現今為了節省記憶體使用率以及減少網路傳輸時間的緣故，影像壓縮不只變得愈越來越受歡迎而且愈來愈受重視。影像壓縮的終極目標，就是盡可能使用少量的儲存空間來記錄大筆的資料，例如JPEG與JPEG2000。其中JPEG的全名為Joint Photographic Experts Group，是一種失真影像壓縮技術。「失真」一詞表示我們無法完美重建或解壓該JPEG壓縮後的圖片，也就是圖片會喪失一些細節、資訊。所以，JPEG在某些應用上無法提供足夠的品質保證，例如：醫學影像、具有複雜紋理的影像等等。縱使JPEG2000提供比JPEG更良好的影像品質以及壓縮率，但它的普及率仍然比不上JPEG；這是因為當我們使用JPEG2000來壓縮影像時，必須將整張影像讀進記憶體的緩衝暫存區裡來做處理，這會造成硬體實現上高昂的記憶體成本與使用量。
誠如上述所提，即使JPEG2000在壓縮領域有著不凡的表現，但是極高的記憶體緩衝暫存區需求導致它仍然不同於JPEG般地普及；對於實作上諸如嵌入式系統和行動裝置等產品而言，記憶體緩衝暫存區的使用量是一個非常重要的考量點。由於大量的緩衝暫存區使用量會導致極高的硬體成本，為此我們提出一套新的壓縮方案來解決該困擾，使用預測編碼並結合JPEG與JPEG2000中離散餘弦轉換以及離散小波轉換的特性來降低緩衝暫存區需求量。
除此之外，我們亦針對可適性算數編碼的機率表提出一套加權後的累計方法，該方法適用於各種既有的資料壓縮技術，像是影像以及文字壓縮等。根據實驗結果，我們提出的加權可適性算數編碼比起靜態算數編碼以及可適性算數編碼，能得到更好的壓縮效果。
近年來，有一類主題在影像壓縮的領域中變得相當熱門，那就是醫學影像壓縮。一般而言，醫學影像中有任何細節上的誤差是不被允許的；因此，失真影像壓縮技術通常是不能使用在醫學影像上的。為此我們針對醫學影像中的其中一種類型，即膠原蛋白影像，提出一種新的無失真壓縮方法；由於膠原蛋白影像的紋理非常複雜，以周圍鄰居像素為基礎的預測方式的無失真壓縮法，並不適用於該類型影像，為此我們提出一套方法，將複雜的紋理簡單化，再進行無失真壓縮。

Image compression is more and more important because it is helpful for saving the memories and reducing the transmission time. Two popular image compression standards are JPEG and JPEG2000. JPEG is an acronym for the Joint Photographic Experts Group, which is a lossy image compression method. “Lossy” means that we cannot reconstruct the original image without error (i.e. some information is lost). Therefore, JPEG may not be suitable in some applications, such as medical image encoding and compressing an image with a complicated texture, etc.
JPEG 2000 has a better compression performance than JPEG. However, it is not as popular as JPEG due to the large requirement of buffer size. When we compress an image with JPEG 2000, we have to input the entire image into the buffer. Thus, it costs a lot of memory to implement JPEG 2000.
In practice, the buffer size requirement is an important issue in many embedded systems and mobile devices. Owing to the fact that the cost of hardware is proportional to the buffer size, we propose a new compression method that is a hybrid of the discrete cosine transform, the discrete wavelet transform, and predictive coding techniques. It has a good compression performance and the required buffer size is as small as that of JPEG.
In addition, we also propose a weighted accumulating method for adjusting the probability table in adaptive arithmetic coding, which can be applied in image compression and text compression. We show the simulation results that our proposed weighted adaptive arithmetic coding has better performance than both the static and the conventional adaptive arithmetic coding schemes.
In recent years, medical image compression becomes more and more popular. In general, a lossy compression method cannot be applied to the medical image because the details in a medical image are important for diagnosis. In this thesis, we also proposed a lossless image compression algorithm to encode collagen images, which are important for diabetes and skin cancer diagnosis. The conventional lossless coding which based on the neighbor-based prediction is not suitable for the complicated collagen image. Therefore, we propose a new method to reduce the complexity of texture in the collagen image and lossless compress the simplified texture after all.

