The developments in wavelet theory have given rise to the wavelet thresholding method, for extracting a signal from noisy data [1,2]. Multiwavelets, wavelets with several scaling functions, have recently been introduced and they offer simultaneous orthogonality, symmetry and short support; which is not possible with ordinary wavelets, also called scalar wavelets [3]. This property makes multiwa...

in this paper, a new numerical method for solving fractional optimal control problems (focps) is presented. the fractional derivative in the dynamic system is described in the caputo sense. the method is based upon biorthogonal cubic hermite spline multiwavelets approxima-tions. the properties of biorthogonal multiwavelets are first given. the operational matrix of fractional riemann-lioville i...

In this paper, a new numerical method for solving fractional optimal control problems (FOCPs) is presented. The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon biorthogonal cubic Hermite spline multiwavelets approximations. The properties of biorthogonal multiwavelets are first given. The operational matrix of fractional Riemann-Lioville in...

A novel approach for constructing symmetric compactly supported biorthogonal multiwavelets with short sequences is proposed in this paper. For some symmetric types of biorthogonal multiwavelet systems, starting from the symmetric properties of scaling and wavelet functions, parameterized symmetric forms of polyphase matrices can be derived. Furthermore, according to the matrix equations of the ...

Multiwavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filterbanks leading to wavelet bases, multiwavelets offer simultaneous orthogonality, symmetry, and short support, which is not possible with scalar two-channel wavelet systems. After reviewing this theory, we examine the use of multiwavelets in a filterbank setting for discrete-time signal and image pro...

An important object in wavelet theory is the scaling function (t), satisfying a dilation equation (t) = P C k (2t ? k). Properties of a scaling function are closely related to the properties of the symbol or mask P (!) = P C k e ?i!k. The approximation order provided by (t) is the number of zeros of P (!) at ! = , or in other words the number of factors (1+e ?i!) in P (!). In the case of multiw...

An effective method based upon Alpert multiwavelets is proposed for the solution of Hallen’s integral equation. The properties of Alpert multiwavelets are first given. These wavelets are utilized to reduce the solution of Hallen’s integral equation to the solution of sparse algebraic equations. In order to save memory requirement and computation time, a threshold procedure is applied to obtain ...

We use vector-valued multiwavelets on compact sets to develop a Galerkin method for systems of integral equations of the second kind. We propose a compression strategy for the coeflieient matrix of the linear system obtained from this method and show that the compressed scheme preserves almost optimal convergence rate of the original scheme and yields a sparse matrix with a bounded condition nu...

Multiwavelets and multiframelets are of interest in several applications such as numerical algorithms and signal processing, due to their desirable properties such as high smoothness and vanishing moments with relatively small supports of their generating functions and masks. In order to process and represent vector-valued discrete data efficiently and sparsely by a multiwavelet transform, a mu...

This paper presents an evaluation of different types and families of multiwavelets in stereo correspondence matching. Different multiwavelet families with different filter types such as balanced versus unbalanced, symmetricsymmetric versus symmetric-antisymmetric are used. Normalized cross correlation is employed to find the best correspondence points and generate a disparity map. In the case o...