Recursive Block Coding for Image Data Compression, Softcover reprint of the original 1st ed. 1990

Recursive Block Coding, a new image data compression technique that has its roots in noncausal models for 1d and 2d signals, is the subject of this book. The underlying theory provides a multitude of compression algorithms that encompass two course coding, quad tree coding, hybrid coding and so on. Since the noncausal models provide a fundamentally different image representation, they lead to new approaches to many existing algorithms, including useful approaches for asymmetric, progressive, and adaptive coding techniques. On the theoretical front, the basic result shows that a random field (an ensemble of images) can be coded block by block such that the interblock redundancy can be completely removed while the individual blocks are transform coded. On the practical side, the artifact of tiling, a block boundary effect, present in conventional block by block transform coding techniques has been greatly suppressed. This book contains not only a theoretical discussion of the algorithms but also exhaustive simulation and suggested methodologies for ensemble design techniques. Each of the resulting algorithms has been applied to twelve images over a wide range of image data rates and the results are reported using subjective descriptions, photographs, mathematical MSE values, and h-plots, a recently proposed graphical representation showing a high level of agreement with image quality as judged subjectively.

1 Introduction.- 1.1 The Need for Data Compression.- 1.2 Data Compression Techniques.- Predictive Coding—DPCM.- Transform Coding.- Karhunen-Lòeve Transform (KLT).- Hybrid Coding.- Vector Quantization (VQ).- 1.3 The Problem—the Tile Effect.- 1.4 Our Approach—Two Source Decomposition.- 1.5 Organization.- 2 RBC—The Theory behind the Algorithms.- 2.1 Introduction.- 2.2 Modeling.- 2.3 Autoregressive Models.- Example—1st-order AR process.- 2.4 Noncausal Models.- Example—noncausal MVR for a 1st-order AR sequence.- 2.5 Two Source Decomposition.- 2.6 The 1d RBC Algorithm.- 2.7 Boundary Response for First Order AR Models.- Transform Domain Solution.- Spatial Domain Solution.- Simple Algorithm for 1st-Order AR Models.- 2.8 2d Minimum Variance Models.- 2.9 Examples of 2d Noncausal Image Models.- The NC1 Model.- Two Source Decomposition.- 2.10 2d Boundary Response via Transform Methods.- Transform Domain Solution.- 2.11 The 2d RBC Algorithm.- 2.12 Approximate Boundary Response.- Spatial Domain Solution.- The Alternative 2d RBG Algorithm.- Bilinear Patches.- Coon’s Patches.- Bicubic Patches.- 2.13 Advantages of RBC.- Removing Interblock Redundancy.- Reducing the Tile Effect.- 3 Bit Allocation and Quantization for Transform Coding.- 3.1 Introduction.- 3.2 Choice of Transform and Quantizer.- Fidelity Criterion.- Transform Domain Distortion.- Optimal Transformation and Quantization.- Transform.- Amplitude Probability Density Function.- Coefficient Variances.- 3.3 Bit Allocation.- Rate-Distortion Functions.- Optimal Bit Allocation.- Shannon Rate Distortion Function.- Approximations.- Huang and Schultheiss.- Wintz and Kurtenbach.- Segall.- Wang and Jain.- General Approximation For Piecewise Exponentials.- The Integral Constraint.- 3.4 Integer Bit Allocation.- General Integer Bit Allocation.- Comments.- 3.5 Zero Level Quantizers.- 3.6 Choice of RD Function for Bit Allocation.- Shannon versus Lloyd-Max.- 3.7 RBC Rate Distortion Analysis.- Id RBC Rate-Distortion Analysis.- 2d RBC Rate-Distortion Analysis.- Alternative Minimization Strategy.- 3.8 Ensemble Design for DCT and RBC.- RBC Variance Reduction.- Variance Reduction With 2d RBC.- 3.9 Color Coding.- 4 Zonal Coding.- 4.1 Introduction.- 4.2 Original Images.- Color Images.- 4.3 Simulation Facilities.- 4.4 Image Quality Measures.- Hosaka Plots (h-plots).- 4.5 1d Coding Results.- 1d DCT Design.- 1d RBC Design.- Discussion of Results.- Ensemble A.- Tiffany.- Ensemble B.- 4.6 2d Coding Results.- 2d DCT Design.- 2d RBC Design.- Discussion of Results.- 4.7 Hybrid Coding.- DPCM Equations.- Bit Allocation.- Hybrid Coding Results.- Hybrid DCT Design.- Hybrid RBC Design.- Discussion of Results.- 4.8 Conclusions.- 5 Adaptive Coding Based on Activity Classes.- 5.1 Introduction.- 5.2 Adaptive DCT.- Design Methodology.- DC Quantizer.- Standard Normalized Variances.- Performance Curve.- Class Rate Allocation.- Coding Methodology.- 5.3 Adaptive RBC.- Design Methodology.- Coding Methodology.- 5.4 Coding Results.- Ensemble Design.- Individual Design.- 5.5 Conclusions.- Future Work.- 6 Adaptive Coding Based on Quad Tree Segmentation.- 6.1 Introduction.- 6.2 Adaptive Segmentation.- 6.3 The Quad Tree Approach.- Residual.- Overlapping Blocks.- Predictor.- Uniformity.- Mean Residual Energy.- Segmentation.- Choosing the Segmentation Parameters.- 6.4 Coding the Segmentation.- Generating Split and Merge Information.- Split and Merge Bits for Fig. 6.4.2.- Prediction Rate.- 6.5 Reconstruction.- Fast Linear Interpolation for N a Power of 2.- Fast Bilinear Interpolation.- Modified Interpolation.- Examples of Reconstructed Images.- 6.6 Coding the Residual.- Choice of Transform.- Choice of Threshold.- 6.7 Results.- Zero Level Quantizers.- 6.8 Conclusions.- 7 QVQ—Vector Quantization of the Quad Tree Residual.- 7.1 Introduction.- 7.2 Vector Quantization.- Advantages of VQ Over Scalar Quantization.- Vector Methods: Transform Coding and VQ.- VQ Design.- Splitting Codewords.- VQ Coding.- Performance Considerations.- 7.3 Differential and Interpolate VQ.- 7.4 VQ of the Quad Tree Residual.- Choosing the Vector Dimension.- Choosing the Training Sequence.- 7.5 Coding Results.- 7.6 Conclusions.- 8 Conclusions.- 8.1 Introduction.- 8.2 New Results.- 8.3 Coding Recommendations.- 8.4 Future Work.- Appendix A Ordinary and Partial Differential and Difference Equations.- A.1 Introduction.- A.2 Second Order Ordinary Differential Equations.- A.3 Second Order Ordinary Difference Equations.- A.4 Second Order Partial Differential Equations.- A.5 Second Order Partial Difference Equations.- Appendix B Properties of the Discrete Sine Transform.- B.1 Introduction.- Definition.- Notation.- Tridiagonal Toeplitz Matrices.- B.2 DST Evaluation Technique.- B.3 Exponential Sequences.- B.4 Constant Sequences.- B.5 Linear Sequences.- B.6 Hyperbolic Sequences.- B.7 Sinusoidal Sequences.- Appendix C Transform Domain Variance Distributions.- C.1 Introduction.- C.2 1d RBC.- Normalized Variance Distribution.- Variance Reduction Ratio.- C.3 1d DCT.- Appendix D Coding Parameters for Adaptive Coding Based on Activity Classes.- D.1 Introduction.- D.2 Adaptive DCT Coding Parameters.- D.3 Adaptive RBC Coding Parameters.- References.