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

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. key words: lossless, image, wavelet, coding, compatible