口試委員會審定書......#
誌謝......i
中文摘要......iii
ABSTRACT......v
CONTENTS......vii
LIST OF FIGURES......xi
LIST OF TABLES......xv
Chapter 1 Introduction......1
Chapter 2 JPEG......3
2.1 PSNR......3
2.2 Flowchart of JPEG Encoder......6
2.3 Correlation between pixels......7
2.4 Color space transformation-RGB to YCbCr & Downsampling......8
2.5 Discrete Cosine Transform (DCT) for JPEG......11
2.5.1 Karhunen-Loeve Transform (KLT):......11
2.5.2 Discrete Cosine Transform (DCT):......11
2.6 Quantization for JPEG......14
2.7 Zigzag-Scanning......16
2.8 Huffman Coding......17
Chapter 3 JPEG 2000 (Part 1)......19
3.1 Forward Multicomponent Transformation......20
Chapter 4 Wavelet Transform......21
4.1 Continuous Wavelet Transform......22
4.1.1 Definition......22
4.1.2 Inverse Wavelet transform......24
4.1.3 Constraints......25
4.2 Continuous Wavelet Transform with Discrete Coefficients......26
4.2.1 Definition......26
4.2.2 Inverse Wavelet Transform......27
4.2.3 Constraints......27
4.3 Discrete Wavelet Transform......28
4.3.1 Concept......28
4.3.2 1-D DWT......28
4.3.3 2-D DWT......30
4.3.4 Inverse DWT......32
4.3.5 Complexity of the Discrete Wavelet Transform......33
4.4 Discrete Wavelet Transform (DWT) for JPEG 2000......35
Chapter 5 JPEG 2000 (Part 2)......37
5.1 Forward Wavelet Transformation......37
5.2 Quantization for JPEG 2000......39
5.3 Tier-1 Encoder......39
5.4 Rate Control......40
5.5 Tier-2 Encoder......40
Chapter 6 Summaries of JPEG and JPEG2000......41
6.1 Summary of JPEG......41
6.2 Summary of JPEG 2000......41
Chapter 7 An Implementation for JPEG Decoder......43
7.1 Read Header......45
7.1.1 Read Quantization Table......46
7.1.2 Read Frame Header......49
7.1.3 Read Huffman Table......50
7.2 Cluster for Huffman Table......56
7.2.1 Introduction......56
7.2.2 Memory Efficient and High Speed Search Huffman Coding......57
7.2.3 Jumping Over the Clusters......57
7.2.4 Example of Decoding a Codeword......58
7.3 Read Bitstream of Huffman coding......60
7.4 Summary......61
Chapter 8 Efficient Compression Algorithm for Less Buffer Size......63
8.1 Introduction......63
8.2 Proposed Method......65
8.2.1 DCT with DWT......66
8.2.2 Quantization......68
8.2.3 Bit Plane Conversion......69
8.2.4 Encoder......70
8.3 Simulation Results......71
8.4 Summary......73
Chapter 9 Weighted Adaptive Arithmetic Coding......75
9.1 Introduction......75
9.2 Review of Arithmetic Coding......77
9.2.1 Conventional Static Arithmetic Coding......77
9.2.2 Conventional Adaptive Arithmetic Coding......81
9.3 Proposed Weighted Adaptive Arithmetic Coding......83
9.4 Simulation Results......87
9.5 Summary......91
Chapter 10 Collagen Image Compression......93
10.1 Introduction......93
10.2 Proposed Collagen Image Compression......95
10.2.1 JPEG Compression and Sampling......98
10.2.2 Context Modeling by Variance......98
10.2.3 Adaptive Arithmetic Coding......100
10.3 Simulation Results......104
10.4 Summary......109
10.5 Acknowledge......110
Chapter 11 Conclusion......111
REFERENCE......113

JPEG and JPEG2000
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[14]Y. W. Huang, and Y. F. Chang, “Wavelet Transform for JPEG 2000 Tutorial,” Advanced Digital Signal Processing, January, 2012

Less Buffer Size
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Weighted Adaptive Arithmetic Coding
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Collagen Image Compression
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[39]A. Arthur, and V. Saravanan. “Efficient medical image compression technique for telemedicine considering online and offline application.” Computing, Communication and Applications (ICCCA), 2012 International Conference on. IEEE, 2012

My Paper List
[40]G. C. Pan, J. J. Ding, Y. W. Huang, and C. W. Huang, “Efficient and less buffer size image compression algorithm based on the mixture of DCTs and DWTs,” Computer Vision, Graphics, and Image Processing, Sun Moon Lake, Taiwan, Aug. 2012
[41]J. J. Ding, Y. W. Huang, P. Y. Lin, S. C. Pei, H. H. Chen, and Y. H. Wang, “Two-dimensional orthogonal DCT expansion in trapezoid and triangular blocks and modified JPEG image compression,” IEEE Trans. Image Processing, accepted, 2013
[42]P. H. Wu, C. C. Chen, J. J. Ding, C. Y. Hsu, and Y. W. Huang, “Salient region detection improved by principle component analysis and boundary information,” IEEE Trans. Image Processing, accepted, 2013
[43]Y. W. Huang, J. J. Ding, H. H. Chen, S. W. Fu, and C. W. Huang, “Collagen Image Compression,” Computer Vision, Graphics, and Image Processing, submitted, National Ilan University, Taiwan, Aug. 2013
[44]H. H. Chen, Y. W. Huang, and J. J. Ding, “Local prediction based adaptive scanning for JPEG and H.264/AVC intra coding,” International Conference on Image Processing, Melbourne, Australia, Sept. 2013
[45]J. J. Ding, Y. W. Huang, and H. H. Chen, “Weighted Adaptive Arithmetic Coding,” Picture Coding Symposium, submitted, San Jose, California, Dec. 2013
[46]Y. W. Huang, G. C. Pan, J. J. Ding, and H. H. Chen, “Less Buffer Sized Efficient Compression Algorithm Based on Column DCTs, Row DWTs, and Predictive Coding,” International Conference on Information, Communications and Signal Processing, submitted, Tainan, Taiwan, Dec. 2013