臺灣博碩士論文加值系統

有別於傳統的JPEG標準新一代的靜態影像壓縮標準，新興的JPEG 2000標準放棄了「離散餘弦轉換」(Discrete Cosine Transform ,DCT) 為主的區塊編碼方式，而改採以「離散小波轉換」(Discrete Wavelet Transform ,DWT)為其主要的轉換核心。另外，因為JPEG 2000 可提供有損與無損的壓縮、漸進式傳輸、大型圖片的壓縮及感興趣區域等功能，因此，JPEG 2000 的設計可滿足非常多樣的應用，如：印表機、無線手機、數位相機、醫療圖像、網際網路及電子商務等。

由於Lifting scheme擁有可快速的完成離散小波轉換、允許區域內計算和具有可還原性等特點，因此JPEG 2000 標準之離散小波轉換採用Lifting scheme方式以完成其轉換。本論文首先提出一擴展方法以對一維離散小波轉換中的串列輸入信號作對稱性擴展。其次，嘗試使用加法器為主之分散式算術以簡化Lifting scheme為基礎的「9 / 7」濾波器架構中各乘法器電路，另外，再以尋找其共用項的方式進一步降低電路成本。而最後，我們以Verilog HDL語言設計本論文中電路架構並在FPGA中驗證電路的正確性。

JPEG 2000 is the emerging standard for coding and compressing still images. JPEG 2000 is based upon a discrete wavelet transformation (DWT), as it compares to the existing JPEG standard that uses the discrete cosine transform (DCT). The JPEG 2000 provides the numerous advantages over the existing JPEG standard. Performance gains include improved compression efficiency at low bit rates or for large images, while new functionalities include, progressive transmission, lossy or lossless compression, and region-of-interest (ROI). The JPEG 2000 standard is being designed to serve a number of different markets and applications such as low bandwidth transmission of images on networks over the Web, Internet, medical imaging, digital photography, e-commerce and scanner applications.
With the advantage of faster implementation of the discrete wavelet transform, fully in-place calculation, and the inverse wavelet transform which can be found by undoing the operations of the forward wavelet transform, the lifting scheme has been chosen in the JPEG 2000 standard. First, we perform a symmetric extension of the input signals. Then, based on the adder-based Distributed Arithmetic(DA), we can use CSD form to reduce the nonzero bits of the 「9 / 7」 filter coefficients and find the share terms of multipliers to reduce the hardware. Finally, the proposed architecture is described in Verilog HDL, synthesized and verified on Xilinx FPGA.

中文摘要……………………………………………………………………………i
英文摘要……………………………………………………………………………ii
誌謝…………………………………………………………………………………iii
目錄…………………………………………………………………………………iv
圖目錄………………………………………………………………………………vii
表目錄……………………………………………………………………………ix
壹、研究背景………………………………………………………………………1
一、JPEG 2000簡介……………………………………………………………1
二、JPEG 2000的特性…………………………………………………………2
三、小波轉換簡介……………………………………………………………7
四、研究動機…………………………………………………………………8
五、論文架構…………………………………………………………………8
貳、離散小波轉換…………………………………………………………………10
一、以捲積實現離散小波轉換………………………………………………10
二、以Lifting scheme實現離散小波轉換……………………………………14
三、軟體實作…………………………………………………………………20
(一) 正向離散小波轉換………………………………………………20
1.二維次頻分解……………………………………………………22
2.垂直次頻分解……………………………………………………23
3.水平次頻分解……………………………………………………26
4.一維次頻分解……………………………………………………28
5.週期對稱性擴展…………………………………………………28
6.一維濾波…………………………………………………………30
(1)「5 / 3」濾波……………………………………………………30
(2)「9 / 7」濾波……………………………………………………31
7.二維分離…………………………………………………………32
(二) 反向離散小波轉換………………………………………………34
1.二維次頻重組……………………………………………………34
2.二維交織…………………………………………………………35
3.水平次頻重組……………………………………………………36
4.垂直次頻重組……………………………………………………36
5.一維次頻重組……………………………………………………36
6.週期對稱性擴展…………………………………………………36
7.一維反濾波………………………………………………………37
(1)「5 / 3」反濾波…………………………………………………37
(2)「9 / 7」反濾波…………………………………………………37
參、分散式算術……………………………………………………………………39
一、ROM為主之分散式算術…………………………………………………39
二、加法器為主之分散式算術………………………………………………41
(一) CSD…………………………………………………………………42
(二) 共用子表示式……………………………………………………44
1.水平共用…………………………………………………………44
2.垂直共用…………………………………………………………46
肆、硬體架構………………………………………………………………………49
一、對稱性擴展………………………………………………………………49
二、濾波器……………………………………………………………………52
1.共用子表示式……………………………………………………57
(1)CSD表示…………………………………………………57
(2)α與γ的共用子表示式……………………………………59
(3)β與δ的共用子表示式……………………………………60
(4)K的共用子表示式……………………………………………62
(5)1 / K的共用子表示式………………………………………63
伍、模擬結果………………………………………………………………………65
一、對稱性擴展結果…………………………………………………………65
二、一維正向離散小波轉換結果……………………………………………70
陸、結論………………………………………………………………………75
一、結論………………………………………………………………………75
二、未來工作…………………………………………………………………75
柒、參考文獻………………………………………………………………………76

