In this note, we announce a general method for the construction of nonseparable orthogonal wavelet bases of L2(Rn), where n ≥ 2. Hence, we prove the existence of such type of wavelet bases for any integer n ≥ 2. Moreover, we show that this construction method can be extended to the construction of n-D multiwavelet matrix filters.

This paper gives an overview of recent achievements of the multiwavelet theory. The construction of multiwavelets is based on a multiresolution analysis with higher multiplicity generated by a scaling vector. The basic properties of scaling vectors such as L-stability, approximation order and regularity are studied. Most of the proofs are sketched.

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

We relate different properties of nonseparable quincunx multiwavelet systems, such as polynomial approximation order, orthonormality and balancing, to conditions on the matrix filters. We give mathematical proofs for these relationships. The results obtained are necessary conditions on the filterbank. This simplifies the design of such systems.

 Abstract: There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used. By using the orthonormality property of basis elements in discretizing the equation, we can reduce an equation to a linear system with small dimension. For ...

The construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. We apply this system as basis functions to solve the fractional differential and integro-differential equations. Biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. Some test pr...