Wavelet-Based Image Coding: An Overview

This chapter presents an overview of wavelet-based image coding. We develop the basics of image coding with a discussion of vector quantization. We motivate the use of transform coding in practical settings and describe the properties of various decorrelating transforms. We motivate the use of the wavelet transform in coding using rate-distortion considerations as well as approximation-theoretic considerations. Finally we give an overview of current coders in the literature.

[1]  John D. Villasenor,et al.  Visual thresholds for wavelet quantization error , 1996, Electronic Imaging.

[2]  Benjamin Belzer,et al.  Wavelet filter evaluation for image compression , 1995, IEEE Trans. Image Process..

[3]  Michael W. Marcellin,et al.  Trellis coded quantization of memoryless and Gauss-Markov sources , 1990, IEEE Trans. Commun..

[4]  Robert M. Gray,et al.  Locally Optimal Block Quantizer Design , 1980, Inf. Control..

[5]  P. P. Vaidyanathan,et al.  Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property , 1987, IEEE Trans. Acoust. Speech Signal Process..

[6]  C. Burrus,et al.  Introduction to Wavelets and Wavelet Transforms: A Primer , 1997 .

[7]  Michael W. Marcellin,et al.  Comparison of different methods of classification in subband coding of images , 1997, IEEE Trans. Image Process..

[8]  Nariman Farvardin,et al.  Optimum quantizer performance for a class of non-Gaussian memoryless sources , 1984, IEEE Trans. Inf. Theory.

[9]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[10]  T. Barnwell,et al.  A procedure for designing exact reconstruction filter banks for tree-structured subband coders , 1984, ICASSP.

[11]  Michel Barlaud,et al.  Image coding using wavelet transform , 1992, IEEE Trans. Image Process..

[12]  Pierre Moulin,et al.  A multiscale relaxation algorithm for SNR maximization in nonorthogonal subband coding , 1995, IEEE Trans. Image Process..

[13]  Adrian S. Lewis,et al.  Image compression using the 2-D wavelet transform , 1992, IEEE Trans. Image Process..

[14]  Herbert Gish,et al.  Asymptotically efficient quantizing , 1968, IEEE Trans. Inf. Theory.

[15]  Michael T. Orchard,et al.  Joint space-frequency segmentation using balanced wavelet packet trees for least-cost image representation , 1997, IEEE Trans. Image Process..

[16]  Gilles Deslauriers,et al.  Symmetric iterative interpolation processes , 1989 .

[17]  P. Schultheiss,et al.  Block Quantization of Correlated Gaussian Random Variables , 1963 .

[18]  Shih-Fu Chang,et al.  Frequency and spatially adaptive wavelet packets , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[19]  Martin Vetterli,et al.  Orthogonal time-varying filter banks and wavelets , 1993, 1993 IEEE International Symposium on Circuits and Systems.

[20]  L. F. Tóth.  Sur la représentation d'une population infinie par un nombre fini d'éléments , 1959 .

[21]  William A. Pearlman,et al.  A new, fast, and efficient image codec based on set partitioning in hierarchical trees , 1996, IEEE Trans. Circuits Syst. Video Technol..

[22]  Edward H. Adelson,et al.  The Laplacian Pyramid as a Compact Image Code , 1983, IEEE Trans. Commun..

[23]  Martin Vetterli,et al.  Wavelets and filter banks: theory and design , 1992, IEEE Trans. Signal Process..

[24]  Kannan Ramchandran,et al.  Joint thresholding and quantizer selection for decoder-compatible baseline JPEG , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[25]  Paul L. Zador,et al.  Asymptotic quantization error of continuous signals and the quantization dimension , 1982, IEEE Trans. Inf. Theory.

[26]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[27]  Michael Unser.  Approximation power of biorthogonal wavelet expansions , 1996, IEEE Trans. Signal Process..

[28]  Avideh Zakhor,et al.  Multirate 3-D subband coding of video , 1994, IEEE Trans. Image Process..

[29]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[30]  Cormac Herley,et al.  Boundary filters for finite-length signals and time-varying filter banks , 1994, Proceedings of IEEE International Symposium on Circuits and Systems - ISCAS '94.

[31]  Michael W. Marcellin,et al.  Adaptive wavelet coding of images , 1994, Proceedings of 1st International Conference on Image Processing.

[32]  Ronald A. DeVore,et al.  Image compression through wavelet transform coding , 1992, IEEE Trans. Inf. Theory.

[33]  Donald L. Duttweiler,et al.  Probability estimation in arithmetic and adaptive-Huffman entropy coders , 1995, IEEE Trans. Image Process..

[34]  Peter No,et al.  Digital Coding of Waveforms , 1986 .

[35]  Mark J. T. Smith,et al.  Exact reconstruction techniques for tree-structured subband coders , 1986, IEEE Trans. Acoust. Speech Signal Process..

[36]  Gottfried Ungerboeck,et al.  Channel coding with multilevel/phase signals , 1982, IEEE Trans. Inf. Theory.

[37]  Michael T. Orchard,et al.  Multiresolution framework for backward motion compensation , 1995, Electronic Imaging.

[38]  M. Victor Wickerhauser,et al.  Adapted wavelet analysis from theory to software , 1994 .

[39]  Olivier Rioul.  Regular wavelets: a discrete-time approach , 1993, IEEE Trans. Signal Process..

