Reversible 2D 9-7 DWT Based on Non-separable 2D Lifting Structure Compatible with Irreversible DWT

Hitoshi KIYA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E94-A    No.10    pp.1928-1936
Publication Date: 2011/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.1928
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
lossless,  image,  wavelet,  coding,  compatible,  

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This paper proposes a reversible two dimensional (2D) discrete wavelet transform (DWT) for lossless coding which is compatible with the irreversible 2D 9-7 DWT for lossy coding in the JPEG 2000. Since all the filters and scalings are factorized into a product of lifting steps, and signal values are rounded into integers, the proposed DWT is reversible and applicable to lossless coding of 2D signals. We replace a part of the separable 2D transfer function of the 2D DWT by a non separable 2D lifting structure, so that the number of rounding operations is decreased. We also investigate performance of the DWT under octave decomposition case and theoretically endorse it. As a result, reduction of the rounding errors due to the replacement was confirmed. It means that compatibility of the reversible DWT to the irreversible 2D 9-7 DWT is improved.