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Nonlinear wavelet transforms for image coding via lifting
Roger L Claypoole1, Geoffrey M Davis, Wim Sweldens
1Department of Electrical and Computer Engineering, Air Force Institute of Technology, Wright-Patterson AFB, OH 45433-7765, USA. r.claypoole@ieee.org
Summary
This study introduces nonlinear wavelet transforms using adaptive linear predictors for improved image compression. These novel transforms show promising results for both model and real-world images.
Area of Science:
- Signal Processing
- Image Analysis
- Applied Mathematics
Background:
- Wavelet transforms are crucial for signal and image processing.
- Existing linear wavelet transforms have limitations in capturing complex data characteristics.
- The lifting framework offers a flexible structure for designing advanced wavelet transforms.
Purpose of the Study:
- To develop and analyze nonlinear wavelet transforms using the lifting framework.
- To investigate key properties like invertibility, stability, and frequency characteristics.
- To explore the extension of nonlinear filter banks for image processing.
Main Methods:
- Utilizing the lifting framework to construct nonlinear wavelet transforms.
- Incorporating adaptive selection of linear predictors to introduce nonlinearity.
- Extending nonlinear filter banks with prediction functions operating on pixel neighborhoods.
Main Results:
- Established invertibility, stability, and synchronization properties for the nonlinear transforms.
- Characterized the frequency behavior of the proposed nonlinear wavelet transforms.
- Demonstrated promising preliminary image compression results on model and real-world datasets.
Conclusions:
- Nonlinear wavelet transforms built with the lifting framework offer significant advantages.
- Adaptive prediction functions enhance the capabilities of nonlinear filter banks.
- The developed techniques show potential for advanced image compression applications.
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