• Title Page (1)
• Graduate Committee Approval (2)
• Author's declaration (3)
• Abstract (4)
• Acknowledgments (6)
• Table of Contents (8)
• List of Figures (10)
• List of Tables (12)
• 1 Introduction (13)
• 2 Background (17)
  • 2.1 Compression (17)
    • 2.1.1 Data Compression (17)
    • 2.1.2 Image compression (19)
    • 2.1.3 Lossy compression (21)
    • 2.1.4 Lossless compression (23)
  • 2.2 Transformation (24)
    • 2.2.1 Transformation Definition (25)
    • 2.2.2 Entropy (27)
    • 2.2.3 Discrete Fourier Transform (28)
    • 2.2.4 Discrete Cosine Transform (30)
    • 2.2.5 Discrete Wavelet Transform (31)
    • 2.2.6 Differential Pulse Code Modulation (33)
    • 2.2.7 Other Transformation and Complexity Evaluation (36)
  • 2.3 Entropy Encoding (38)
    • 2.3.1 Huffman Encoding (39)
    • 2.3.2 Arithmetic Coding (40)
    • 2.3.3 Golomb Coding and LZW (42)
• 3 Related Work (43)
  • 3.1 Medical Imaging and Compression (43)
  • 3.2 Real Timing (45)
  • 3.3 Hardware Implementation (46)
    • 3.3.1 Efficient Hardware Implementation (48)
  • 3.4 Lossless JPEG (49)
  • 3.5 JPEG-LS (50)
  • 3.6 JPEG2000 (51)
  • 3.7 Limitations of Previous Methods (52)
• 4 Method (54)
  • 4.1 Motivation (54)
  • 4.2 Proposed Method (55)
  • 4.3 Transformation (57)
    • 4.3.1 Engine (57)
    • 4.3.2 Inverse Transform (66)
    • 4.3.3 Lossless and Visually lossless Transformation (67)
    • 4.3.4 Near-Lossless and Lossy Transformation (68)
    • 4.3.5 Evaluation of the New Transformation (69)
  • 4.4 Entropy Encoding (70)
    • 4.4.1 Suited Huffman Encoder (70)
    • 4.4.2 Combining Transformation and Encoder (72)
  • 4.5 Computational Complexity (73)
  • 4.6 Error resilience (74)
• 5 Experimental Result (76)
  • 5.1 Introduction (76)
  • 5.2 RS Image Transformation (78)
  • 5.3 Medical Image Transformation (80)
  • 5.4 Compression Ratio Comparison (82)
  • 5.5 Signal to Noise Ratio (83)
  • 5.6 Functionality (84)
• 6 Conclusion and Future Work (86)
• References (89)
• A List of Abbreviation (94)