Orthogonal transformation operation theorem of a spatial universal uniform rotating magnetic field and its application in capsule endoscopy

According to the anti-phase sine current superposition theorem, the orientation, the magnetic flux density, the angular speed and the rotational direction of the spatial universal rotating magnetic field (SURMF) can be controlled within the tri-axial orthogonal square Helmholtz coils (TOSHC). Nevertheless, three coupling direction angles of the normal vector of the SURMF in the Descartes coordinate system cannot be separately controlled, thus the adjustment of the orientation of the SURMF is difficult and the flexibility of the robotic posture control is restricted. For the dimension reduction and the decoupling of control variables, the orthogonal transformation operation theorem of the SURMF is proposed based on two independent rotation angular variables, which employs azimuth and altitude angles as two variables of the three-phase sine current superposition formula derived by the orthogonal rotation inverse transformation. Then the unique control rules of the orientation and the rotational direction of the SURMF are generalized in each spatial quadrant, thus the scanning of the normal vector of the SURMF along the horizontal or vertical direction can be achieved through changing only one variable, which simplifies the control process of the orientation of the SURMF greatly. To validate its feasibility and maneuverability, experiments were conducted in the animal intestine utilizing the innovative dual hemisphere capsule robot (DHCR) with active and passive modes. It was demonstrated that the posture adjustment and the steering rolling locomotion of the DHCR can be realized through single variable control, thus the orthogonal transformation operation theorem makes the control of the orientation of the SURMF convenient and flexible significantly. This breakthrough will lay a foundation for the human-machine interaction control of the SURMF.

An iterative algorithm of NWTLS-EC for three dimensional-datum transformation with large rotation angle

The Gauss-Markov （GM） model and the Errors-in-Variables （EIV） model are frequently used to perform 3D coordinate transformations in geodesy and engineering surveys. In these applications, because the observation errors in original coordinates system are also taken into account, the latter is more accurate and reasonable than the former. Although the Weighted Total Least Squares （WTLS） technique has been intro- duced into coordinate transformations as the measured points are heteroscedastic and correlated, the Variance- Covariance Matrix （VCM） of observations is restricted by a particular structure, namely, only the correlations of each points are taken into account. Because the 3D datum transformation with large rotation angle is a non- linear problem, the WTLS is no longer suitable in this ease. In this contribution, we suggested the nonlinear WTLS adjustments with equality constraints （NWTLS-EC） for 3D datum transformation with large rotation an- gle, which removed the particular structure restriction on the VCM. The Least Squares adjustment with Equality （LSE） constraints is employed to solve NWTLS-EC as the nonlinear model has been linearized, and an iterative algorithm is proposed with the LSE solution. A simulation study of 3D datum transformation with large rotation angle is given to insight into the feasibility of our algorithm at last.

An Orthogonal Wavelet Transform Fractionally Spaced Blind Equalization Algorithm Based on the Optimization of Genetic Algorithm

An orthogonal wavelet transform fractionally spaced blind equalization algorithm based on the optimization of genetic algorithm(WTFSE-GA) is proposed in viewof the lowconvergence rate,large steady-state mean square error and local convergence of traditional constant modulus blind equalization algorithm(CMA).The proposed algorithm can reduce the signal autocorrelation through the orthogonal wavelet transform of input signal of fractionally spaced blind equalizer,and decrease the possibility of CMA local convergence by using the global random search characteristics of genetic algorithm to optimize the equalizer weight vector.The proposed algorithm has the faster convergence rate and smaller mean square error compared with FSE and WT-FSE.The efficiency of the proposed algorithm is proved by computer simulation of underwater acoustic channels.

