臺灣博碩士論文加值系統

在數位影像處理的領域，JPEG-2000使用離散小波轉換為其壓縮標準。因此，近年來，二維順向與反向離散小波轉換被當成一個強大的工具，用於影像編解碼的系統。由於二維順向與反向離散小波轉換需要大量的運算，因此，需要設計一個高效能的晶片或者是以FPGA實現。在分解端的核心是順向離散小波轉換，而合成端，反向離散小波轉換要順向轉換產生的係數恢復成原始影像。
本論文提出兩個二維順向與反向離散小波轉換，針對大小為 的影像僅需要 運算時間，第一個部份提出一個高效能順向轉換架構，包括一個轉換模組，位址產生器，以及記憶體模組。轉換模組有一致且規則的架構，簡單的控制電路。第二個部份反向轉換架構是利用平行與管線化的運算，達到高速的運算架構。兩個架構都可以達到100%的硬體使用率，而且適用於二維數位影像處理，如JPEG-2000。
所提出的架構皆以Verilog硬體描述語言來實現，再使用Synopsys的Design Compiler進行電路合成。最後再使用Synopsys的Astro，配合TSMC的0.18 製程技術自動合成出晶片。

In the field of digital image processing, the JPEG-2000 standard uses the discrete wavelet transform for image compression; hence, the two-dimensional (2-D) forward discrete wavelet transform (FDWT)/ inverse DWT (IDWT) has recently been used as a powerful tool for image coding/decoding systems. 2-D FDWT/IDWT demands massive computations, hence, it requires a parallel and pipelined architecture to implement high-efficiency application-specific integrated circuits (ASIC) or field programmable gate array (FPGA). At the heart of the analysis stage of the system is the FDWT. In the synthesis stage, the IDWT recovers the original image from the coefficients of FDWT.
This paper proposes two architectures with computing time for 2-D FDWT and IDWT. The first high-efficiency architecture comprises a transform module, an address generator, and a RAM module. The transform module has uniform and regular structure, simple control flow. The second architecture features parallel and pipelined computation and high throughput, both of the proposed architectures are 100% hardware-utilization and suitable for 2-D digital image processing, such as JPEG-2000.
The proposed VLSI architectures are realized with Verilog HDL, synthesized by the Synopsys Design Compiler. Finally, the layouts for those designs are generated with the Synopsys Astro Tools in a 0.18 1P6M CMOS technology.

目錄
英文摘要．．．．．．．．．．．．．．．．．．．．．．．．．Ⅰ
摘要．．．．．．．．．．．．．．．．．．．．．．．．．．．Ⅱ
誌謝．．．．．．．．．．．．．．．．．．．．．．．．．．．Ⅲ
目錄．．．．．．．．．．．．．．．．．．．．．．．．．．．Ⅳ
圖目錄．．．．．．．．．．．．．．．．．．．．．．．．．．Ⅶ
表目錄．．．．．．．．．．．．．．．．．．．．．．．．．．Ⅹ
第一章 導論 ．．．．．．．．．．．．．．．．．．．．．．1
1.1 研究背景 ．．．．．．．．．．．．．．．．．．．．．1
1.2 相關研究與研究目的 ．．．．．．．．．．．．．．．．2
1.3 章節概要 ．．．．．．．．．．．．．．．．．．．． 3
第二章 離散小波轉換 ．．．．．．．．．．．．．．．．．．4
2.1 前言 ．．．．．．．．．．．．．．．．．．．．．．．4
2.2 離散小波轉換 ．．．．．．．．．．．．．．．．．．．4
2.3 旋積分式離散小波轉換 ．．．．．．．．．．．．．．．5
2.3.1 一維順向離散小波轉換 ．．．．．．．．．．．．．．5
2.3.2 一維反向離散小波轉換 ．．．．．．．．．．．．．．7
2.4 二維離散小波轉換 ．．．．．．．．．．．．．．．．．8
2.4.1 分離式二維離散小波轉換 ．．．．．．．．．．．．．9
2.4.2 非分離式二維離散小波轉換 ．．．．．．．．．．．10
2.4.3 應用於二維影像的分解 ．．．．．．．．．．．．．12
第三章 高效能架構之二維離散小波轉換．．．．．．．．．．14
3.1 前言．．．．．．．．．．．．．．．．．．．．．．．14
3.2 實現分離式二維順向離散小波轉換．．．．．．．．．．14
3.2.1 圖層式架構 ．．．．．．．．．．．．．．．．．．15
3.2.2 多相分解．．．．．．．．．．．．．．．．．．．．16
3.3 邊界問題．．．．．．．．．．．．．．．．．．．．．27
3.3.1 Zero-padding extension ．．．．．．．．．．．．．．27
3.3.2 Periodic extension．．．．．．．．．．．．．．．．．28
3.4 效能比較．．．．．．．．．．．．．．．．．．．．．31
第四章 高效能架構之二維反向離散小波轉換．．．．．．．．34
4.1 前言．．．．．．．．．．．．．．．．．．．．．．．34
4.2 實現分離式二維反向離散小波轉換．．．．．．．．．．34
4.2.1 圖層式架構 ．．．．．．．．．．．．．．．．．．35
4.2.2 多相分解．．．．．．．．．．．．．．．．．．．．36
4.3 邊界問題．．．．．．．．．．．．．．．．．．．．．46
4.3.1 Zero-padding extension ．．．．．．．．．．．．．．46
4.3.2 Periodic extension．．．．．．．．．．．．．．．．．46
4.4 效能比較．．．．．．．．．．．．．．．．．．．．．48
第五章 模擬結果 ．．．．．．．．．．．．．．．．．．．．50
5.1 設計流程圖．．．．．．．．．．．．．．．．．．．．50
5.2 模擬結果．．．．．．．．．．．．．．．．．．．．．51
第六章 結論．．．．．．．．．．．．．．．．．．．．．．55
參考文獻．．．．．．．．．．．．．．．．．．．．．．．．．57

