A general scheme for finding the static rate–distortion optimized ordering for the bits of the coefficients of all subbands of an N-level dyadic biorthogonal DWT
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https://doi.org/10.1016/j.image.2018.06.017 |
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Título
A general scheme for finding the static rate–distortion optimized ordering for the bits of the coefficients of all subbands of an N-level dyadic biorthogonal DWTFecha de publicación
2018Editor
ElsevierISSN
0923-5965; 1879-2677Cita bibliográfica
Rubino, Eduardo M., et al. "A general scheme for finding the static rate–distortion optimized ordering for the bits of the coefficients of all subbands of an N-level dyadic biorthogonal DWT." Signal Processing: Image Communication, 2018, vol. 67, p. 210-230Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://www.sciencedirect.com/science/article/pii/S0923596518306003Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
The expected distortion decrease per bit attained by conveying the significance and refinement information of transform coefficients is derived taking into consideration their Probability Distribution Function (PDF) ... [+]
The expected distortion decrease per bit attained by conveying the significance and refinement information of transform coefficients is derived taking into consideration their Probability Distribution Function (PDF) and their entropy. A general scheme for finding the static rate–distortion optimized ordering for the bits of the coefficients for all subbands of a generic -level dyadic biorthogonal Discrete Wavelet Transform (DWT) is given by weighting their distortion decrease per bit using the gain of each decomposition subband. Specific formulation for the Exponential Power Distribution (EPD) family is given and closed formulae are derived for the special cases of the Uniform and Laplace distributions. It is shown that under certain circumstances some refinement information of larger magnitude coefficients should be conveyed before the significant information of the current ones. The results can be applied by both conventional context modeling entropy coding algorithms or by set-partitioning algorithms which use multiple lists to keep track of significant and refinement coefficients. A very fast set-partitioning compression algorithm (Depth Embedded Block Tree — DEBT) has been developed based on variable-depth blocks and trees which uses the results presented here and achieves excellent compression ratios along with many other desired properties, e.g., embedded rate–distortion optimized lossy or lossless stream, quality or resolution scalability, and region of interest, among others. Tests show that the rate–distortion curves of most images show a significant improvement when using the weighting derived by the appropriate Exponential Power Distribution fitting in comparison to using a priori standard Uniform or Laplace Probability Distribution Function when using a non orthogonal Discrete Wavelet Transform. [-]
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Signal Processing: Image Communication, 2018, vol. 67, p. 210-230Proyecto de investigación
The authors would like to thank the financial support of the Brazilian government agency MEC/CAPES/CNPq/FAPDF (11637.60.28528.08072016), the Spanish Ministry of Economy and Competitiveness under grants DPI2014-57746-C3 (MERBOTS) and DPI2017-86372-C3-1-R (TWINBOTS), the Universitat Jaume I under grant P1-1B2015-68 (MASUMIA), and Generalitat Valenciana (PROMETEO/2016/066).Derechos de acceso
© 2018 Elsevier B.V. All rights reserved.
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