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研究生:曾建銘
研究生(外文):Chien-Ming Tseng
論文名稱:利用FPGA設計JPEG2000中之離散小波轉換
論文名稱(外文):Implementation of Wavelet Transform in JPEG 2000 Using FPGA
指導教授:曾建誠曾建誠引用關係
指導教授(外文):Chien-Cheng Tseng
學位類別:碩士
校院名稱:國立高雄第一科技大學
系所名稱:電腦與通訊工程所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:78
中文關鍵詞:JPEG 2000離散小波轉換共享子表示式
外文關鍵詞:lifting schemesubexpression sharingdiscrete wavelet transformJPEG 2000
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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


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