The Determination of Critical-Sampling Scheme of Preprocessing for Multiwavelets Decomposition as 1st and 2nd Orders of Approximations.
N. K. Wafi, Z. J. M. Saleh, W. A. Mahmoud · DOAJ (DOAJ: Directory of Open Access Journals) · 2005
One of the important differences between multiwavelets and scalar wavelets is that each channel in the filter bank has a vector-valued input and a vector-valued output. A scalar-valued input signal must somehow be converted into a suitable vector-valued signal. This conversion is called preprocessing. Preprocessing is a mapping process which is done by a prefilter. A postfilter just does the opposite. The most obvious way to get two input rows from a given signal is to repeat the signal. Two rows go into the multifilter bank. This procedure is called Repeated Row which introduces oversampling of the data by a factor of 2. For data compression, where one is trying to find compact transform representations for a dataset, it is imperative to find critically sampled multiwavelet transforms schemes which this paper focuses on finding a simple and easy to follow algorithm for its computation. One famous multiwavelet filter used here is the GHM filter proposed by Geronimo, Hardian, and Massopust. The GHM basis offers a combination of orthogonality, symmetry, and compact support, which can not be achieved by any scalar wavelet basis. Using a computer program for the proposed method, an example test on Lena image is verified which shows image properties after a single level decomposition and the reconstructed image after reconstruction.