IEEE Press, vol.3, pp.876-880.
[12] M.D.Adams and F.Kossentini. Reversible integer-to-integer wavelet transforms for image compression: Performance evaluation and analysis. IEEE Trans. Image Processing, 9(6), pp. 1010-1024,2000.
[13] J.Reichel, G.Menegaz, M.J.Nadenau, and M.Kunt. Integer Wavelet Transform for Embedded Lossy to Lossless Image Compression, IEEE Trans. Image Processing, 10(3), pp. 383-392, 2001.
[14] A. Zandi, J.D.Allen, E.L.Schwartz and M.Boliek. CREW: Compression with Reversible Embedded Wavelets. Processings. DCC 1995 Data Compression Conference, pp. 212-221.
[15]C.A.Christopoulos, T.Ebrahimi and A.N.Skodras.JPEG2000:The New Still Picture Compression Standard. http://www.eecs.harvard.edu/~michaelm/E126/jpegb.pdf
[16]David B.H.Tay. Rationalizing the Coefficients of Popular Biorthogonal Filters. IEEE Transactions on Circuits and Systems for Video Technology, Vol.10, No.6, September 2000, pp. 998-1005.
[17][美]崔锦泰著，程正兴译，小波分析导论，西安：西安交通大学出版社，1995
[18]程正兴，小波分析算法与应用，西安：西安交通大学出版社，1998
[19]潘爱民，王国印，Visual c++技术内幕（第四版），清华大学出版社，2001
[20]胡广书，数字信号处理——理论、算法与实现，清华大学出版社，2002
[21]勒中鑫，数字图像信息处理，国防工业出版社，2003