Two-dimensional integer wavelet transform with reduced influence of rounding operations

Abstract

If a system for lossless compression of images applies a decorrelation step, this step must map integer input values to integer output values. This can be achieved, for example, using the integer wavelet transform (IWT). The non-linearity, introduced by the obligatory rounding steps, is the main drawback of the IWT, since it deteriorates the desired filter characteristic. This paper discusses different methods for reducing the influence of rounding in 5/3 and 9/7 filter banks. A novel combination of two-dimensional implementations of the JPEG2000 9/7 filter bank with new filter coefficients is proposed and the effects of the methods on lossless image compression are investigated. In addition, these filter banks are compared to the 9/7 Deslauriers-Dubuc filter bank (97DD). The analysed two-dimensional implementations generally perform better than their one-dimensional counterparts in terms of compression ratio for natural images. On average, the 2D 97DD filter bank performs best. In addition, it has been found that the compression results cannot be improved by simply reducing the number of lifting steps via 2D implementations of the JPEG2000 9/7 filter bank. Only the 2D implementation with a minimum number of lifting steps, in combination with modified lifting coefficients, leads to fewer bits per pixel than the separable implementation on average for a selected set of images. © 2012 Strutz and Rennert.