Matrix Expression of the Orthogonal Wavelet (Packets) Transform

Matrix expression of finite orthogonal wavelet transform of finite impulse response signal is more valuable for theoretical analysis and understanding. However, clear deduction for matrix expression has not been provided yet. In this paper, the formulation to generate the re-lated matrix is put forward and the theorem on the orthogonality of this matrix proved. This effort deploys a basis for more deeper and wider applications in chemical processes. *

Efficiency Analysis of the Autofocusing Algorithm Based on Orthogonal Transforms

Efficiency of the autofocusing algorithm implementations based on various orthogonal transforms is examined. The algorithm uses the variance of an image acquired by a sensor as a focus function. To compute the estimate of the variance we exploit the equivalence between that estimate and the image orthogonal expansion. Energy consumption of three implementations exploiting either of the following fast orthogonal transforms: the discrete cosine, the Walsh-Hadamard, and the Haar wavelet one, is evaluated and compared. Furthermore, it is conjectured that the computation precision can considerably be reduced if the image is heavily corrupted by the noise, and a simple problem of optimal word bit-length selection with respect to the signal variance is analyzed.

An Algorithm to Reduce Compression Ratio in Multimedia Applications

In recent years,it has been evident that internet is the most effective means of transmitting information in the form of documents,photographs,or videos around the world.The purpose of an image compression method is to encode a picture with fewer bits while retaining the decompressed image’s visual quality.During transmission,this massive data necessitates a lot of channel space.In order to overcome this problem,an effective visual compression approach is required to resize this large amount of data.This work is based on lossy image compression and is offered for static color images.The quantization procedure determines the compressed data quality characteristics.The images are converted from RGB to International Commission on Illumination CIE La^(∗)b^(∗);and YCbCr color spaces before being used.In the transform domain,the color planes are encoded using the proposed quantization matrix.To improve the efficiency and quality of the compressed image,the standard quantization matrix is updated with the respective image block.We used seven discrete orthogonal transforms,including five variations of the Complex Hadamard Transform,Discrete Fourier Transform and Discrete Cosine Transform,as well as thresholding,quantization,de-quantization and inverse discrete orthogonal transforms with CIE La^(∗)b^(∗);and YCbCr to RGB conversion.Peak to signal noise ratio,signal to noise ratio,picture similarity index and compression ratio are all used to assess the quality of compressed images.With the relevant transforms,the image size and bits per pixel are also explored.Using the(n,n)block of transform,adaptive scanning is used to acquire the best feasible compression ratio.Because of these characteristics,multimedia systems and services have a wide range of possible applications.

A Novel Radial Basis Function Neural Network Approach for ECG Signal Classification

ions in the ECG signal.The cardiologist and medical specialistfind numerous difficulties in the process of traditional approaches.The specified restrictions are eliminated in the proposed classifier.The fundamental aim of this work is tofind the R-R interval.To analyze the blockage,different approaches are implemented,which make the computation as facile with high accuracy.The information are recovered from the MIT-BIH dataset.The retrieved data contain normal and pathological ECG signals.To obtain a noiseless signal,Gaborfilter is employed and to compute the amplitude of the signal,DCT-DOST(Discrete cosine based Discrete orthogonal stock well transform)is implemented.The amplitude is computed to detect the cardiac abnormality.The R peak of the underlying ECG signal is noted and the segment length of the ECG cycle is identified.The Genetic algorithm(GA)retrieves the primary highlights and the classifier integrates the data with the chosen attributes to optimize the identification.In addition,the GA helps in performing hereditary calculations to reduce the problem of multi-target enhancement.Finally,the RBFNN(Radial basis function neural network)is applied,which diminishes the local minima present in the signal.It shows enhancement in characterizing the ordinary and anomalous ECG signals.

Stiffness Analysis of Spherical Parallel Mechanism U_(P+R) with 2-DOF

As one of the typical less-mobility parallel mechanisms, the spherical parallel mechanism Up.s with two degrees of freedom （2-DOF） possess high order overconstraints, and the calculation of its stiffness is partly different with general parallel mechanisms owing to the bars in each branch are assumed to be arc-shaped. By means of small deformation superposition principle, the relationship between the angle displacement and line displacement of moving platform and the forces acted on the branches were derived out. Based on the results of static analysis, the relationship between the applied force, the line displacement and the angle displacement of the mechanism was set up. And then the stiffness matrix was obtained. The six principal stiffness of the mechanism and the corresponding directions were achieved by the orthogonal transformation. The numerical calculation was performed and the results showed that the principal stiffness and directions are varied with the pose-position of the mechanism, and the principal stiffness is gradually enlarged when it is far away from the anigin. In addition, the torsion stiffness is much greater and the line deformation stiffness is smaller, the difference between the two parts is huge. The research content of this paper supplies the theoretical foundation for the further engineering design and application of the spherical parallel mechanism.

