Vector-valued wavelets and vector filter banks

In this paper, we introduce vector-valued multiresolution analysis and vector-valued wavelets for vector-valued signal spaces. We construct vector-valued wavelets by using paraunitary vector filter bank theory. In particular, we construct vector-valued Meyer wavelets that are band-limited. We classify and construct vector-valued wavelets with sampling property. As an application of vector-valued wavelets, multiwavelets can be constructed from vector-valued wavelets. We show that certain linear combinations of known scalar-valued wavelets may yield multiwavelets. We then present discrete vector wavelet transforms for discrete-time vector-valued (or blocked) signals, which can be thought of as a family of unitary vector transforms     

Construction of Arbitrary Dimensional Biorthogonal Multiwavelet Using Lifting Scheme

This paper focuses on the construction of multidimensional biorthogonal multiwavelets and the perfect reconstruction multifilter banks. Based on the Hermite-Neville filter, two lifting structures have been proposed and systematically investigated, and a general design framework has been developed for building biorthogonal multiwavelets and Hermite interpolation filter banks with any multiplicity for any lattice in any dimension with any number of primal and dual vanishing moments. The construction is an important generalization of the Neville-based lifting scheme and inherits all of the advantages of lifting schemes such as fast transform, in-place computation and integer-to-integer transforms. Our multi wavelet systems preserve most of the desirable properties for applications, such as interpolating, short support, symmetry, and high vanishing moments.     

Optimal multifilter banks: design, related symmetric extensiontransform, and application to image compression

The design of optimal multifilter banks and optimum time-frequency resolution multiwavelets with different objective functions is discussed. The symmetric extension transform related to multifilter banks with symmetric properties is presented. It is shown that such a symmetric extension transform is nonexpensive. More optimal multifilter banks for image compression are constructed, and some of them are used in image compression. Experiments show that optimal multifilter banks have better performances in image compression than Daubechies' orthogonal wavelet filters and Daubechies' least asymmetric wavelet filters, and for some images, they even have better performances than the scalar (9,7)-tap biorthogonal wavelet filters. Experiments also show that the symmetric extension transform provided in this paper improves the rate-distortion performance compared with the periodic extension transform     

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     

Orthogonal multiwavelets with optimum time-frequency resolution

A procedure to design orthogonal multiwavelets with good time-frequency resolution is introduced. Formulas to compute the time-durations and the frequency-bandwidths of scaling functions and multiwavelets are obtained. Parameter expressions for the matrix coefficients of the multifilter banks that generate symmetric/antisymmetric scaling functions and multiwavelets supported in [O,N] are presented for N=2,...,6. Orthogonal multiwavelets with optimum time-frequency resolution are constructed, and some optimal multifilter banks are provided     

Reconstruction and Decomposition Algorithms for Biorthogonal Multiwavelets

We construct biorthogonal multiwavelets (abbreviated to wavelets) in a weighted Hilbert space L ²(E,) where E is a compact subset in . A recursive formula for biorthogonal wavelet construction is presented. The construction of the initial wavelets is reformulated as the solution of a certain matrix completion problem. A general solution of the matrix completion problem is identified and expressed conveniently in terms of any given particular solution. Several particular solutions are proposed. Reconstruction and decomposition algorithms are developed for the biorthogonal wavelets. Special results for the univariate case E=[0,1] are obtained.     

A general approach for analysis and application of discretemultiwavelet transforms

This paper proposes a general paradigm for the analysis and application of discrete multiwavelet transforms, particularly to image compression. First, we establish the concept of an equivalent scalar (wavelet) filter bank system in which we present an equivalent and sufficient representation of a multiwavelet system of multiplicity r in terms of a set of r equivalent scalar filter banks. This relationship motivates a new measure called the good multifilter properties (GMPs), which define the desirable filter characteristics of the equivalent scalar filters. We then relate the notion of GMPs directly to the matrix filters as necessary eigenvector properties for the refinement masks of a given multiwavelet system. Second, we propose a generalized, efficient, and nonredundant framework for multiwavelet initialization by designing appropriate preanalysis and post-synthesis multirate filtering techniques. Finally, our simulations verified that both orthogonal and biorthogonal multiwavelets that possess GMPs and employ the proposed initialization technique can perform better than the popular scalar wavelets such as Daubechies'D8 wavelet and the D(9/7) wavelet, and some of these multiwavelets achieved this with lower computational complexity     

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     

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.     

