Non-separable quadruple lifting structure for four-dimensional integer Wavelet Transform with reduced rounding noise

Abstract

The Wavelet Transform (WT) in JPEG 2000 is using a ‘separable’ lifting structure, where the one-dimensional (1D) transform is put into multidimensional image signal of its spatial and temporal dimensions. A ‘non-separable’ three-dimensional (3D) structure as the existing method is used to minimize its lifting steps. The ‘non-separable’ 3D structure in the (5,3) type transform for lossless coding is proved to reduce the rounding noise inside it. However, in the (9,7) type transform for lossy coding, the rounding noise inside the ‘non-separable’ 3D structure has increased. This paper proposed a new ‘non-separable’ two-dimensional (2D) structure for integer implementation of a four-dimensional (4D) quadruple lifting WT. Since the order of the original lifting step is preserved, the total amount of the rounding noise observed in pixel values of the decoded image is significantly reduced, and the lossy coding performance for 4D input signal is increased.