Variable Additive Preconditioning Procedures

Marchenko multiple elimination (MME) is a data-driven scheme capable of attenuating internal multiples of all orders, provided that the seismic data amplitudes are correctly normalized using an optimal global scale factor (SF). MME tends to be inefficient when the optimal SF is unknown, highlighting its dependence on a SF. This work combines the MME scheme with an adaptive filter based on a U-Net neural network to reduce this dependence. The results prove that the proposed approach effectively removes internal multiples even when the optimal SF is unavailable.

The atomic and bond dipole moment derivative properties associated with the total infrared absorption intensity of the methylidyne, methylene, and methyl free radicals, and of methane, have been calculated by means of the ab initio STO-3G algorithm. These properties include the coordinate-dependent atomic polar tensors and the following invariant quantities: the dipole derivatives for a bond stretch, mean atomic dipole moment derivatives, atomic anisotropies, and the effective atomic charges. Three sets of calculations were conducted for each species by combining the experimental or theoretically determined equilibrium molecular geometry with the standard or optimum orbital exponent scaling factors. The relationship between each of these dipole derivative properties and, in turn, the equilibrium geometry, the carbon and hydrogen scaling factors, and the number of bonded hydrogen atoms is analyzed. According to any calculation, it is found that the calculated dipole derivative value for a C–H stretch in methane is negative, which agrees with the experimentally deduced results, but is positive for all the radicals, except the doublet state of CH. Furthermore, it is shown that the optimum scaling factors must be used in the calculations in order to consistently obtain good agreement between theory and experiment. Based on both the theoretical equilibrium geometry and the optimum scaling factors of a species, the following trends are exhibited by this homologous series of hydrocarbons: (1) The dipole derivative magnitude for a C–H bond stretch is a monotonic increasing function of the product of the carbon and hydrogen scaling factors. (2) The effective charge of carbon increases as the optimum size of the carbon valence shell increases, and decreases as additional hydrogens are bonded to the carbon. (3) The hydrogen effective charge generally decreases as the number of hydrogens increases. (4) The mean dipole derivative of hydrogen is a monotonic decreasing function of the number of C–H bonds, and is negative only for methane. (5) Calculations on the doublet and quartet electronic states of CH yield different values for the dipole moment, the effective charge, and the anisotropy, the dipole derivatives for a bond stretch have opposite directions.

Atmospheric tomography, i.e., the reconstruction of the turbulence profile in the atmosphere, is a challenging task for adaptive optics (AO) systems for the next generation of extremely large telescopes. Within the AO community, the solver of first choice is the so-called Matrix Vector Multiplication (MVM) method, which directly applies the (regularized) generalized inverse of the system operator to the data. For small telescopes this approach is feasible, however, for larger systems such as the European Extremely Large Telescope (ELT), the atmospheric tomography problem is considerably more complex, and the computational efficiency becomes an issue. Iterative methods such as the Finite Element Wavelet Hybrid Algorithm (FEWHA) are a promising alternative. FEWHA is a wavelet-based reconstructor that uses the well-known iterative preconditioned conjugate gradient (PCG) method as a solver. The number of floating point operations and the memory usage are decreased significantly by using a matrix-free representation of the forward operator. A crucial indicator for the real-time performance are the number of PCG iterations. In this paper, we propose an augmented version of FEWHA, where the number of iterations is decreased by 50% using an augmented Krylov subspace method. We demonstrate that a parallel implementation of augmented FEWHA allows the fulfilment of the real-time requirements of the ELT.

A novel sine transform based preconditioned conjugate gradient (PCG) method for signal restoration is presented. If the bandwidth 2? +1 in the model matrix is a constant, then the asymptotic complexity for the new algorithm is O(N) per iterative step, where Nis the order of the model. This complexity is reduced by an order of magnitude in comparison with the known fast Fourier transform (FFT) technique proposed recently in the literature. Moreover, if ? has a size similar to N, then the new PCG method is accomplished by the fast sine transform (FST) and the fast Hartley transform (FHT). The computational and storage cost per preconditioning step for the new PCG method is reduced by 50% as compared to the FFT approach. To stabilize the computation, a special Tikhonov regularization is introduced. Numerical experimentations show that the new PCG method is of a speedy convergence rate. The new PCG methods maintain less computational complexity per iterative step and have a better convergence rate than the other known PCG methods.

This study presents an efficacy comparison of iterative solution methods for solving the compressible-fluid Reynolds equation in modeling air- or gas-lubricated bearings. A direct fixed-point iterative (DFI) method and Newton’s method are employed to transform the Reynolds equation in a form that can be solved iteratively. The iterative solution methods examined are the Gauss–Seidel method, the successive over-relaxation (SOR) method, the preconditioned conjugate gradient (PCG) method, and the multigrid method. The overall solution time is affected by both the transformation method and the iterative method applied. In this study, Newton’s method shows its effectiveness over the straightforward DFI method when the same iterative method is used. It is demonstrated that the use of an optimal relaxation factor is of vital importance for the efficiency of the SOR method. The multigrid method is an order faster than the PCG and optimal SOR methods. Also, the multigrid and PCG methods involve an extended coding work and are less flexible in dealing with gridwork and boundary conditions. Consequently, a compromise has to be made in terms of ease of use as well as programming effort for the solution of the compressible-fluid Reynolds equation.

