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Reversible wavelet filter banks with side informationless spatially adaptive low-pass filters

[+] Author Affiliations
Charith Abhayaratne

University of Sheffield, Department of Electronic and Electrical Engineering, Mappin Street, Sheffield, South Yorkshire S1 3JD, United Kingdom

J. Electron. Imaging. 20(3), 033012 (August 25, 2011). doi:10.1117/1.3624491
History: Received September 24, 2010; Accepted July 20, 2011; Revised April 08, 2011; Published August 25, 2011; Online August 25, 2011
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Wavelet transforms that have an adaptive low-pass filter are useful in applications that require the signal singularities, sharp transitions, and image edges to be left intact in the low-pass signal. In scalable image coding, the spatial resolution scalability is achieved by reconstructing the low-pass signal subband, which corresponds to the desired resolution level, and discarding other high-frequency wavelet subbands. In such applications, it is vital to have low-pass subbands that are not affected by smoothing artifacts associated with low-pass filtering. We present the mathematical framework for achieving 1-D wavelet transforms that have a spatially adaptive low-pass filter (SALP) using the prediction-first lifting scheme. The adaptivity decisions are computed using the wavelet coefficients, and no bookkeeping is required for the perfect reconstruction. Then, 2-D wavelet transforms that have a spatially adaptive low-pass filter are designed by extending the 1-D SALP framework. Because the 2-D polyphase decompositions are used in this case, the 2-D adaptivity decisions are made nonseparable as opposed to the separable 2-D realization using 1-D transforms. We present examples using the 2-D 5/3 wavelet transform and their lossless image coding and scalable decoding performances in terms of quality and resolution scalability. The proposed 2-D–SALP scheme results in better performance compared to the existing adaptive update lifting schemes.

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© 2011 SPIE and IS&T

Citation

Charith Abhayaratne
"Reversible wavelet filter banks with side informationless spatially adaptive low-pass filters", J. Electron. Imaging. 20(3), 033012 (August 25, 2011). ; http://dx.doi.org/10.1117/1.3624491


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