The Determination of Critical-Sampling Scheme of Preprocessing for Multiwavelets Decomposition as 1st and 2nd Orders of Approximations.

K. Wafi, N.; J. M. Saleh, Z.; A. Mahmoud, W.

	The Determination of Critical-Sampling Scheme of Preprocessing for Multiwavelets Decomposition as 1st and 2nd Orders of Approximations.
Al-Khwarizmi Engineering Journal
Article 1, Volume 1, Issue 1, 2005, Pages 26-37
Authors
N. K. Wafi; Z. J. M. Saleh; W. A. Mahmoud
Abstract
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.
Keywords
Discrete Multiwavelete Transform; Inverse Discrete Multiwavelete Transform; critical; Sampling; Schema of Processing

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