Design and Implementation of New Computation Method for Multiwavelets Decomposition as 1't and 2nd Approximations

Abstract

One of the important differences between multiwaveletsand scalar wavelets is that each channel in the filter bank has avector-valued output as scalar-valued input signal mustsomehow be converted into a suitable vector-valued signal .Thisconversion is called preprocessing[1]. Preprocessing is mappingprocess which is done by a prefilter. A postfilter just does theopposite. The most obvious way to get two input rows from agiven signal to repeat the signal [2]. Two rows go to into thernultifilter bank. This procedure is called "Repeated row" whichintroduce over sampling of data by a factor of 212]. Two rowsgo into the multifilter bank. For data compression , where one istrying to find compact transform representation for a dataset[3],it is imperative to find critically sampled multiwavelet transformschemes which this paper focus on finding a simple and easy tofollow algorithm for its computation. One famous multiwaveletfilter used here is the GHM filter proposed by Geronimo. TheGHM basis offers a combination of orthogonally, symmetry,and compact support, which can not be achieved by any scalarwavelet basis [4]. Using a computer program for the proposedmethod, an example test on tiger image is verified which showsimage properties after a single level decomposition and thereconstructed image after reconstruction'