Dual Wavelet Research Articles

Multilayered Secure Medical Image Transmission with High Payload Using Double Density Dual Tree Discrete Wavelet Transform

Multilayered Secure Medical Image Transmission with High Payload Using Double Density Dual Tree Discrete Wavelet Transform

Characterizations of dual multiwavelet frames of periodic functions

We prove characterizations of dual multiwavelet frames for [Formula: see text] constructed from a pair of [Formula: see text]-periodic multirefinable generators. Based on the notion of the Mixed Fundamental sequence we derive Mixed Extension Principles dictating the construction of dual wavelet masks with respect to given refinement masks and we show that these Principles characterize dual framelets.

An Improved Image Fusion and Segmentation using FLICM with GA for Medical Diagonosis

Background: Medical image fusion has become a common term used in medical diagnostics and treatment. Now a day's numerous wavelet transform based fusion methods proposed for overcoming the spectral distortion in the conventional fusion techniques such as PCA and IHS. DWT based image fusion process has the spatial distortion and lack of information. So selecting suitable wavelet transform for fusion is an important task. Method: In the proposed system, Dual tree Discrete Wavelet transform based Fusion and GA based FLICM segmentation is proposed. First, two different types of medical images-MRI and CT are decomposed by Dual tree Discrete Wavelet Transform (DDWT). Next, DDWT coefficients from two input images are fused pixel-by pixel by choosing the average of the approximation coefficients. Findings: Genetic algorithm is applied for the fused image in order to generate the optimal cluster centers of its own. From the clusters the affected portion cells are identified using FLICM segmentation process. Improvements: The performance of the proposed method is tested for various medical images and the results are analyzed. The fusion results shows DDWT based fusion technique provides around 5db improved PSNR performance when compared to the DWT based fusion. The GA optimizer based FLICM segmentation technique reduces the computation time. For various medical images the segmentation time is approximately reduced as half when compared to the FLICM segmentation technique without GA.

Divergence-Free Wavelets on the Hypercube: General Boundary Conditions

On the n-dimensional hypercube, for given \(k\in {\mathbb {N}}\), wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space \(H^k((0,1)^n)^n\) with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and suitable dual wavelets can be constructed to be locally supported. The construction of the isotropic wavelet bases is restricted to the square, but that of the anisotropic wavelet bases applies for any space dimension n.

Periodic Wavelet Frames on Local Fields of Positive Characteristic

ABSTRACTPeriodic wavelet frames have gained considerable popularity in recent years, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. In this article, we introduce the concept of periodic wavelet frame on local fields of positive characteristic and show that under weaker conditions the periodization of any wavelet frame constructed by the unitary extension principle with dilation factor 𝔭−1 is a periodic wavelet frame on local fields. Moreover, based on the mixed extension principle and Fourier-based techniques of the wavelet frames, we present an explicit method for a pair of dual periodic wavelet frames on local fields of positive characteristic.

Image De-Noising with the Aid of Dual Tree Wavelet Transform And Artificial Bee Colony Optimization Algorithm

Image De-Noising with the Aid of Dual Tree Wavelet Transform And Artificial Bee Colony Optimization Algorithm

Construction of Periodic Wavelet Frames Generated by the Walsh Polynomials

An explicit method for the construction of a tight wavelet frame generated by the Walsh polynomials with the help of extension principles was presented by Shah (Shah, 2013). In this article, we extend the notion of wavelet frames to periodic wavelet frames generated by the Walsh polynomials on R+ by using extension principles. We first show that under some mild conditions, the periodization of any wavelet frame constructed by the unitary extension principle is still a periodic wavelet frame on R + . Then, we construct a pair of dual periodic wavelet frames generated by the Walsh polynomials on R + using the machinery of the mixed extension principle and Walsh–Fourier transforms.

On extensions of wavelet systems to dual pairs of frames

It is an open problem whether any pair of Bessel sequences with wavelet structure can be extended to a pair of dual frames by adding a pair of singly generated wavelet systems. We consider the particular case where the given wavelet systems are generated by the multiscale setup with trigonometric masks and provide a positive answer under extra assumptions. We also identify a number of conditions that are necessary for the extension to dual (multi-) wavelet frames with any number of generators, and show that they imply that an extension with two pairs of wavelet systems is possible. Along the way we provide examples that demonstrate the extra flexibility in the extension to dual pairs of frames compared with the more popular extensions to tight frames.

Biorthogonal Wavelet Construction Using Homotopy Method

The biorthogonal wavelets families are usedwidely because they have compact support, complete symmetry and linear phase. According to Bezout’s theorem,the biorthogonal wavelets available now are only some particular examples of total solutions. The quantity of solutions is decided jointly by the scaling function vanishingmoment N and dual vanishing moment N. The relationship of N, N and solutions’ quantity is discussed in detail.According to the constraint conditions which the compactbiorthogonal wavelets satisfy, a number of biorthogonalwavelets are constructed in which the global convergenthomotopy method is used for different N and N. The filter coefficients and plots of scaling function, dual scalingfunction, wavelet function and dual wavelet function aregiven.