A new approach to the design of biorthogonal triplet half-band filter banks using generalized half-band polynomials

This paper presents a novel approach to design a class of biorthogonal triplet half-band filter banks based on the generalized half-band polynomials. The filter banks are designed with the help of three-step lifting scheme (using three kernels). The generalized half-band polynomial is used to construct these three kernels by imposing the number of zeros at \(z=-1\) . The maximum number of zeros imposed for the three kernels is half of the order of half-band polynomial ( \(K/2\) for \(K\) order polynomial). The three kernels give a set of constraints on the coefficients of half-band polynomial by imposing the zeros. In addition to structural perfect reconstruction and linear phase, the proposed filter banks provide better frequency selectivity, more similarity between analysis and synthesis filters (measure of near-orthogonality), and good time–frequency localization. The proposed technique offers more flexibility in the design of filters using two degrees of freedom. Some examples have been presented to illustrate the method.     

Fast estimation of continuous Karhunen-Loeve eigenfunctions usingwavelets

This paper develops a new wavelet method for the fast estimation of continuous Karhunen-Loeve eigenfunctions. The method of snapshots is modified by projecting the ensemble functions onto orthogonal or biorthogonal interpolating function spaces. Under well-behaved piecewise smooth polynomial ensemble functions, the size of the covariance matrix produced is greatly reduced, without sacrificing much accuracy. Moreover, the covariance matrix C˜ may be easily decomposed such that C˜ = A^T A, and thus, the more stable singular value decomposition (SVD) algorithm may be applied. An interpolating scheme that reduces the computation of projecting the ensemble functions onto the biorthogonal subspace to a single sample is also developed. Furthermore, by projecting the ensemble functions onto wavelet spaces, the covariance matrix may be sparsified by a multiresolution decomposition. Error bounds for the eigenvalues between the sparsified and nonsparsified covariance matrix are also derived     

Integral Cryptanalysis on Full MISTY1

MISTY1 is a block cipher designed by Matsui in 1997. It was well evaluated and standardized by projects, such as CRYPTREC, ISO/IEC, and NESSIE. In this paper, we propose a key recovery attack on the full MISTY1, i.e., we show that 8-round MISTY1 with 5 FL layers does not have 128-bit security. Many attacks against MISTY1 have been proposed, but there is no attack against the full MISTY1. Therefore, our attack is the first cryptanalysis against the full MISTY1. We construct a new integral characteristic by using the propagation characteristic of the division property, which was proposed in EUROCRYPT 2015. We first improve the division property by optimizing the division property for a public S-box and then construct a 6-round integral characteristic on MISTY1. Finally, we recover the secret key of the full MISTY1 with \(2^{63.58}\) chosen plaintexts and \(2^{121}\) time complexity. Moreover, if we use \(2^{63.994}\) chosen plaintexts, the time complexity for our attack is reduced to \(2^{108.3}\). Note that our cryptanalysis is a theoretical attack. Therefore, the practical use of MISTY1 will not be affected by our attack.     

Some New Expressions for Nakagami Fading Based on Order Statistics

Alternative representations based on order statistics are derived for the probability of error for orthogonal, biorthogonal, and transorthogonal signaling. Short programs in are developed for the computation of these representations and to furnish evidence to show that their performance is superior to the traditional Monte Carlo approach.

Convergence behavior of non-equidistant sampling series

The convergence of sampling series with non-equidistant sampling points cannot be guaranteed for the Paley–Wiener space if the class of sampling patterns is not restricted. In this paper we consider sampling patterns that are made of the zeros of sine-type functions and analyze the local and global convergence behavior of the sampling series. It is shown that oversampling is necessary for global uniform convergence. If no oversampling is used there exists for every sampling pattern a signal such that the peak value of the approximation error grows arbitrarily large. Furthermore, we use the findings to derive results about the mean-square convergence behavior of the sampling series for bandlimited wide-sense stationary stochastic processes. Finally, a procedure is given to construct functions of sine type and possible sampling patterns.     

Higher order modes on usual waveguides

In the following paper some different kinds of microwave guides will be inspected under main aspect of higher order modes. The knowledge of these modes is important for field matching problems at discontinuities and for suppressing propagation of higher order modes by geometrical variations. In some cases it is sufficient to know their principal behaviour. They will be calculated in paper by the often used orthogonal expansion. This method allows to determine all kinds of waves: propagating, damping and complex waves. The following guides are inspected:

1. rectangular waveguides,
2. circular waveguides,
3. L-shaped waveguides,
4. double ridged rectangular waveguides,
5. unilateral finlines with one slot,
6. unilateral finlines with two slots,
7. shielded microstrip lines,
8. circular image guides,
9. rectangular waveguides with dielectric slab,
10. H-guides.

