JPEG2000是一種新一代的影像壓縮標準，最早是由聯合圖像專家群(Joint Photographic Experts Group)於西元2000年時所發布制定的標準，其國際標準號為ISO/IEC 15444-1，其制訂了JPEG2000的核心編碼系統，其中包含了基本的JPEG2000影像壓縮的特性和壓縮後的檔案編碼資料格式及其檔案附檔名(.jp2、.j2c)等。在JPEG2000影像壓縮標準中，又可分為失真影像壓縮和無失真影像壓縮，其中在失真影像壓縮中和前一代的JPEG影像壓縮標準相比，在相同的壓縮影像品質下，JPEG2000可以有更好的壓縮率，且不會產生如JPEG影像壓縮後的塊狀模糊(類似馬賽克)情況。
在奈米世代下由於電晶體的微小化，造成積體電路在製造過程中發生製程參數漂移以及電子元件之量子效應等因素，導致晶片良率下降使電路不正常運作。容誤(Error-Tolerant)為一嶄新的觀念，不僅可辨識完全無缺陷之待測電路，更致力於辨識當中雖有缺陷但在應用上仍可以接受之部分，由於人類的感官系統靈敏度的關係，對於多媒體影像、聲音些微的變化不易察覺，因此對於製造過程中產生缺陷使電路運算結果有些微瑕疵，而造成對多媒體影像訊號、聲音訊號產生些微的變化，極可能根本無法察覺其表現出來的行為與正確結果的差異，因此容誤的觀念將可有效提升可用晶片數量，使晶片製造成本大幅下降。
本論文的主要目的在研究於JPEG2000影像編碼流程中的算術運算電路發生錯誤時，所造成的錯誤運算結果，是否會對所壓縮之影像造成無法容忍之錯誤結果。JPEG2000算術運算電路中主要可分為無失真壓縮之離散小波轉換、失真壓縮之離散小波轉換、量化器等三個部分，本論文將分別針對上述三個部分做電路的容誤特性分析。分析結果顯示使用者可根據可接受的影像品質及產品應用輕易辨識最容易受錯誤影響之電路模組，並以最低成本重新設計可容誤之算術運算電路，使其在不同的應用中達到最大的錯誤可接受度。

JPEG2000 is a new image compression standard formulated by Joint Photographic Experts Group in 2000. There are two modes for image compression in JPEG2000 standard: lossless compression mode and lossy compression mode. Compare with JPEG image compression standard, JPEG2000 can achieve higher compression ratio with the same quality of compressed images, and no blocking artifacts will be generated after images are compressed.
Due to the shrinking of transistors, the problems of low yield, low reliability and short lifetime become more serious. Conventional test methods that do not consider human insensitivity to minor noises in audio or video signals may discard many electronic products containing some manufacturing defects. Error-tolerance, which aims to identify not only defect-free chips but also acceptable ones from the discarded parts by the conventional test methodologies, is a promising method to improve the effective yield of chips.
In this thesis we analyzed the effects of defects in JPEG2000 image compression circuit on the image quality. Here we focus on the arithmetic computation circuitry in a JPEG 2000 encoder design, namely the discrete wavelet transform and quantization modules. We inject faults in these two parts and then carefully discuss the resulting fault effects in terms of PSNR (Peak Signal to Noise Ratio) and SSIM (Structural Similarity). The experimental results show that some chips with defects will be accepted and we classified them to some different levels for applications. We also provided some re-design suggestions so that will cost down and raising yield.

論文審定書 i
誌謝 ii
中文摘要 iii
Abstract iv
目錄 v
表目錄 vii
圖目錄 ix
第一章 緒論 1
1.1 研究背景 1
1.2 研究動機 2
1.3 論文貢獻 4
1.4 章節介紹 5
第二章 背景及相關文獻回顧 6
2.1 JPEG2000影像編碼流程 6
2.2 離散小波轉換 13
2.2.1 傳統式離散小波轉換架構 14
2.2.2 上提式離散小波轉換架構 16
2.3 量化 20
2.4 容誤 (Error Tolerance) 22
2.5 熵編碼 24
第三章 JPEG2000編碼器 – 硬體電路設計與實現 27
3.1 上提式5/3離散小波轉換 27
3.2 上提式9/7離散小波轉換 31
3.3 JPEG2000影像編碼之量化器 35
第四章 JPEG2000編碼器容誤特性分析及設計探討 38
4.1 無失真壓縮 44
4.1.1 無失真壓縮之容誤分析 44
4.1.2 無失真壓縮之設計探討 49
4.2 失真壓縮且不進行量化 51
4.2.1 失真壓縮且不進行量化之容誤分析 51
4.2.2 失真壓縮且不進行量化之設計探討 56
4.3 失真壓縮搭配高量化步階 58
4.3.1 失真壓縮搭配高量化步階之容誤分析 58
4.3.2 失真壓縮搭配高量化步階之設計探討 63
4.4 失真壓縮搭配中量化步階 65
4.4.1 失真壓縮搭配中量化步階之容誤分析 65
4.4.2 失真壓縮搭配中量化步階之設計探討 70
4.5 失真壓縮搭配低量化步階之容誤分析 72
4.5.1 失真壓縮搭配低量化步階之容誤分析 72
4.5.2 失真壓縮搭配低量化步階之設計探討 77
4.6針對固接錯誤於電路中之容誤分析及設計探討 79
第五章 結論及未來展望 81
參考文獻 82

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