Pre-wavelet bases in Lebesgue spaces

Under the decay condition, we have constructed the dual wavelet basis of a pre-wavelet basis. The frame operators of both bases are bijective on Lebesgue spaces. Both bases are also unconditional bases for Lebesgue spaces.

A Construction of Dual Wavelet and its Applications in Image Edge Detection

A Construction of Dual Wavelet and its Applications in Image Edge Detection

Duality for Frames

The subject of this article is the duality principle, which, well beyond its stand at the heart of Gabor analysis, is a universal principle in frame theory that gives insight into many phenomena. Its fiber matrix formulation for Gabor systems is the driving principle behind seemingly different results. We show how the classical duality identities, operator representations and constructions for dual Gabor frames are in fact aspects of the dual Gramian matrix fiberization and its sole duality principle, giving a unified view to all of them. We show that the same duality principle, via dual Gramian matrix analysis, holds for dual (or bi-) systems in abstract Hilbert spaces. The essence of the duality principle is the unitary equivalence of the frame operator and the Gramian of certain adjoint systems. An immediate consequence is, for example, that, even on this level of generality, dual frames are characterized in terms of biorthogonality relations of adjoint systems. We formulate the duality principle for irregular Gabor systems which have no structure whatsoever to the sampling of the shifts and modulations of the generating window. In case the shifts and modulations are sampled from lattices we show how the abstract matrices can be reduced to the simple structured fiber matrices of shift-invariant systems, thus arriving back in the well understood territory. Moreover, in the arena of multiresolution analysis (MRA)-wavelet frames, the mixed unitary extension principle can be viewed as the duality principle in a sequence space. This perspective leads to a construction scheme for dual wavelet frames which is strikingly simple in the sense that it only needs the completion of an invertible constant matrix. Under minimal conditions on the MRA, our construction guarantees the existence and easy constructability of non-separable multivariate dual MRA-wavelet frames. The wavelets have compact support and we show examples for multivariate interpolatory refinable functions. Finally, we generalize the duality principle to the case of transforms that are no longer defined by discrete systems, but may have discrete adjoint systems.

English

-De-noising is used to remove the noise from corrupted image, while retaining the edges and other detailed features as much as possible.. Filtering of these images is required to maximize the original content and suppress the effect of noise generated from random source. In this paper, we have evaluated and compared performances of modified de-noising method and the local adaptive real oriented dual tree wavelet image de-noising method. We have evaluated and compared performances of modified de-noising method and the local adaptive real oriented dual tree wavelet image de-noising method. These methods are compared with other based on PSNR (Peak signal to noise ratio) between original image and noisy image and PSNR between original image and de-noised image.

Noise Reduction of Enhanced Images UsingDual Tree Complex Wavelet Transform and Shrinkage Filter

The project presents that noise reduction of enhanced images using Dual tree complex wavelet transform and Bivariate shrinkage filter.Enhanced image gets affected during contrast enhancement process.So the denoising process will be handled to reduce distortion under Dual tree complex wavelet transform domain. Initially noisy image pixels are decorrelated to obtain coarser and finer components and more noise details are contaminated in high frequency subbands. In order to reduce the spatial distortion during filtering, bivariate shrinkage function used in the DTCWT domain.The effect of noise in the images can be reduced by using either spatial filtering or transform domain filtering. In transform domain wavelet method provide better de-noising while preserving the details of images like edges. In order to increase the quality of the super resolved image, preserving the edges is essential.The guided filter is not directly applicable for sparse inputs like strokes. It also shares a common limitation of other explicit filter,it may have halos near some edges.In order to overcome these disadvantages Dual Tree Complex Wavelet Transform (DTCWT) is used which provide perfect reconstruction over the traditional wavelet transform.Experimental results show that the resultant algorithms produce images with better visual quality and at the same time performance can be improved.Evaluation is carried out in terms of various parameters such as Peak Signal to Noise Ratio, mean Structural Similarity and Coefficient of Correlation.

Study of Periodic Frames and Trivariate Tight Wavelet Frames and Applications in Materials Engineering

It is shown that there exists a frame wavelet with fast decay in the time domain and compact support in the frequency domain generating a wavelet system whose canonical dual frame cannot be generated by an arbitrary number of generators. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions.

