{ In this paper we discuss wavelet thresholding in the context of scalar orthogonal, scalar biorthogonal, multiple orthogonal and multiple biorthogonal wavelet transforms. Two types of multiwavelet thresholding are considered: scalar and vector. Both of them take into account the covariance structure of the transform. The form of the universal threshold is carefully formulated. The results of n...

We present new multiwavelet transforms of multiplicity 2 for manipulation of discrete-time signals. The transforms are implemented in two phases: 1) Pre (post)-processing, which transforms the scalar signal into a vector signal (and back) and 2) wavelet transforms of the vector signal. Both phases are performed in a lifting manner. We use the cubic interpolatory Hermite splines as a predicting ...

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...

This paper investigates the emerging notion of multiwavelets in the context of multirate filter banks, and applies a multiwavelet system to image coding and signal denoising. Multiwavelets are of interest because their constituent filters can be simultaneously symmetric and orthogonal (this combination is impossible for 2-band PR-QMFs), and because one can obtain higher orders of approximation ...

It is very important for generating an orthonormal multiwavelet system to construct a conjugate quadrature filter (CQF). In this paper, a general method of constructing a length-J + 1 CQF with multiplicity r and scale a from a length-J CQF is obtained. As a special case, we study generally the construction of a length-J + 1 CQF with multiplicity 2 and scale 2 which can generate a compactly supp...

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 ...

(Bi)orthogonal (multi)wavelets on the real line have been extensively studied and employed in applications with success. A lot of problems are defined bounded intervals or domains. Therefore, it is important both theory application to construct all possible wavelets some desired properties from (bi)orthogonal line. Vanishing moments compactly supported key property for sparse wavelet representa...

Content based image Retrieval has become one of the most active research areas in the past few years .CBIR system using multiwavelet based features with high retrieval rate and less computational complexity is proposed in this paper. Multiwavelets offer simultaneous orthogonality, symmetry and short support. This property made it a powerful tool for feature extraction of images in the database....

Abstract: In this article a numerical method is proposed to approximate the solution of the system of integrodifferential equations describing biological species living together. The method is based upon Legendre multiwavelet approximations. The properties of Legendre multiwavelet are first presented. These properties together with Ritz-Galerkin method are then utilized to reduce the equations ...

This paper evaluates the performance of various biorthogonal filters using adaptive synthesis filter banks for image compression. The adaptive synthesis filter banks are used to exploit the phase diversity of synthesis filters in subband coding system. Odd length biorthogonal filters are used because even length filters exhibit fractional delay in compression. It is shown that adaptive synthesi...