SYMBOLIC VERSOR COMPRESSION ALGORITHM

In an inner-product space, an invertible vector generates a reflection with respect to a hyperplane, and the Clifford product of several invertible vectors, called a versor in Clifford algebra, generates the composition of the corresponding reflections, which is an orthogonal transformation. Given a versor in a Clifford algebra, finding another sequence of invertible vectors of strictly shorter length but whose Clifford product still equals the input versor, is called versor compression. Geometrically, versor compression is equivalent to decomposing an orthogonal transformation into a shorter sequence of reflections. This paper proposes a simple algorithm of compressing versors of symbolic form in Clifford algebra. The algorithm is based on computing the intersections of lines with planes in the corresponding Grassmann-Cayley algebra, and is complete in the case of Euclidean or Minkowski inner-product space.

Implementation of the Contract

This is a fimdamental relationship ＂contract＂ in Hilbert geometric axiom system. But the axiom system does not define how contracts are implemented, requires only basic objects and relations contracts to meet the basic axioms I - V . But in Euclidean geometry is intuitive to put a ＂contract＂ understood as a ＂movement.＂ Now we are in the framework of Hilbert geometric axiom system, to ＂contract＂ and we have been accustomed to ＂movement＂ link, for simplicity, we have limited the discussion to the Euclidean plane geometry.

Mathematical treatment of wave propagation in acoustic waveguides with n curved interfaces

There are some curved interfaces in ocean acoustic waveguides. To compute wave propagation along the range with some marching methods, a flattening of the internal interfaces and a transforming equation are needed. In this paper a local orthogonal coordinate transform and an equation transformation are constructed to flatten interfaces and change the Helmholtz equation as a solvable form. For a waveguide with a flat top, a fiat bottom and n curved interfaces, the coefficients of the transformed Helmholtz equation are given in a closed formulation which can be thought of as an extension of the formal work related to the equation transformation with two curved internal interfaces. In the transformed horizontally stratified waveguide, the one-way reformulation based on the Dirichlet-to-Neumann （DtN） map is then used to reduce the boundary value problem to an initial value problem. Numerical implementation of the resulting operator Riccati equation uses a large range step method to discretize the range variable and a truncated local eigenfunction expansion to approximate the operators. This method is particularly useful for solving long range wave propagation problems in slowly varying waveguides. Furthermore, the method can also be applied to wave propagation problems in acoustic waveguides associated with varied density.

Compression and reconstruction of speech signals based on compressed sensing

Based on the approximate sparseness of speech in wavelet basis,a compressed sensing theory is applied to compress and reconstruct speech signals.Compared with one-dimensional orthogonal wavelet transform(OWT),two-dimensional OWT combined with Dmeyer and biorthogonal wavelet is firstly proposed to raise running efficiency in speech frame processing,furthermore,the threshold is set to improve the sparseness.Then an adaptive subgradient projection method(ASPM)is adopted for speech reconstruction in compressed sensing.Meanwhile,mechanism which adaptively adjusts inflation parameter in different iterations has been designed for fast convergence.Theoretical analysis and simulation results conclude that this algorithm has fast convergence,and lower reconstruction error,and also exhibits higher robustness in different noise intensities.

