Non-Separable 3D Integer Wavelet Transform for Lossless Data Compression

Abstract

This paper proposes a three-dimensional (3D) integer wavelet transform with reduced amount of rounding noise. Non-separable multi-dimensional lifting structures are introduced to decrease the total number of lifting steps. Since the lifting step contains a rounding operation, variance of the rounding noise generated due to the rounding operation inside the transform is reduced. This paper also investigates performance of the transform from various aspects such as 1) variance of the noise in frequency domain and those in pixel domain, 2) the rate distortion curve in lossy coding mode and the entropy rate in lossless coding mode, 3) computational time of the transforms, and 4) feature comparison with other methods. The proposed wavelet transform has a merit that its output signal, apart from the rounding noise, is exactly the same as the conventional separable structure which is a cascade of 1D structure. Due to this compatibility, it becomes possible to utilize legacy of previously designed 1D wavelet transforms with preferable properties such as the regularity. Furthermore, total amount of the rounding noise which is generated due to integer expression of signal values inside the transform is significantly reduced. This is because the total number of rounding operations is decreased by introducing the non-separable multi-dimensional lifting structure which includes multi-dimensional memory accessing. It contributes to increase coding performance of a system based on the 3D wavelet transform. As a result of experiments, it was observed that the proposed method increases performance of data compression of various 3D input signals.