Generalized wavelet decompositions in image compression: arbitrary subbands and parallel algorithms

New methods for lossy image compression based on gener- alized wavelet decompositions have been introduced recently. Unlike in the classical wavelet decomposition scheme, it is possible to use differ- ent scaling and wavelet functions at every scale by using nonstationary multiresolution analyses. This freedom in using different functions can be exploited for adaptive compression techniques. We extend this approach to arbitrary subbands (e.g., in a wavelet packet scheme), combine it with the best basis algorithm, and introduce efficient techniques for using these algorithms on parallel computers. © 1997 Society of Photo-Optical Instru- mentation Engineers. (S0091-3286(97)02805-5) Subject terms: image compression; wavelets; adaptive methods; parallel algo- rithms.

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

[2]  Jian Lu.  Parallelizing Mallat Algorithm for 2-D Wavelet Transforms , 1993, Inf. Process. Lett..

[3]  Hassane Essafi,et al.  Wavelet Transform On Connection Machine And Sympati 2 , 1993 .

[4]  Thomas Hopper.  Compression of gray-scale fingerprint images , 1994, Defense, Security, and Sensing.

[5]  Mahn-ling Woo.  Parallel Discrete Wavelet Transform on the Paragon MIMD Machine , 1995, PPSC.

[6]  Amir Averbuch,et al.  Image compression using wavelet transform and multiresolution decomposition , 1996, IEEE Trans. Image Process..

[7]  Pamela C. Cosman,et al.  Vector quantization of image subbands: a survey , 1996, IEEE Trans. Image Process..

[8]  Jack J. Dongarra,et al.  The PVM Concurrent Computing System: Evolution, Experiences, and Trends , 1994, Parallel Comput..

[9]  Mats Holmström.  Parallelizing the Fast Wavelet Transform , 1995, Parallel Comput..

[10]  A. Cohen.  Non-stationary Multiscale Analysis , 1994 .

[11]  T. Nishitani,et al.  VLSI architectures for discrete wavelet transforms , 1993, IEEE Trans. Very Large Scale Integr. Syst..

[12]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[13]  Ronald R. Coifman,et al.  Signal processing and compression with wavelet packets , 1994 .

[14]  Kevin C. McGill,et al.  Algorithm 735: Wavelet transform algorithms for finite-duration discrete-time signals , 1994, TOMS.

[15]  C. Chui.  Wavelets: A Tutorial in Theory and Applications , 1992 .

[16]  Benoit M. Macq,et al.  Optimization of linear multiresolution transforms for scene adaptive coding , 1993, IEEE Trans. Signal Process..

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

[18]  Chaitali Chakrabarti,et al.  Efficient realizations of the discrete and continuous wavelet transforms: from single chip implementations to mappings on SIMD array computers , 1995, IEEE Trans. Signal Process..

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

[20]  Andrew K. Chan,et al.  Parallel implementation of wavelet decomposition/reconstruction algorithms , 1994, Defense, Security, and Sensing.

[21]  Benoit M. Macq,et al.  Signal-adapted multiresolution transform for image coding , 1992, IEEE Trans. Inf. Theory.

[22]  Andreas Uhl.  Image compression using non-stationary and inhomogeneous multiresolution analyses , 1996, Image Vis. Comput..

[23]  Carl Taswell.  Near-best basis selection algorithms with non-additive information cost functions , 1994, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis.

[24]  John W. Woods,et al.  Subband coding of images , 1986, IEEE Trans. Acoust. Speech Signal Process..

[25]  Andreas Uhl,et al.  Wavelet Packet Best Basis Selection on Moderate Parallel MIMD Architectures , 1996, Parallel Comput..

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

[27]  Mary Jane Irwin,et al.  Discrete wavelet transforms in VLSI , 1992, [1992] Proceedings of the International Conference on Application Specific Array Processors.

[28]  Anil K. Jain,et al.  Image data compression: A review , 1981, Proceedings of the IEEE.

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

[30]  C. Chui,et al.  Wavelets : theory, algorithms, and applications , 1994 .