Integer Implementation of 3D Wavelet Transform for Lossy Data Compression

Abstract— A new non-separable 2D structure is proposed for integer implementation of a 3D lifting wavelet transform. It reduces total amount of rounding noise due to expressing signal values as integers inside the transform. In the existing method, a non-separable 3D structure is used to minimize lifting steps. It contributes to decrease delay from input to output. As it decreases total number of rounding operations which are source of the rounding error, total amount of the rounding noise was also reduced in the (5,3) type transform for lossless coding. However, it was found that it is not true in the (9,7) type transform for lossy coding. In this paper, introducing a non-separable 2D structure instead of the 3D structure, a new transform with reduced number of lifting steps is proposed. Since the proposed method does not change order of the original lifting steps, total amount of the rounding noise observed in pixel values of the decoded image is significantly reduced. Upper bound of quality of decoded images in lossy coding is also improved.