This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F in terms of the elements of E via a map a : I → G. A fundamental set of equalities are shown betwee...

G-frames are natural generalizations of frames which cover many other recent generalizations of frames, e.g., bounded quasi-projectors, frames of subspaces, outer frames, oblique frames, pseudo-frames and a class of timefrequency localization operators. Moreover, it was shown that g-frames are equivalent to stable space splittings. In this paper, we study the stability of g-frames. We first pre...

in this paper we introduce continuous $g$-bessel multipliers in hilbert spaces and investigate some of their properties. we provide some conditions under which a continuous $g$-bessel multiplier is a compact operator. also, we show the continuous dependency of continuous $g$-bessel multipliers on their parameters.

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...

Starting with Hermite cubic splines as the primal multigenerator, first a dual multigenerator onR is constructed that consists of continuous functions, has small support, and is exact of order 2. We then derive multiresolution sequences on the interval while retaining the polynomial exactness on the primal and dual sides. This guarantees moment conditions of the corresponding wavelets. The conc...

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 ...