     

Topology control in constant rate mobile ad hoc networks

Topology control is the problem of assigning power levels to the nodes of an ad hoc network so as to create a specified network topology while minimizing the energy consumed by the network nodes. While considerable theoretical attention has been given to the issue of topology control in wireless ad hoc networks, all of that prior work has concerned stationary networks. When the nodes are mobile, there is no algorithm that can guarantee a graph property (such as network connectivity) throughout the node movement. In this paper we study topology control in mobile wireless ad hoc networks (MANETs). We define a mobility model, namely the constant rate mobile network (CRMN) model, in which we assume that the speed and direction of each moving node are known. The goal of topology control under this model is to minimize the maximum power used by any network node in maintaining a specified monotone graph property. Network connectivity is one of the most fundamental monotone properties. Under the CRMN model, we develop general frameworks for solving both the decision version (i.e. for a given value p > 0, will a specified monotone property hold for the network induced by assigning the power value p to every node?) and the optimization version (i.e. find the minimum value p such that the specified monotone property holds for the network induced by assigning the power value p to every node) of the topology control problems. Efficient algorithms for specific monotone properties can be derived from these frameworks. For example, when the monotone property is network connectivity, our algorithms for the decision and optimization versions have running times of O(n ² log² n) and O(n ⁴ log² n), respectively. Our results represent a step towards the development of efficient and provably good distributed algorithms for topology control problems for MANETs.     

Six Order Cascaded Power Line Notch Filter for ECG Detection Systems with Noise Shaping

This paper presents the design of an operational transconductance amplifier-C (OTA-C) notch filter for a portable Electrocardiogram (ECG) detection system. A six order cascaded filter is utilized to reduce the effect of the power line interference at (50/60 Hz). The proposed filter is based on a programmable balanced OTA circuit. Based on this, PSPICE post layout simulation results for the extracted filter using 0.25  \(\upmu \) m technology and operating under \(\pm \) 0.8 V voltage supply are also given. The six order notch filter provides a notch depth of 65 dB (43 dB for 4th order), input referred noise spectral density with noise shaping of 9  \(\upmu \) Vrms/ \(\surd \) Hz at the pass band frequencies and 9 mVrms/ \(\surd \) Hz at the notch (zero) frequency which provide noise shaping for the ECG signal. These results demonstrate the ability of the filter to be used for ECG signal filtering which is located within 150 Hz.     

对称—反对称多小波滤波器组的参数化构造及其在图像压缩中的应用

本文给出了一类对称—反对称多小波滤波器组参数化设计方法,并在此基础上提出了新的多小波零树编码方案.实验表明,与常用的9-7单小波相比,我们所设计的双正交对称—反对称多小波可使编码性能有较大幅度的改善.     

Recursive biorthogonal interpolating wavelets and signal-adaptedinterpolating filter banks

In this paper, by combining the ideas of the recursive wavelets with second-generation wavelets, a family of recursive biorthogonal interpolating wavelets (RBIWs) is developed. The RBIWs have simple shape parameter vectors on each level, which allows a multichannel decomposition algorithm and provides, a flexible structure for designing signal-adapted interpolating filter banks. In the single-level case, an efficient approach to design an optimum two-channel biorthogonal interpolating filter bank is proposed, which maximizes the coding gain under the traditional quantization noise assumption. Furthermore, in the multilevel case, using level-wise optimization of the shape parameter vectors, signal-adapted tree-structured recursive biorthogonal interpolating filter banks (RBIFBs) are designed, which are efficient in computation and can remarkedly improve the coding gain. Finally, numerical results demonstrate the effectiveness of the proposed methods     

Design of complex adaptive multiresolution directional filter bank and application to pansharpening

This paper proposes a new 2-D transform design, namely complex adaptive multiresolution directional filter bank, to represent the spatial orientation features of an input image adaptively. The proposed design is completely shift invariant and represents the input image by one low-pass and multiscale N directional band-pass subbands. Here, N represents estimated number of dominant directions present in the input image. Our design consists of two main filter bank stages. A fix partitioned complex-valued directional filter bank (CDFB) is at the core of the design followed by a novel partition filter bank stage. Fine partitioning of the CDFB subbands is used to get the adaptive nature of the proposed transform. The partitioning decision is made based on the directional significance of range of CDFB subband angle selectivity in the input image. Partition filter bank stage which nonuniformly partitions the CDFB subbands provides total N dominant direction selective subbands. Local orientation map of the input image is used to determine the dominant directions and hence N. For better sparsity properties, we design the multiresolution stage with filters having high vanishing moments and better frequency selectivity. Applicability of the proposed adaptive design is shown for pansharpening of multispectral images. Our proposed pansharpening approach is evaluated on images captured using QuickBird and IKONOS-2 satellites. Results obtained using the proposed approach on these datasets show considerable improvements in qualitative as well as quantitative evaluations when compared to state-of-the-art pansharpening approaches including transform-based methods.