Felix C. A. Fernandes and C. Sidney Burrus Department of Electrical and Computer Engineering, Rice University, Houston, TX 77251{1892, USA ABSTRACT In this paper we investigate multiwavelet systems whose scaling functions have disjoint support. We demonstrate that, with the exception of a trivial case, this property may not be attained by two band multiwavelet systems. We show that to enjoy thi...

We characterize the orthogonal frames and orthogonal multiwavelet frames in L2 R with matrix dilations of the form Df x √ |detA|f Ax , where A is an arbitrary expanding d × d matrix with integer coefficients. Firstly, through two arbitrarily multiwavelet frames, we give a simple construction of a pair of orthogonal multiwavelet frames. Then, by using the unitary extension principle, we present ...

In this study, we propose a new image fusion method by combining Multiwavelet with Contourlet transform. Firstly, transform the source multifocus images successively by Multiwavelet and Conotourlet. Secondly, we employ the LEM rule to fuse the lowpass coefficients and PCCN rule to fuse the hightpass coefficients. Finally, inversely transform the fused coefficients successively by Contourlet and...

This paper highlights the differences between traditional wavelet and multiwavelet bases with equal approximation order. Because multiwavelet bases normally lack important properties that traditional wavelet bases (of equal approximation order) possess, the associated discrete multiwavelet transform is less useful for signal processing unless it is preceded by a preprocessing step (prefiltering...

An algebraic approach to the design of different binds of discrete wavelet transforma (orthogonal and biorthogonal single-/multiwavelet transforms, multiwavelet-like transforma) is taken. The different transfomrs are anaL ysed with respect to computational efforts, approzimation properties and symmetry. The design of the orthogonal and biorthogonal single-/multiwavelets requires the solution of...

This paper describes a basic difference between multiwavelets and scalar wavelets that explains, without using zero moment properties, why certain complications arise in the implementation of discrete multiwavelet transforms. Assuming we wish to avoid the use of prefilters in implementing the discrete multiwavelet transform, it is suggested that the behavior of the iterated filter bank associat...

This paper describes the first steps toward a multiwavelet system that may retain the advantages of a traditional multiwavelet system while alleviating some of its disadvantages. We attempt to achieve this through the introduction of a novel property — the disjoint support of the multiscaling functions. We derive the conditions on the matrix filter coefficients that guarantee the disjoint suppo...

Multiwavelet transform has received attention in image watermarking because it is possible to construct multiwavelets that simultaneously possess desirable properties. Since the choice of appropriate multiwavelet basis is a critical issue that affects the quality of the watermarked image and the robustness of the watermark, we selected five different multiwavelet bases in this paper to evaluate...

This paper proposes a method to obtain optimal 2-order approximation preserving prefilters for a given orthogonal unbalanced multiwavelet basis. This procedure uses the prefilter construction introduced in [3]. The prefilter optimization scheme exploits the Taylor series expansion of the prefilter combined with the multiwavelet. Using the DGHM multiwavelet with the obtained optimal prefilter, w...

In this paper we are to find the optimum multiwavelet for compression of electrocardiogram (ECG) signals and then, selecting it for using with SPIHT codec. At present, it is not well known which multiwavelet is the best choice for optimum compression of ECG. In this work, we examine different multiwavelets on 24 sets of ECG data with entirely different characteristics, selected from MIT-BIH dat...