Abstract
This paper reduces the total number of lifting steps of a two dimensional (2D) discrete wavelet transform (DWT) under the constraint that the DWT has full compatibility with a given separable 2D DWT. In a DWT composed of several lifting steps in cascade, a lifting step must wait for a calculation result of its previous lifting step. Therefore more lifting steps bring about longer latency from the input to the output. In this paper, we reduce the total number of lifting steps of a quadruple lifting DWT which is widely utilized as the 9/7 DWT in the JPEG 2000 international standard for image data compression. Firstly, we introduce basic properties for modification of signal flow structure inside a DWT without changing its output. Secondly, we convert the separable 2D quadruple lifting DWT into the non-separable 2D DWT utilizing the basic properties so that the total number of the lifting steps is reduced. As a result, the lifting steps were reduced to 75[%]. Finally, we evaluate the proposed non-separable 2D DWT in respect of compatibility with the conventional separable 2D DWT.