Construction of the matched multiple knot B-spline wavelets on a bounded interval

In order to solve a boundary value problem using Galerkin's method, the selection of basis functions plays a crucial rule. When the solution of a boundary value problem is not enough smooth or the domain is irregular, multiple knot B-spline wavelets (MKBSWs) with locally compact support are appropriate basis functions. However, to have globally continuous basis functions, a matching across the subdomain interfaces is required. In other words, MKBSWs that are non-zero in the interelement boundaries should be matched. In this paper, we present the primal and dual matched multiple knot B-spline scaling and wavelet functions whose main properties of smoothness and biorthogonality are kept.

SPECTRAL RADIUS OF BIORTHOGONAL WAVELETS WITH ITS APPLICATION

Abstract. In this paper, a 2-circular matrix theory is developed, anda concept of spectral radius for biorthogonal wavelet is introduced. Wepropose a novel design method by minimizing the spectral radius and ob-tain a wavelet which has better performance than the famous 9-7 waveletin terms of image compression coding. 1. IntroductionOver the last two decades, wavelets have become a fundamental tool in manyareas of applied mathematics and engineering ranging from signal and imageprocessing to numerical analysis. In her celebrated paper [2], Daubechies in-troduced a general method to construct compactly supported wavelets. It iswell known that 2-band orthogonal wavelet suffers from severe constraint con-ditions. For instance, nontrivial symmetric 2-band orthogonal wavelet doesnot exist except the Haar wavelet [3]. Biorthogonal wavelet enjoy two im-portant properties of linear phase and higher vanishing moments, was studied[4, 8, 11, 12]. Vetterli and Herley studied theory and design for biorthogonalwavelet [9] and Cohen gave another biorthogonal wavelet family [6]. GuoqiuWang constructed wavelet filters with free paraments based on 2-circular ma-trix method [1]. Even though the research on biorthogonal wavelet is relativelymature, further study is still valuable.Let (ψ, ψe) be a pair of dual wavelet functions,(1.1) ψ

Algorithm for constructing symmetric dual framelet filter banks

Dual wavelet frames and their associated dual framelet filter banks are often constructed using the oblique extension principle. In comparison with the construction of tight wavelet frames and tight framelet filter banks, it is indeed quite easy to obtain some particular examples of dual framelet filter banks with or without symmetry from any given pair of low-pass filters. However, such constructed dual framelet filter banks are often too particular to have some desirable properties such as balanced filter supports between primal and dual filters. From the point of view of both theory and application, it is important and interesting to have an algorithm which is capable of finding all possible dual framelet filter banks with symmetry and with the shortest possible filter supports from any given pair of low-pass filters with symmetry. However, to our best knowledge, this issue has not been resolved yet in the literature and one often has to solve systems of nonlinear equations to obtain nontrivial dual framelet filter banks. Given the fact that the construction of dual framelet filter banks is widely believed to be very flexible, the lack of a systematic algorithm for constructing all dual framelet filter banks in the literature is a little bit surprising to us. In this paper, by solving only small systems of linear equations, we shall completely settle this problem by introducing a step-by-step efficient algorithm to construct all possible dual framelet filter banks with or without symmetry and with the shortest possible filter supports. As a byproduct, our algorithm leads to a simple algorithm for constructing all symmetric tight framelet filter banks with two high-pass filters from a given low-pass filter with symmetry. Examples will be provided to illustrate our algorithm. To explain and to understand better our algorithm and dual framelet filter banks, we shall also discuss some properties of our algorithms and dual framelet filter banks in this paper.

Assessment of earthquake early warning potential from KiK-Net seismograms of 2000–2011 north and east Japan events

An earthquake early warning alert system with a high degree of accuracy and precision and measured in sec- ondsisanecessitytosavemanylivesinJapan,oneofthemost tectonically active countries of the world. In this paper, we estimate the potential value for early warning of crustal and intraslab earthquakes recorded at the KiK-Net network. The work reported here is similar to that of the early warning analysis system of California and uses new comprehensive data from northernand eastern Japan (Hokkaido and Tohoko). Anattempt wasalsomadetoanalyzewhether theslopesofthe regression lines obtained for Californian events (all are crustal events)aresimilar tothoseobtainedfor HokkaidoandTohoko crustal events. We also analyzed whether there was any dif- ferencebetweentheslopesobtainedfromJapanesecrustaland intraslab earthquakes. The poor correlation of the higher mag- nitude (>5.5) with predominant period implied quite a limited predictability of predominant frequency. This was evident from the scattered plot obtained for higher magnitudes. These limitations led us to use a discrete wavelet transform- automated algorithm based on the bi-orthogonal construction with two and four vanishing moments for the primal and dual wavelets.

Application of Semiorthogonal B-Spline Wavelets for the Solutions of Linear Second Kind Fredholm Integral Equations

In this paper, the linear semiorthogonal compactly supported B-spline wavelets together with their dual wavelets have been applied to approximate the solutions of Fredholm integral equations of the second kind. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of in tegral equations to some algebraic equations. The method is computationally attractive, and application of it has been demonstrated thr ough illustrative examples.