In this paper, we propose a two dimensional (2D) non-separable adaptive directional lifting (ADL) structure for discrete wavelet transform (DWT) and its image coding application. Although a 2D non-separable lifting structure of 9/7 DWT has been proposed by interchanging some lifting, we generalize a polyphase representation of 2D non-separable lifting structure of DWT. Furthermore, by introducing the adaptive direc-tional filteringingto the generalized structure, the 2D non-separable ADL structure is realized and applied into image coding. Our proposed method is simpler than the 1D ADL, and can select the different transforming di-rection with 1D ADL. Through the simulations, the proposed method is shown to be efficient for the lossy and lossless image coding performance. key words: two dimensional non-separable lifting structure, discrete wavelet transform, adaptive directional filtering, lossy and lossless image coding
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[Show abstract][Hide abstract] ABSTRACT: An integer transform is used in lossless-lossy coding since it can reconstruct an input signal without any loss at output of the backward transform. Recently, its number of lifting steps is reduced as well as delay from input to output introducing multi-dimensional memory accessing. However it has a problem that quality of the reconstructed signal in lossy coding has its upper bound in the rate distortion curve. This is because the noise generated by rounding operations in each lifting step inside the integer transform does not contribute to data compression. This paper tries to reduce the rounding noise observed at output of the integer transform introducing channel scaling inside the transform. As a result of experiments, it was observed that the proposed method improves quality of the decoded signal in lossy coding mode.
"Its performance was investigated from various point of views in  . Even though these non-separable 2D DWTs have widely applied for more flexible filtering in  , only few attempts have so far been made at the 3D signal processing case. Therefore, we extend the previous discussions on 2D case to 3D case. "
[Show abstract][Hide abstract] ABSTRACT: This report reduces the total number of lifting steps in a 3D quadruple lifting DWT (discrete wavelet transform). In the JPEG 2000 international standard, the 9/7 quadruple lifting DWT has been widely utilized for image data compression. It has been also applied to volumetric medical image data analysis. However, it has long delay from input to output due to cascading four (quadruple) lifting steps per dimension. We reduce the total number of lifting steps introducing 3D direct memory accessing under the constraint that it has backward compatibility with the conventional DWT in JPEG 2000. As a result, the total number of lifting steps is reduced from 12 to 8 (67 %) without significant degradation of data compression performance.
"Flexibility of directional 2D filtering is also restricted. Therefore several 'non-separable' 2D DWTs have been reported to make it free from restrictions under the 'separable' 2D structure         . A non-separable 2D structure composed of double lifting DWTs (5/3 filter bank) defined by JPEG 2000 for lossless coding is reported in  . "