High-order balanced multiwavelets: theory, factorization, anddesign

This paper deals with multiwavelets and the different properties of approximation and smoothness associated with them. In particular, we focus on the important issue of the preservation of discrete-time polynomial signals by multifilterbanks. We introduce and detail the property of balancing for higher degree discrete-time polynomial signals and link it to a very natural factorization of the refinement mask of the lowpass synthesis multifilter. This factorization turns out to be the counterpart for multiwavelets of the well-known zeros at π condition in the usual (scalar) wavelet framework. The property of balancing also proves to be central to the different issues of the preservation of smooth signals by multifilterbanks, the approximation power of finitely generated multiresolution analyses, and the smoothness of the multiscaling functions and multiwavelets. Using these new results, we describe the construction of a family of orthogonal multiwavelets with symmetries and compact support that is indexed by increasing order of balancing. In addition, we also detail, for any given balancing order, the orthogonal multiwavelets with minimum-length multifilters     

Boundary filter design for multiwavelets

When designing boundary filters for multiwavelets, perfect reconstruction and moment conditions are two of the most important criteria to be considered. Since the filter coefficients of multiwavelets are expressed in the form of matrices, the moment conditions for multiwavelets do not relate to the filter coefficients in a simple way as for scalar wavelets. The authors first formulate the moment conditions of multiwavelets and then use them as the criteria for the optimisation of the boundary multifilters. They then apply the proposed optimisation scheme to the design of boundary multifilters for CL and GHM multiwavelets. The optimised boundary filters possess the desired perfect reconstruction property and vanishing moments that allow them to reduce the boundary artefact by up to 75% as compared with the traditional approach.     

Wavelet transforms for vector fields using omnidirectionally balanced multiwavelets

Vector wavelet transforms for vector-valued fields can be implemented directly from multiwavelets; however, existing multiwavelets offer surprisingly poor performance for transforms in vector-valued signal-processing applications. In this paper, the reason for this performance failure is identified, and a remedy is proposed. A multiwavelet design criterion known as omnidirectional balancing is introduced to extend to vector transforms the balancing philosophy previously proposed for multiwavelet-based scalar-signal expansion. It is shown that the straightforward implementation of a vector wavelet transform, namely, the application of a scalar transform to each vector component independently, is a special case of an omnidirectionally balanced vector wavelet transform in which filter-coefficient matrices are constrained to be diagonal. Additionally, a family of symmetric-antisymmetric multiwavelets is designed according to the omnidirectional-balancing criterion. In empirical results for a vector-field compression system, it is observed that the performance of vector wavelet transforms derived from these omnidirectionally-balanced symmetric-antisymmetric multiwavelets is far superior to that of transforms implemented via other multiwavelets and can exceed that of diagonal transforms derived from popular scalar wavelets.     

FIR filter order reduction: balanced model truncation andHankel-norm optimal approximation

Two different algorithms for approximating FIR by IIR filters are treated: truncation of the balanced model and the Hankel-norm optimal approximation. Both are assessed for approximation fidelity, as well as for intrinsic computational efficiency. Examples show surprisingly good relative performance of the balanced model truncation, suggesting that frequently this method will be operationally preferable     

Balanced multiwavelets theory and design

This article deals with multiwavelets, which are a generalization of wavelets in the context of time-varying filter banks and with their applications to signal processing and especially compression. By their inherent structure, multiwavelets are fit for processing multichannel signals. This is the main issue in which we are interested. First, we review material on multiwavelets and their links with multifilter banks and, especially, time-varying filter banks. Then, we have a close look at the problems encountered when using multiwavelets in applications, and we propose new solutions for the design of multiwavelets filter banks by introducing the so-called balanced multiwavelets     

A new closed form method for design of variable bandwidth linear phase FIR filter using Bernstein multiwavelets

In this paper, a new method for the design of variable bandwidth linear-phase finite impulse response filters using Bernstein polynomial Multiwavelets is proposed. In this method, approximation has been achieved by linearly combining the fixed coefficient linear phase filters with Bernstein multiwavelets, which are used to tune bandwidth of the filter. Optimisation has been achieved by minimising the mean square error between the desired and actual filter response which leads to a system of linear equations. The matrix elements can be expressed in form of Toeplitz-plus-Hankel matrix, which reduces the computational complexity. The simulation results illustrate significant improvement in errors in passband (e_p), and stopband (e_s) as compared to earlier published work.     

均匀传输线路的基本方程及其在施工中的应用

对信号在电缆中传输作出了理论分析，根据这理论对施工作出指导，并举出施工生产中应用该理论解决问题的实例。     

Incoherent bipolar tap microwave photonic filter based on balanced bridge electro-optic modulator

A novel all-optical technique to implement bipolar taps in an incoherent photonic filter is demonstrated. The use of all-optical techniques for the implementation of filters is inherently wideband and reduces the need for electronic interfaces. The technique is based on the utilisation of the complementary outputs of a commercially available balanced bridge electro-optic modulator, in which taps of the same polarity are generated from a common output arm.     