[40]  Jelena Kovacevic,et al.  Wavelets and Subband Coding , 2013, Prentice Hall Signal Processing Series.

[41]  Antonio Ortega,et al.  Adaptive quantization of image subbands with efficient overhead rate selection , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[42]  K Ramchandran,et al.  Best wavelet packet bases in a rate-distortion sense , 1993, IEEE Trans. Image Process..

[43]  C. Chrysafis,et al.  Efficient context-based entropy coding for lossy wavelet image compression , 1997, Proceedings DCC '97. Data Compression Conference.

[44]  Jerome M. Shapiro,et al.  Embedded image coding using zerotrees of wavelet coefficients , 1993, IEEE Trans. Signal Process..

[45]  Allen Gersho,et al.  Globally optimal vector quantizer design by stochastic relaxation , 1992, IEEE Trans. Signal Process..

[46]  M. Vetterli.  Filter banks allowing perfect reconstruction , 1986 .

[47]  Michael T. Orchard,et al.  Image coding based on mixture modeling of wavelet coefficients and a fast estimation-quantization framework , 1997, Proceedings DCC '97. Data Compression Conference.

[48]  John W. Woods,et al.  A filter based bit allocation scheme for subband compression of HDTV , 1992, IEEE Trans. Image Process..

[49]  Thierry BLUzAbstract.  SIMPLE REGULARITY CRITERIA FOR SUBDIVISION SCHEMES , 1997 .

[50]  Javier Garcia-Frías,et al.  An analytical treatment of channel-induced distortion in run length coded subbands , 1997, Proceedings DCC '97. Data Compression Conference.

[51]  Min Wang,et al.  Entropy-constrained trellis coded quantization , 1991, [1991] Proceedings. Data Compression Conference.

[52]  R. Ladner.  Entropy-constrained Vector Quantization , 2000 .

[53]  Ronald R. Coifman,et al.  Entropy-based algorithms for best basis selection , 1992, IEEE Trans. Inf. Theory.

[54]  Truong Q. Nguyen,et al.  Wavelets and filter banks , 1996 .

[55]  Yair Shoham,et al.  Efficient bit allocation for an arbitrary set of quantizers [speech coding] , 1988, IEEE Trans. Acoust. Speech Signal Process..

[56]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[57]  Bernd Girod,et al.  Subband Image Coding , 1996 .

[58]  Kannan Ramchandran,et al.  Tilings of the time-frequency plane: construction of arbitrary orthogonal bases and fast tiling algorithms , 1993, IEEE Trans. Signal Process..

[59]  Wim Sweldens,et al.  Building your own wavelets at home , 2000 .

[60]  Allen Gersho,et al.  Asymptotically optimal block quantization , 1979, IEEE Trans. Inf. Theory.

[61]  Joan L. Mitchell,et al.  JPEG: Still Image Data Compression Standard , 1992 .

[62]  Y. Arai,et al.  A Fast DCT-SQ Scheme for Images , 1988 .

[63]  Michael T. Orchard,et al.  Wavelet packets-based image coding using joint space-frequency quantization , 1994, Proceedings of 1st International Conference on Image Processing.

[64]  Sumit Chawla,et al.  Image coding using optimized significance tree quantization , 1997, Proceedings DCC '97. Data Compression Conference.

[65]  I. Balasingham,et al.  On the relevance of the regularity constraint in subband image coding , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[66]  Roberto H. Bamberger,et al.  Optimum classification in subband coding of images , 1994, Proceedings of 1st International Conference on Image Processing.

[67]  Hamid Jafarkhani,et al.  Adaptive image coding based on the discrete wavelet transform , 1994, Proceedings of 1st International Conference on Image Processing.

[68]  Aaron D. Wyner,et al.  Coding Theorems for a Discrete Source With a Fidelity CriterionInstitute of Radio Engineers, International Convention Record, vol. 7, 1959. , 1993 .

[69]  Michael T. Orchard,et al.  Space-frequency quantization for wavelet image coding , 1997, IEEE Trans. Image Process..

[70]  N. Ahmed,et al.  Discrete Cosine Transform , 1996 .

[71]  T. Cover,et al.  Rate Distortion Theory , 2001 .

[72]  Wim Sweldens,et al.  Lifting scheme: a new philosophy in biorthogonal wavelet constructions , 1995, Optics + Photonics.

[73]  Kenneth Rose,et al.  Multimode image coding for noisy channels , 1997, Proceedings of ICC'97 - International Conference on Communications.

[74]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[75]  K. H. Barratt.  Digital Coding of Waveforms , 1985 .

[76]  Allen Gersho,et al.  Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.

[77]  Martin Vetterli,et al.  Splitting a signal into subsampled channels allowing perfect reconstruction , 1985 .

[78]  W. Sweldens,et al.  Quadrature formulae and asymptotic error expansions for wavelet approximations of smooth functions , 1994 .

[79]  Kenneth Zeger,et al.  Progressive image coding for noisy channels , 1997, IEEE Signal Processing Letters.

[80]  C. Smith,et al.  Adaptive Coding of Monochrome and Color Images , 1977, IEEE Trans. Commun..

[81]  C. Brislawn.  Classification of Nonexpansive Symmetric Extension Transforms for Multirate Filter Banks , 1996 .