參考文獻
[1]S. Mallat, “Multifrequency channel decompositions of images and wavelet models,” IEEE Trans. Acoust., Speech, Signal Processing, vol.37, pp. 2091-2110, 1989.
[2]S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. & Mach. Intell., vol. 11, pp. 674-693, July 1989.
[3]A. N. Akansu and R. A. Haddad, Multiresolution Signal Decomposition: Transform, Subbands and Wavelets. New York: Academic, 1992.
[4]I. Sodagar, H.-J. Lee, P. Hatrack, and Y.-Q. Zhang, “Scalable wavelet coding for synthetic/natural hybrid images,” IEEE Trans. Circuits and Systems for Video Technology, vol. 9, pp. 244-254, Mar. 1999.
[5]D. Taubman, “High performance scalable image compression with EBCOT,” IEEE Trans. Image Processing, vol. 9, pp. 1158-1170, July 2000.
[6]R. Kronland-Martinet, J. Morlet, and A. Grossman, “Analysis of sound patterns through wavelet transform,” Int. J. Pattern Recognit. Artif. Intell., vol. 1, no. 2, pp.273-302, 1987.
[7]G. Beylkin, R. Coifman, and V. Rokhlin, Wavelet in Numerical Analysis in Wavelets and their Applications. New York: Jones and Bartlett, 1992.
[8]ISO/IEC ISO/IEC 15444-1 “Information Technology JPEG 2000 Image Coding System”, 2000.
[9]A. S. Lewis and G. Knowles, “VLSI architecture for 2-D Daubechies wavelet transform without multipliers,” Electronic Letters, vol.27, no.2 pp 171-173, 1991.
[10]K. Parhi and T. Nishitani, “VLSI architectures for discrete wavelet transforms,” IEEE Trans. VLSI Systems, vol. 1, no. 2, pp. 191-202, 1993.
[11]C. Chakrabarti and M. Vishwanath, “Efficient realizations of the discrete and continuous wavelet transforms: From single chip implementations to mappings on SIMD array computers,” IEEE Trans. Signal Processing, vol. 43, no. 5, pp. 759-771, 1995.
[12]M. Vishwanath, R. M. Owens, and M. J. Irwin, “VLSI architectures for the discrete wavelet transform,” IEEE Trans. Circuits Syst. –II, vol. 42, no. 5, pp. 305-316, May 1995.
[13]Jijun Chen and M. A. Bayoumi, “A scalable systolic array architecture for 2-D discrete wavelet transforms,” in Proc. IEEE VLSI Signal Processing workshop, 1995, pp. 303-312.
[14]P. Wu and L. Chen, “An efficient architecture for two-dimensional discrete wavelet transform,” IEEE Trans. Circuits and Systems for video Tech., vol. 11, no. 4, pp.536-545, 2001.
[15]F. Marino, “Two fast architectures for the direct 2-D discrete wavelet transform- Signal Processing,” IEEE Trans. Signal Processing, vol. 49, no. 6, pp.1248-1347, 2001.
[16]A. Grossmann and J. Morlet, “Decompostion of hardy functions into square integrable wavelets of constant shape,” SLAMJ. Math. Anal., vol. 15, pp. 723-736, 1984.
[17]I. Daubechies, “Orthonormal based of compactly supported wavelets,” Communications on Pure and Applied Mathematics, vol. 41, pp. 909-996, 1988.
[18]M. Ferretti, D. Rizzo, “Handling borders in systolic architectures for the 1-D discrete wavelet transform for perfect reconstruction,” IEEE Trans. Signal Processing, vol. 48, no.5, pp.1365-1378, May 2000.
[19]G. Strang and T. Q. Nquyen, Wavelets and Filter Banks. Wellesley-Cambridge Press, 1996.
[20]I. Daubechies, Ten Lectures on Wavelets, 1st ed. Philadelphia PA: SIAM, 1992.
[21]P. –C. Wu, C. –T. Huang, L. –G. Chen, “ An efficient architecture for two-dimensional inverse discrete wavelet transform,” in Proc. IEEE International Symposium on Circuits and Systems, vol. 2, May 2002, pp. II-312- II-315.
[22]C. Chakrabarti and C. Mumford, “Efficient realizations of analysis and synthesis filters based on the 2-D discrete wavelet transform,” in Proc. the Int. Conf. on Acoustics, Speech and Signal Processing, May 1996, pp. 3256-3259.
[23]Christos Chrysafis and Antonio Ortega, “Line-based, reduced memory, wavelet image compression,” IEEE Trans. Image Processing, vol. 9, no. 3, March 2000.
[24]戴顯權，資料壓縮，紳藍出版社，民90年。