Multimodality Medical Image Fusion Based on Pixel Significance with Edge-Preserving Processing for Clinical Applications

Multimodal medical image fusion has attained immense popularity in recent years due to its robust technology for clinical diagnosis.It fuses multiple images into a single image to improve the quality of images by retaining significant information and aiding diagnostic practitioners in diagnosing and treating many diseases.However,recent image fusion techniques have encountered several challenges,including fusion artifacts,algorithm complexity,and high computing costs.To solve these problems,this study presents a novel medical image fusion strategy by combining the benefits of pixel significance with edge-preserving processing to achieve the best fusion performance.First,the method employs a cross-bilateral filter(CBF)that utilizes one image to determine the kernel and the other for filtering,and vice versa,by considering both geometric closeness and the gray-level similarities of neighboring pixels of the images without smoothing edges.The outputs of CBF are then subtracted from the original images to obtain detailed images.It further proposes to use edge-preserving processing that combines linear lowpass filtering with a non-linear technique that enables the selection of relevant regions in detailed images while maintaining structural properties.These regions are selected using morphologically processed linear filter residuals to identify the significant regions with high-amplitude edges and adequate size.The outputs of low-pass filtering are fused with meaningfully restored regions to reconstruct the original shape of the edges.In addition,weight computations are performed using these reconstructed images,and these weights are then fused with the original input images to produce a final fusion result by estimating the strength of horizontal and vertical details.Numerous standard quality evaluation metrics with complementary properties are used for comparison with existing,well-known algorithms objectively to validate the fusion results.Experimental results from the proposed research article exhibit superior performance compared to other competing techniques in the case of both qualitative and quantitative evaluation.In addition,the proposed method advocates less computational complexity and execution time while improving diagnostic computing accuracy.Nevertheless,due to the lower complexity of the fusion algorithm,the efficiency of fusion methods is high in practical applications.The results reveal that the proposed method exceeds the latest state-of-the-art methods in terms of providing detailed information,edge contour,and overall contrast.

Scale-Dependent Representations of Relief Based on Wavelet Analysis

Automatic generalization of geographic information is the core of multi_scale representation of spatial data,but the scale_dependent generalization methods are far from abundant because of its extreme complicacy.This paper puts forward a new consistency model about scale_dependent representations of relief based on wavelet analysis,and discusses the thresholds in the model so as to acquire the continual representations of relief with different details between scales.The model not only meets the need of automatic generalization but also is scale-dependent completely.Some practical examples are given.

h-ADAPTIVITY ANALYSIS BASED ON MULTIPLE SCALE REPRODUCING KERNEL PARTICLE METHOD

An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes（SNN） and local-Delaunay-triangulation（LDT） techniques, which were suitable and effective for h-adaptivity analysis on 2-D problems with the regular or irregular distribution of the nodes. The results of multiresolution and h- adaptivity analyses on 2-D linear elastostatics and bending plate problems demonstrate that the improper high-gradient indicator will reduce the convergence property of the h- adaptivity analysis, and that the efficiency of the LDT node refinement strategy is better than SNN, and that the presented h-adaptivity analysis scheme is provided with the validity, stability and good convergence property.

MULTIRESOLUTION ANALYSIS, SELF-SIMILAR TILINGS AND HAAR WAVELETS ON THE HEISENBERG GROUP

In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L^2（H^d） by using self-similar tilings for the acceptable dilations on the Heisenberg group.

Study on spillover effect of copper futures between LME and SHFE using wavelet multiresolution analysis

Research on information spillover effects between financial markets remains active in the economic community. A Granger-type model has recently been used to investigate the spillover between London Metal Exchange(LME) and Shanghai Futures Exchange(SHFE) ,however,possible correlation between the future price and return on different time scales have been ignored. In this paper,wavelet multiresolution decomposition is used to investigate the spillover effects of copper future returns between the two markets. The daily return time series are decomposed on 2n(n=1,…,6) frequency bands through wavelet mul-tiresolution analysis. The correlation between the two markets is studied with decomposed data. It is shown that high frequency detail components represent much more energy than low-frequency smooth components. The relation between copper future daily returns in LME and that in SHFE are different on different time scales. The fluctuations of the copper future daily returns in LME have large effect on that in SHFE in 32-day scale,but small effect in high frequency scales. It also has evidence that strong effects exist between LME and SHFE for monthly responses of the copper futures but not for daily responses.

SOME TOPICS ON WAVELET ANALYSIS

A review of the advance in the theory of wavelet analysis in recent years is given.

Application of wavelet analysis to fault diagnosis of angular measuring system

For fault diagnosis, signal singularity and irregularity discontinuity fraction are very significant characteristics of signal. The discontinuity of output signal represents a system fault . In an angular measuring system, function transformer uses two D/A convertors, output circuit fault of a D/A convertor brings about discontinuity of one phase input voltage amplitude of inductosyn, results in a system error exceeding the allowable error and reduces the system accuracy. This is the reason why discontinuity is detected. Fourier transform has no resolution ability in angular domain, but wavelet can analyse signal in angular and frequency domains. So we decompose the error signal of angular measuring system by wavelet, detect the signal singularity at high frequency layer and find out the accurate position of it.