Energy-based adaptive orthogonal FRIT and its application in image denoising

Efficient representation of linear singularities is discussed in this paper. We analyzed the relationship between the ＂wrap around＂ effect and the distribution of FRAT （Finite Radon Transform） coefficients first, and then based on study of some properties of the columnwisely FRAT reconstruction procedure, we proposed an energy-based adaptive orthogonal FRIT scheme （EFRIT）. Experiments using nonlinear approximation show its superiority in energy concentration over both Discrete Wavelet Transform （DWT） and Finite Ridgelet Transform （FRIT）. Furthermore, we have modeled the denoising problem and proposed a novel threshold selecting method. Experiments carried out on images containing strong linear singularities and texture components with varying levels of addictive white Gaussian noise show that our method achieves prominent improvement in terms of both SNR and visual quality as compared with that of DWT and FRIT.

A numerical local orthogonal transform method forstratified waveguides

Flattening of the interfaces is necessary in computing wave propagation along strati?ed waveguides in large range step sizes while using marching methods. When the supposition that there exists one horizontal straight line in two adjacent interfaces does not hold, the previously suggested local orthogonal transform method with an analytical formulation is not feasible. This paper presents a numerical coordinate transform and an equation transform to perform the transforms numerically for waveguides without satisfying the supposition. The boundary value problem is then reduced to an initial value problem by one-way reformulation based on the Dirichlet-to-Neumann (DtN) map. This method is applicable in solving long-range wave propagation problems in slowly varying waveguides with a multilayered medium structure.

Finding Symmetry Groups of Some Quadratic Programming Problems

Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations.In particular,a knowledge of the symmetries may help decrease the problem dimension,reduce the size of the search space by means of linear cuts.While the previous studies of symmetries in the mathematical programming usually dealt with permutations of coordinates of the solutions space,the present paper considers a larger group of invertible linear transformations.We study a special case of the quadratic programming problem,where the objective function and constraints are given by quadratic forms.We formulate conditions,which allow us to transform the original problem to a new system of coordinates,such that the symmetries may be sought only among orthogonal transformations.In particular,these conditions are satisfied if the sum of all matrices of quadratic forms,involved in the constraints,is a positive definite matrix.We describe the structure and some useful properties of the group of symmetries of the problem.Besides that,the methods of detection of such symmetries are outlined for different special cases as well as for the general case.

Discrete Time Mean-variance Analysis with Singular Second Moment Matrixes and an Exogenous Liability

We apply the dynamic programming methods to compute the analytical solution of the dynamic mean-variance optimization problem affected by an exogenous liability in a multi-periods market model with singular second moment matrixes of the return vector of assets. We use orthogonai transformations to overcome the difficulty produced by those singular matrixes, and the analytical form of the efficient frontier is obtained. As an application, the explicit form of the optimal mean-variance hedging strategy is also obtained for our model.

The minimal genus problem in rational surfaces CP^2#nCP^2

There are three key ingredients in the study of the minimal genus problem for rational surfaces CP2#nCP2: the generalized adjunction formula, the action of the orthogonal group of the Lorentz space and the geometric construction. In this paper, we prove the uniqueness of the standard form (see Definition 1.1 and Theorem 1.1) of a 2-dimensional homology class under the action of the subgroup of the Lorentz orthogonal group that is realized by the diffeomorphisms of CP2#nCP2.Using the geometric construction, we determine the minimal genera of some classes (see Theorem 1.2).

Visualization of a Turbulent Jet Using Wavelets

An application of multiresolution image analysis to turbulence was investigated in this paper, in order to visualize the coherent structure and the most essential scales governing turbulence. The digital imaging photograph of jet slice was decomposed by two-dimensional discrete wavelet transform based on Daubechies, Coifman and Baylkin bases. The best choice of orthogonal wavelet basis for analyzing the image of the turbulent structures was first discussed. It is found that these orthonormal wavelet families with index N<10 were inappropriate for multiresolution image analysis of turbulent flow. The multiresolution images of turbulent structures were very similar when using the wavelet basis with the higher index number, even though wavelet bases are different functions. From the image components in orthogonal wavelet spaces with different scales, the further evident of the multi-scale structures in jet can be observed, and the edges of the vortices at different resolutions or scales and the coherent structure can be easily extracted.