The Duals of Fusion Frames for Experimental Data Transmission Coding of High Energy Physics

The experimental data transmission is an important part of high energy physics experiment. In this paper, we connect fusion frames with the experimental data transmission implement of high energy physics. And we research the utilization of fusion frames for data transmission coding which can enhance the transmission efficiency, robust against erasures, and so forth. For this application, we first characterize a class of alternate fusion frames which are duals of a given fusion frame in a Hilbert space. Then, we obtain the matrix representation of the fusion frame operator of a given fusion frame system in a finite-dimensional Hilbert space. By using the matrix representation, we provide an algorithm for constructing the dual fusion frame system with its local dual frames which can be used as data transmission coder in the high energy physics experiments. Finally, we present a simulation example of data coding to show the practicability and validity of our results

Construction of Bivariate Nonseparable Compactly Supported Orthogonal Wavelets

A method for constructing bivariate nonseparable compactly supported orthogonal scaling functions, and the corresponding wavelets, using the dilation matrixM:=2n=2n[1001],(d=detM=22n≥4,n∈ℕ)is given. The accuracy and smoothness of the scaling functions are studied, thus showing that they have the same accuracy order as the univariate Daubechies low-pass filterm0(ω), to be used in our method. There follows that the wavelets can be made arbitrarily smooth by properly choosing the accuracy parameterr

Construction of Fusion Frame Systems in Finite Dimensional Hilbert Spaces

We first investigate the construction of a fusion frame system in a finite-dimensional Hilbert space F when its fusion frame operator matrix is given and provides a corresponding algorithm. The matrix representations of its local frame operators and inverse frame operators are naturally obtained. We then study the related properties of the constructed fusion frame systems. Finally, we implement the construction of fusion frame systems which behave optimally for erasures in some special sense in signal transmission

Construction of Fusion Frame Systems in Finite Dimensional Hilbert Spaces

We first investigate the construction of a fusion frame system in a finite-dimensional Hilbert space n when its fusion frame operator matrix is given and provides a corresponding algorithm. The matrix representations of its local frame operators and inverse frame operators are naturally obtained. We then study the related properties of the constructed fusion frame systems. Finally, we implement the construction of fusion frame systems which behave optimally for erasures in some special sense in signal transmission

Optimal Dual Frames For Communication Coding With Probabilistic Erasures

Assume that a frame is preselected for encoding in a communication system. We investigate the optimal dual frames for signal reconstruction (decoding) which minimize the maximal error when the probabilistic erasures occur in the transmission process from the perspective of mathematical theory of frames. We set up a probability model under which we define the probability optimal (PO) dual frames for a given frame when the frame-based coding involves probabilistic erasures. We obtain a sufficient and necessary condition under which the canonical dual frame is the unique PO dual frame. Additionally, we derive some general sufficient conditions for which the canonical dual frame is either not optimal or it is optimal but not the unique optimal one. We present two simulation examples to compare the reconstruction effects when both the PO dual frames and the general optimal (GO) dual frames are used for reconstruction. © 2011 IEEE

Probability Modelled Optimal Frames For Erasures

We establish a probability model for constructing optimal Parseval frames when erasures occur during the transmission process of the frame coefficient data set. Such frames are called probability modelled (PM) optimal frames for erasures. While (PM) optimal frames exist for all erasures, it is usually difficult to construct them. We characterize all the PM optimal frames for one and two erasures, and propose an algorithm to construct these frames. Examples are given to demonstrate the construction and to compare the decoding/reconstruction effects when both PM optimal Parseval frames and uniform length Parseval frames are used for encoding. © 2013 Elsevier Inc. All rights reserved

New Block Triangular Preconditioners for Saddle Point Linear Systems with Highly Singular (1,1) Blocks

We establish two types of block triangular preconditioners applied to the linear saddle point problems with the singular (1,1) block. These preconditioners are based on the results presented in the paper of Rees and Greif (2007). We study the spectral characteristics of the preconditioners and show that all eigenvalues of the preconditioned matrices are strongly clustered. The choice of the parameter is involved. Furthermore, we give the optimal parameter in practical. Finally, numerical experiments are also reported for illustrating the efficiency of the presented preconditioners

Criteria of the Nonsingular H-Matrices

Abstract The nonsingular H-matrices play an important role in the study of the matrix theory and the iterative method of systems of linear equations, etc. It has always been searched how to verify nonsingular H-matrices. In this paper, nonsingular H-matrices is studies by applying diagonally dominant matrices, irreducible diagonally dominant matrices and comparison matrices and several practical criteria for identifying nonsingular H-matrices are obtained