Model identification of hydraulic flight simulator based on improved particle swarm optimization and wavelet analysis

A new model identification method of hydraulic flight simulator adopting improved panicle swarm optimization （PSO） and wavelet analysis is proposed for achieving higher identification precision. Input-output data of hydraulic flight simulator were decomposed by wavelet muhiresolution to get the information of different frequency bands. The reconstructed input-output data were used to build the model of hydraulic flight simulator with improved particle swarm optimization with mutation （IPSOM） to avoid the premature convergence of traditional optimization techniques effectively. Simulation results show that the proposed method is more precise than traditional system identification methods in operating frequency bands because of the consideration of design index of control system for identification.

FRAME MULTIRESOLUTION ANALYSIS AND INFINITE TREES IN BANACH SPACES ON LOCALLY COMPACT ABELIAN GROUPS

We extend the concept of frame multiresolution analysis to a locally compact abelian group and use it to define certain weighted Banach spaces and the spaces of their antifunctionals. We define analysis and synthesis operators on these spaces and establish the continuity of their composition. Also, we prove a general result to characterize infinite trees in the above Banach spaces of antifunctionals. This paper paves the way for the study of corresponding problems associated with some other types of Banach spaces on locally compact abelian groups including modulation spaces.

Some Applications of E-wavelet Multipliers

Let E= .A measurable function v is called an E- waveletmultiplier if (vψ) is an E-wavelet whenever ψ is an E-wavelet. Some characterizations and applications of E-wavelet multiplier were considered in [1]. In this paper, we give some other applications of E-wavelet multiplier, and prove that the set of all MRA E-wavelets is arcwise connected.

Notes on the Scaling Function

Two properties are given in this paper about the scaling function: suppose Vj; j ∈ Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transform of φ is a continuous real function, compactly supported, then φ(0) ≠ 0 and when supp φ = [a1,b1]∪[a2,b2](b1 < a2,0 < a2), then we havea1 ≤ 0, 0 < b1, a1 < b2/2 ≤ b1, 2π < b2 - a1 ≤ 8π.

APPLICATION OF WAVELET THEORY IN RESEARCHON WEIGHT FUNCTION OF MESHLESS METHOD

Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given.

Construction of Orthogonal Vector-valued Wavelets and Characteristics of Vector-valued Wavelet Packets

The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2（R, C^n） from these wavelet packets.

The Construction of a Class of Compactly Supported Orthogonal Matrix-valued

In this paper,we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets.We obtain a necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets by means of paraunitary vector filter bank theory.A method for constructing a class of compactly supported orthogonal matrix-valued wavelets is proposed by using multiresolution analysis method and matrix theory.

On the aliasing error in a class of bidimensional wavelet subspaces

This paper addresses the aliasing error in multiresolution analysis associated with a 2× 2 dilation expression of the Fourier transform of the aliasing error optimal L^2（R^2）-norm estimation of the aliasing error. the setting of a class of bidimensional matrix of determinant ±2. The explicit is established, from which we obtain an

MIXED SCHEME FOR IMAGE EDGE DETECTION BASED ON WAVELET TRANSFORM

A mixed scheme based on Wavelet Transformation (WT) is proposed for image edge detection. The scheme combines the wavelet transform and traditional Sobel and LoG (Laplacian of Gaussian) operator edge-detection algorithms. The precise theory analysis is given to show that the wavelet transformation has an advantage for signal processing. Simulation results show that the new scheme is better than only using the Sobel or LoG methods. Complexity analysis is also given and the conclusion is acceptable, therefore the proposed scheme is effective for edge detection.

Multiresolution Finite Element Method Based on a New Locking-Free Rectangular Mindlin Plate Element

A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace sequence whose basis functions are constructed of scaling and shifting on the element domain of basic full node shape function. The basic full node shape function is constructed by extending the split node shape function of a traditional Mindlin plate element to other three quadrants around the coordinate zero point. As a result, a new rational MRA concept together with the resolution level (RL) is constituted for the element. The traditional 4-node rectangular Mindlin plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The analysis clarity of a plate structure is actually determined by the RL, not by the mesh. Thus, the accuracy of a plate structural analysis is replaced by the clarity, the irrational MRA by the rational and the mesh model by the RL that is the discretized model by the integrated.

PESEDOSPECTRAL-MULTIWAVELET-GALERKIN METHOD FOR ADVECTION-DIFFUSION PROBLEM WITH COMPLEX BOUNDARY

The element of pesedospectral-multiwavelet-Galerkin method, and how tocombine it with penalty method for treating boundary conditions are given. Multiwavelet bases don'toverlap on the given scale, and possess the same compact set in a group of several functions, sothey can be directly used to the numerical discretion on the finite interval. Numerical tests showthat general boundary conditions can be enforced with the penalty method, and thatpesedospectral-multiwavelet-Galerkin method can well track the solutions' development. This alsoproves that pesedospectral-multiwavelet-Galerkin method is effective.

Wavelet-Galerkin Solutions forDifferential Equations

In order to get over the difficulty of introducing boundary conditions in solving differential equations by Daubechies wavelet, in this paper the wavelet-Galerkin numerical method is suggested to solve the differential equations, especially for the differential equation with boundary layer. The numberical results show that the algorithm described in this paper is effective both in the precision and the ability of detecting boundary layer position.

CONSTRUCTION OF REAL-VALUED MULTIVARIATE WAVELETS

In this papert we give a method to construct multivqriate wavelets for skewsymmetric scaling function. Such wavelets have some desirable properties, e,g.t they are real-valued and orthogonal if the scaling function is real-valued and orthonormalrespectively.