Two digital filters ( ) and ( ) are said to be biorthogonal partners of each other if their cascade ( ) ( ) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filterbank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of equalization, especially, fractional...

Translation invariant (TI) single wavelet de-noising was developed by Coifman and Donoho and they show that TI is better than non-TI single wavelet de-noising. On the other hand, Strela et al. have found that non-TI multiwavelet de-noising gives better results than non-TI single wavelets. In this paper we extend Coifman and Donoho's TI single wavelet de-noising scheme to multiwavelets. Experime...

With the development of micro electronics and information technology, there are more pixels in unit area of the imaging device. The high resolution images with more pixels can be obtained easily. But the high resolution images have huge data volume. It is difficult to transmit, to process, to store high resolution images. So compressing images is an important technology to reduce the requisite ...

In the paper, two pre-processing methods for load forecast sampling data including multiwavelet transformation and chaotic time series are introduced. In addition, multi neural network for load forecast including BP artificial neural network, RBF neural network and wavelet neural network are introduced, too. Then, a combination load forecasting model for power load based on chaotic time series,...

The joint spectral radius ρ of 2 matrices is related to the boundedness of all their products. Calculating ρ is known to be NP-hard. In this work we estimate the joint spectral radius associated to a bidimensional separable multiwavelet, in order to analyze its Hölder continuity. To the author’s knowledge this has not been done. The analysis aims at testing the aplicability of the multiwavelet ...

An efficient projection procedure is derived for use of orthogonal multiwavelets in the analysis of discrete data sequences. A family of simple prefilters corresponding to numerical quadrature evaluation of the projection integrals provides exact results for locally-polynomial data. The full approximation order of the multiwavelet basis can thus always be enabled. For nonpolynomial signals, the...

This paper presents the evaluation of robustness for image watermarking techniques in the multiwavelet transform domain. The first one is based on the concept of the watermarking technique that has been designed in the previous chapter and the second one is based on the code division multiple access (CDMA) technique. The embedding information is a visually recognizable pattern which can be extr...

In this paper, we obtain equivalent conditions relating oblique projections to biorthogonal Riesz bases and angles between closed linear subspaces of a Hilbert space. We also prove an extension theorem in the biorthogonal setting, which leads to biorthogonal multiwavelets.

This paper presents a new secret image sharing method using multiwavelet transform in a general framework with the associated preand post-filtering to achieve an efficient representation of secret images at a low bit rate. It adopts a set partitioning in hierarchical trees (SPIHT) codec to enhance compactness of the data for processing in an image-sharing scheme. Because multiple data channels ...

This paper investigates the efficiency of unbalanced versus balanced multiwavelets in stereo correspondence matching. A multiwavelet transform is first applied to a pair of stereo images to decorrelate them into a number of subbands. Information in the approximation subbands of an unbalanced multiwavelet carries different spectral content of the input image while the balanced multiwavelet appro...