交指滤波器结构设计的改进

本文首先简述了有关定位原理,然后讨论了交指滤波器原来用定位块定位装配和经改进后用设计基准定位的区别,并分析计算两者的定位误差。计算结果证明,改进后在同样零件加工精度情况下,其装配后的误差减少一半以上。     

A 10.7-MHz fully balanced,high-Q, 87-dB-dynamic-range current-tunable Gm-C bandpass filter

A 10.7-MHz fully balanced, high-Q, wide-dynamic-range current-tunable Gm-C bandpass filter is presented. The technique is relatively simple based on two fully balanced components, i.e. an adder and a low-Q-based bandpass filter. The Q factor is approximately equal to a typically high and constant value of a common-emitter current gain (β) and is, for the first time, independent of variables such as a center frequency. Possible solutions for good stability of the Q factor with temperature are suggested. Not only can the need for additional Q-tunable circuits be greatly reduced, the sensitivity of the Q factor can be greatly improved. Sensitivities of either the Q factor or the center frequency are constant between 1 and −1 and are no longer strongly affected by the Q factor or variables. As a simple example at 10.7 MHz, the paper demonstrates the high-Q factor of 121, the low total output noise of 5.303 μV_rms, the 3rd-order intermodulation-free dynamic range (IMFDR₃) of 74.45 dB and the wide dynamic range of 87.45 dB at 1% IM₃. The center frequency is current tunable over three orders of magnitude. Comparisons to other 10.7-MHz Gm-C approaches are also included.     

Greedy construction of load‐balanced virtual backbones in wireless sensor networks

Inspired by the backbone concept in wired networks, a virtual backbone is expected to bring substantial benefits to routing in wireless sensor networks (WSNs). A connected dominating set (CDS) is used as a virtual backbone for efficient routing and broadcasting in WSNs. Most existing works focus on constructing a minimum CDS, a k‐connect m‐dominating CDS, a minimum routing cost CDS, or a bounded‐diameter CDS. However, the load‐balance factor is not considered for CDSs in WSNs. In this paper, a greedy‐based approximation algorithm is proposed to construct load‐balanced CDS in a WSN. More importantly, we propose a new problem: the Load‐balanced Allocate Dominatee problem. Consequently, we propose an optimal centralized algorithm and an efficient probability‐based distributed algorithm to solve the Load‐balanced Allocate Dominatee problem. For a given CDS, the upper and lower bounds of the performance ratio of the distributed algorithm are analyzed in the paper. Through extensive simulations, we demonstrate that our proposed methods extend network lifetime by up to 80% compared with the most recently published CDS construction algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

Parametrization construction of biorthogonal wavelet filter banks for image coding

We construct popular biorthogonal wavelet filter banks (BWFBs) having the linear phase and arbitrary multiplicity of vanishing moments (VMs). A novel parametrization construction technique, which is based on the theory of Diophantine equation, is presented and explicit one-parameter expressions of the BWFBs are derived. Using the expressions, any one-parameter family of BWFBs with different VMs can be constructed, and ten families, i.e., 5/7, 6/6, 9/7, 6/10, 5/11, 10/6, 13/7, 6/14, 17/11, and 10/18 families, are constructed here. The free parameter can be used to optimize the resulting BWFBs with respect to other criteria. In particular, in each family, three specific BWFBs with attractive features are obtained by adjusting the free parameter: the first has optimum coding gain and rational coefficients; the second which also has rational coefficients is very close to a quadrature mirror filter (QMF) bank; and the third which has binary coefficients can realize a multiplication-free discrete wavelet transform. In addition, four BWFBs are systematically verified to exhibit performance competitive to several state-of-the-art BWFBs for image compression, and yet require lower computational costs. This work was supported by the National Natural Science Foundation of China under Grant 60021302     

Block flipping and white space distribution for wirelength minimization

Floorplanning plays an important role in the physical design of very large scale integration (VLSI) circuits. Traditional floorplanners use heuristics to optimize a floorplan based on multiple objectives. Besides traditional floorplanning approaches, some post-floorplanning steps can be applied to consider block flipping, pin assignment and white space distribution to optimize the performance. If we can consider the above three optimizations simultaneously as a post-floorplanning step, the total wirelength can be further reduced without modifying the original floorplan topology. Experimental results show that our approach can handle these issues simultaneously and wirelength can be further improved with a small penalty in runtime. Thus, this approach is highly desirable to be incorporated into a floorplanner as a post-processing step for wirelength optimization.     