In conventional adaptive variable step size (VSS) maximum power point tracking (MPPT) algorithms, a scaling factor is utilized to determine the required perturbation step. However, the performance of the adaptive VSS MPPT algorithm is essentially decided by the choice of scaling factor. In this paper, a neural network assisted variable step size (VSS) incremental conductance (IncCond) MPPT method is proposed. The proposed method utilizes a neural network to obtain an optimal scaling factor that should be used in current irradiance level for the VSS IncCond MPPT method. Only two operating points on the characteristic curve are needed to acquire the optimal scaling factor. Hence, expensive irradiance and temperature sensors are not required. By adopting a proper scaling factor, the performance of the conventional VSS IncCond method can be improved, especially under rapid varying irradiance conditions. To validate the studied algorithm, a 400 W prototyping circuit is built and experiments are carried out accordingly. Comparing with perturb and observe (P&O), α-P&O, golden section and conventional VSS IncCond MPPT methods, the proposed method can improve the tracking loss by 95.58%, 42.51%, 93.66%, and 66.14% under EN50530 testing condition, respectively.

ADAPTIVE MODELING FOR BIT RATE CONTROL

Today, single image haze removal has attracted much attention in the community of image restoration. A popular type of approach is based on dark channel prior (DCP) because of its simplicity and effectiveness. One of the problems in the original DCP scheme is the fixed scaling factors for atmospheric light and transmittance. This paper attempts to replace them with optimal scaling factors obtained by the whale optimization algorithm (WOA). However, the WOA requires a reference to find the optimal scaling factors. To avoid using full reference in the optimization process, we adopt a half-reference that requires no ground-truth image. The proposed approach is justified by several examples and compared with the DCP scheme and a modified DCP scheme. The proposed approach shows its superiority over the comparison schemes in most of the examples, but has an overexposure or less dehazed problems in the rest of the examples. More research should be conducted on the proposed approach for better performance.

In order to improve the low spatial resolution of remote sensed LST, two methods based on multiple scale factors are proposed. Considering the optimal scale factor is usually not unique under environment of different land cover types, a stratified linear regression model is built, which shows a higher accuracy than global linear regression with one scale factor. In view of the relationship between scale factor and LST showing fluctuant under different conditions, such as season, size of scale and land cover type, where the errors of linear regression model often come from, a method of downscaling based on BP neural network is proposed. Multiple scale factors as input, this method shows as almost precise as the first method globally, especially for mountainous areas and mixed areas, which shows a stronger robustness.

We study nonlinear inverse problems of the form F ( x ) = y , and their stable solution via iterative regularization methods, in particular by Newton-type methods, which are well-known for their fast convergence for well-posed problems. A basic step of Newton’s method consists of calculating the update Δ x k via solution of a linearized equation , which will in general be ill-posed if the nonlinear problem is. Thus, for ill-posed problems, the linearized equations have to be solved by some regularization method. In particular for large scale problems, e.g., inverse problems in partial differential equations, where F ( x ) is only defined implicitly via the solution of a PDE, iterative methods have to be used for this purpose. In order to keep the overall effort, i.e., the overall number of iterations, as small as possible, appropriate preconditioning has to be applied. We propose and analyse a general preconditioning strategy in Hilbert scales, and show that the overall number of iterations can be reduced to about the square root by preconditioning. Moreover, in many examples differential operators can be used as preconditioners, and thus preconditioning is almost for free. The theoretical results are illustrated in numerical examples. A comparison with preconditioned Landweber iteration shows that the iteration numbers can be further reduced, if fast iterative methods, e.g., the v -methods, are used for the solution of the linearized problems.

In this paper, first, we use the Rich type iterative method for numerical solution of nonlinear fuzzy Fredholm integral equation. The main structure of this method is based on the Richardson iterative method and trapezoidal quadrature formula for Numerical solution of nonlinear fuzzy integral equations. Convergence, error analysis and numerical stability of the proposed method are also discussed.

This paper establishes, in the case of CMOS buffer chains, that along with an optimum scaling factor there exists an equivalent optimum P-to-N transistor ratio which minimises latency. An optimum triple-point of buffer number, P-to-N ratio and scaling factor is identified which provides a process-specific absolute minimum latency. It is further determined that for any number of buffers, the corresponding optimum P-to-N transistor ratio and optimum buffer scaling factor can be calculated simultaneously, through numerical approximation of the points of intersection of two transcendental equations.

Parallel diagonally implicit Runge-Kutta-Nyström methods

Data from expression arrays must be comparable before it can be analyzed rigorously on a large scale. Accurate normalization improves the comparability of expression data because it seeks to account for sources of variation obscuring the underlying variation of interest. Undesirable variation in reported expression levels originates in the preparation and hybridization of the sample as well as in the manufacture of the array itself, and may differ depending on the array technology being employed. Published research to date has not characterized the degree of variation associated with these sources, and results are often reported without tight statistical bounds on their significance. We analyze the distributions of reported levels of exogenous control species spiked into samples applied to 1280 Affymetrix arrays. We develop a model for explaining reported expression levels under an assumption of primarily multiplicative variation. To compute the scaling factors needed for normalization, we derive maximum likelihood and maximum a posteriori estimates for the parameters characterizing the multiplicative variation in reported spiked control expression levels. We conclude that the optimal scaling factors in this context are weighted geometric means and determine the appropriate weights. The optimal scaling factor estimates so computed can be used for subsequent array normalization.

The need for securing multimedia content from being intercepted is a prominent research issue. This work proposes an optimised video steganography model that improves imperceptibility and robustness by extracting keyframes and calculating the optimal scaling factor. The squirrel search algorithm (SSA) is used to extract keyframes since it ensures distinct position updation processes through Levy flying and predator features, whilst the grasshopper optimisation and ant lion optimisation algorithms are hybridised to compute the optimal value of the scaling factor. In terms of imperceptibility and robustness, the simulation results suggest that the proposed approach outperforms existing data-hiding models. It also discovers the optimal scaling factor in under ten iterations, indicating that the fastest convergence rate is possible.