[1]ISO/IEC 10918-1,”Information technology - Digital Compression and Coding of Continuous-tone Still Images: Requirements and Guidelines,” 1994 [2]S. Subhasis, ”Image Compression - from DCT to Wavelets: A Review," ACM Crossroads, http://www.acm.org/crossroads/xrds6-3/sahaimgcoding.html[3]ISO/IEC 15444-1:2000, “Information Technology - JPEG 2000 image coding system - Part 1: Core coding system,” March 2000[4]C. Christopoulos, A. Skodras, and T. Ebrahimi, “The JPEG2000 still image coding system: an overview” IEEE Trans. Consumer Electronics, Vol: 46, No. 4, Nov. 2000, pp.: 1103 —1127[5]M. Charrier, D.S. Cruz, and M. Larsson, “JPEG2000, the next millennium compression standard for still images,” IEEE Int. Conf. Multimedia Computing and Systems, Vol: 1 , 1999, pp. 131 -132[6]M. W. Marcellin, M. J. Gormish, A. Bilgin, and M. P. Boliek, ”An overview of JPEG-2000,”in Data Compression Conference 2000, Mar. 2000, pp. 523—541[7]A. Skodras, C. Christopoulos, and T. Ebrahimi, “The JPEG 2000 still image compression standard,” IEEE Signal Processing Magazine, Vol: 18, No. 5 , Sept. 2001 Page(s): 36 —58[8]A. Harr, "Zur theorie der othogonalem Funktionensysteme," Mathematsche Annalen, 69 , 1910, pp. 331-371[9]A. Grossmann　and　J. Morlet, “ Decomposition　of　Hardy　functions into　Square　Integrable　Wavelets　of　Constant　Shape,”　SIAM　J. Math. Anal.　Vol. 15, July　1984 pp.723-736[10]S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Analysis Machine Intelligence, vol. 11, No. 7, pp. 674—693, 1988.[11]I. Daubechies, ”Orthonormal Bases of Compactly Supported Wavelets,” Communications on Pure and Applied Mathematics, Vol. 41 , 1988, pp. 909-996[12]S. H. Nawab, and T. F. Quatieri, "Short-time Fourier Transform", in Advances in Spectrum Analysis and Array Processing, vol.1 of 2, S. Haykin, Ed. New York: Prentic Hall, 1990.[13]B.E. Usevitch, “A tutorial on modern lossy wavelet image compression: foundations of JPEG 2000,” IEEE Signal Processing Magazine, Vol. 18, No5 , Sept. 2001, pp. 22 —35[14]W. Sweldens. “The lifting scheme: A construction of second generation wavelets,” SIAM J. Math. Anal, Vol. 29, No. 2, March 1998, pp.511-546 [15]胡俊光,” 快速小波轉換之研究” ，國立臺灣大學資訊工程學研究所碩士論文，2001[16]W. Sweldens, “The Lifting Scheme: A new philosophy in biorthogonal wavelet constructions”, Wavelet Applications in Signal and Image Processing III, Proc. SPIE 2569, 1995, pp. 68-79[17]I. Daubechies and W. Sweldens "Factoring wavelet transforms into lifting steps," Journal of Fourier Analysis Applications, Vol. 4, No. 3,1998, pp. 247-269[18]C.-J. Lian, K.-F. Chen, H.-H. Chen, and L.-G. Chen” Lifting based discrete wavelet transform architecture for JPEG2000,” IEEE Int. Symposium on Circuits and Systems, ISCAS 2001. , Vol: 2 , 2001, pp. 445 -448 [19]K. Wiatr and E. Jamro,” Constant coefficient multiplication in FPGA structures” Euromicro Conf. 2000. Vol. 1, 2000, pp. 252 -259 [20]S.A. White, “Applications of distributed arithmetic to digital signal processing: a tutorial review,” IEEE Signal Processing Magazine, Vol. 6, No. 3 , July 1989 pp. 4 —19[21]R. Hartley, “Optimization of canonic signed digit multipliers for filter design”Circuits and Systems, 1991., IEEE Int. Sympoisum , 1991, pp. 1992 -1995 [22]W. Pan, A. Shams, and M.A. Bayoumi, “NEDA: a new distributed arithmetic architecture and its application to one dimensional discrete cosine transform,” IEEE Workshop on Signal Processing Systems, 1999 pp. 159 —168[23]T.-S. Chang and C.-W. Jen, “Hardware-efficient implementations for discrete function transforms using LUT-based FPGAs,” IEE Proceedings on Computers and Digital Techniques , Vol. 146, No. 6 , Nov. 1999 pp. 309 —315[24]T.-S. Chang, C.-S. Kung, and C.-W. Jen “A simple processor core design for DCT/IDCT,” IEEE Trans. Circuits and Systems for Video Technology, Vol. 10, No. 3 , April 2000 pp. 439 —447[25]J.-M. Jou, Y.-H. Shiau, and C.-C. Liu “Efficient VLSI architectures for the biorthogonal wavelet transform by filter bank and lifting scheme” IEEE Int. Symposium on Circuits and Systems, 2001, pp. 529 -532