WMatrices, Nonorthogonal Multiresolution Analysis, and Finite Signals of Arbitrary Length.pdfVIP

W Matrices Nonorthogonal Multiresolut i on Analysis and Finite Signals of Arbitrary Length Man Kam Kwong and P T Peter Tang Mathematics and Computer Science Division Argonne National Lab oratory Argonne IL Email kwongmcs anl g ov tangmcs an lg ov Intro duction Wavelet theory and discrete wavelet transforms have had great impact on the eld of signal and image pro cessing For references to the extensive literature on the sub ject we refer to the bibliographies found in In this pap er we prop ose a new class of discrete transforms It includes the classical Haar and Daub echies transforms Our transforms treat the endp oints of a signal in a dierent manner from that of conventional techniques This new approach allows us eciently to handle signals of any length thus one is not restricted to work with signal or image sizes that are multiples of a p ower of A dierent metho d for dealing with signals of arbitrary length was given earlier by Taswell and McGill Our metho d do es not lengthen the output signal and do es not require an additional b o okkeeping vector  This is an abridged version of a forthcoming pap er This work was supp orted by the Oce of Scientic Computing US Department of Energy under Contract W Eng An exciting result is the uncovering of a new and simple transform pre sented in Section that p erforms very well for compression purp oses It has compact supp ort of length and so is its inverse The co ecients are symmetrical and the asso ciated scaling function is fairly smo oth it is the quadratic Bspline The asso ciated dual wavelet has vanishing moments up to