Utility‐driven construction of balanced data routing trees in wireless sensor networks

In wireless sensor networks, achieving load balancing in an energy‐efficient manner to improve the network lifetime as much as possible is still a challenging problem because in such networks, the only energy resource for sensor nodes is their battery supplies. This paper proposes a game theoretical‐based solution in the form of a distributed algorithm for constructing load‐balanced routing trees in wireless sensor networks. In our algorithm, load balancing is realized by adjusting the number of children among parents as much as possible, where child adjustment is considered as a game between the parents and child nodes; parents are considered as cooperative players, and children are considered as selfish players. The gained utility by each node is determined by means of some utility functions defined per role, which themselves determine the behavior of nodes in each role. When the game is over, each node gains the maximum benefit on the basis of its utility function, and the balanced tree is constructed. The proposed method provides additional benefits when in‐network aggregation is applied. Analytical and simulation results are provided, demonstrating that our proposed algorithm outperform two recently proposed benchmarking algorithms [1, 2], in terms of time complexity and communication overhead required for constructing the load‐balanced routing trees. Copyright © 2012 John Wiley & Sons, Ltd.     

On the construction of invertible filter banks on the 2-sphere

The theories of signal sampling, filter banks, wavelets, and "overcomplete wavelets" are well established for the Euclidean spaces and are widely used in the processing and analysis of images. While recent advances have extended some filtering methods to spherical images, many key challenges remain. In this paper, we develop theoretical conditions for the invertibility of filter banks under continuous spherical convolution. Furthermore, we present an analogue of the Papoulis generalized sampling theorem on the 2-Sphere. We use the theoretical results to establish a general framework for the design of invertible filter banks on the sphere and demonstrate the approach with examples of self-invertible spherical wavelets and steerable pyramids. We conclude by examining the use of a self-invertible spherical steerable pyramid in a denoising experiment and discussing the computational complexity of the filtering framework.     

Rotation and flipping robust region binary patterns for video copy detection

Many video fingerprints have been proposed to handle the video transformations problems when the original contents are copied and redistributed. However, most of them did not take into account flipping and rotation transformations. In this paper, we propose a novel video fingerprint based on region binary patterns, aiming to realize robust and fast video copy detection against video transformations including rotation and flipping. We extract two complementary region binary patterns from several rings in keyframes. These two kinds of binary patterns are converted into a new type of patterns for the proposed video fingerprint which is robust against rotation and flipping. The experimental results demonstrated that the proposed video fingerprint is effective for video copy detection particularly in the case of rotation and flipping. Furthermore, our experimental results proved that the proposed method allows for high storage efficiency and low computation complexity, which is suitable for practical video copy system.     

Data-driven and optimal denoising of a signal and recovery of its derivative using multiwavelets

Multiwavelets are relative newcomers into the world of wavelets. Thus, it has not been a surprise that the used methods of denoising are modified universal thresholding procedures developed for uniwavelets. On the other hand, the specific of a multiwavelet discrete transform is that typical errors are not identically distributed and correlated, whereas the theory of the universal thresholding is based on the assumption of identically distributed and independent normal errors. Thus, we suggest an alternative denoising procedure based on the Efromovich-Pinsker algorithm. We show that this procedure is optimal over a wide class of noise distributions. Moreover, together with a new cristina class of biorthogonal multiwavelets, which is introduced in this paper, the procedure implies an optimal method for recovering the derivative of a noisy signal. A Monte Carlo study supports these conclusions.     

Classification brain MR images through a fuzzy multiwavelets based GMM and probabilistic neural networks

In this paper, a new approach for classification of brain tissues into White Matter, Gray Matter, Cerebral Spinal Fluid, Glial Matter, Connective and MS lesion in multiple sclerosis is introduced. This work considers fuzzy multiwavelets, Gaussian Mixture Model (GMM) and Weighted Probabilistic Neural Networks (WPNN) for the classification of the brain tissues. Multiwavelet packet transformation is employed on brain MR images. Since multiwavelet packet transformation yields larger number of subbands compared to multiwavelet and wavelet transformations, we have proposed a fuzzy-set based theory for selection of the subbands. In contrast to the standard method of subband selection, guided by the criteria of signal energy, our method is based on the discriminatory features from the multiwavelet packet transformation coefficients. Singular values are then computed from the selected subbands. The singular values of lower magnitudes are truncated for effective classification of brain tissues in the presence of noise. Probability density functions of the remaining singular values are modeled as GMM. Model parameters are estimated using stochastic EM (SEM). They are used as features for the classification. The classification is carried out using WPNN. Experiments have been carried out using the data sets composed of three modalities of brain MR images, namely T1 and T2 relaxation times and proton density weighted MR images. Experimental results prove that the proposed approach gives better classification rate at various noise levels compared to existing approaches.