An efficient structure and algorithm for image representation using nonorthogonal basis images

This paper presents a new recursive parallel mixed transform technique employing a projection algorithm for image representation. Image coders which employ subsets of nonorthogonal basis images chosen from two or more transform domains have been shown to consistently yield higher image quality than those based on one transform for a fixed compression ratio. However, these techniques have not been widely employed since existing formulations have either lacked rigorous development or suffered from high computational complexity and convergence problems. The algorithm presented herein overcomes these limitations. The algorithm is rigorously formulated, conditions for convergence are derived, and computational considerations are examined. Results of simulations are presented which demonstrate excellent performance in terms of energy compaction.

[1]  R. R. Clarke.  Transform coding of images , 1985 .

[2]  Zhifeng Zhang,et al.  Adaptive time-frequency decompositions , 1994 .

[3]  Alexander Graham,et al.  Kronecker Products and Matrix Calculus: With Applications , 1981 .

[4]  Richard Bronson,et al.  Schaum's Outline of Theory and Problems of Matrix Operations , 1988 .

[5]  K. R. Rao,et al.  Orthogonal Transforms for Digital Signal Processing , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[7]  W. B. Mikhael,et al.  An efficient representation of nonstationary signals using mixed-transforms with applications to speech , 1995 .

[8]  Victor DeBrunner,et al.  Lapped multiple bases realizations for the transform coding of still images , 1994, Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers.

[9]  Andreas Spanias,et al.  Mixed Fourier/Walsh transform scheme for speech coding at 4.0 kbit/s , 1992 .

[10]  W. B. Mikhael,et al.  Application of multitransforms for lossy image representation , 1994 .

[11]  W.B. Mikhael,et al.  Fidelity enhancement of transform based image coding using non-orthogonal basis images , 1996, 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96.

[12]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[13]  B. Parlett.  The Symmetric Eigenvalue Problem , 1981 .

[14]  W.B. Mikhael,et al.  An efficient structure and algorithm for the mixed transform representation of signals , 1995, Conference Record of The Twenty-Ninth Asilomar Conference on Signals, Systems and Computers.

[15]  Åke Björck,et al.  Algorithms for Linear Least Squares Problems , 1991 .

[16]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[17]  Thomas Kailath,et al.  Linear Systems , 1980 .

[18]  William A. Pearlman,et al.  A New Method for Nonorthogonal Signal Decomposition , 1994, J. Vis. Commun. Image Represent..