Singular Weighting Research Articles

Quaternion Chromaticity Contrast Preserving Decolorization Method Based on Adaptive Singular Value Weighting

Color image decolorization can not only simplify the complexity of image processing and analysis, improving computational efficiency, but also help to preserve the key information of the image, enhance visual effects, and meet various practical application requirements. However, with existing decolorization methods it is difficult to simultaneously maintain the local detail features and global smooth features of the image. To address this shortcoming, this paper utilizes singular value decomposition to obtain the hierarchical local features of the image and utilizes quaternion theory to overcome the limitation of existing color image processing methods that ignore the correlation between the three channels of the color image. Based on this, we propose a singular value adaptive weighted fusion quaternion chromaticity contrast preserving decolorization method. This method utilizes the low-rank matrix approximation principle to design a singular value adaptive weighted fusion strategy for the three channels of the color image and implements image decolorization based on singular value adaptive weighting. To address the deficiency of the decolorization result obtained in this step, which cannot maintain global smoothness characteristics well, a contrast preserving decolorization algorithm based on quaternion chromaticity distance is further proposed, and the global weighting strategy obtained by this algorithm is integrated into the image decolorization based on singular value adaptive weighting. The experimental results show that the decolorization method proposed in this paper achieves excellent results in both subjective visual perception and objective evaluation metrics.

Accurate least-squares PN scaling based on problem optical thickness for solving neutron transport problems

In this paper, we present an accurate and robust scaling operator based on material optical thickness (OT) for the least-squares spherical harmonics (LSPN) method for solving neutron transport problems. LSPN without proper scaling is known to be erroneous in highly scattering medium, if the optical thickness of the material is large. A previously presented scaling developed by Manteuffel et al. does improve the accuracy of LSPN in problems where the material is optically thick. With that method, however, essentially no scaling is applied in optically thin materials, which can lead to an erroneous solutions in the presence of a highly scattering medium. Another scaling approach, called the reciprocal-removal (RR) scaled LSPN, which is equivalent to the self-adjoint angular flux (SAAF) equation, has numerical issues in highly-scattering materials due to a singular weighting. We propose a scaling based on optical thickness that improves the solution in optically thick media while avoiding the singularity in the SAAF formulation.

大規模データの俯瞰とターゲットデータの抽出に対する文書‐単語行列の特異値分解と特異値による重みづけの有効性

大規模データの俯瞰とターゲットデータの抽出に対する文書‐単語行列の特異値分解と特異値による重みづけの有効性

On solving periodic Riccati equations

AbstractNumerically reliable algorithms to compute the periodic non‐negative definite stabilizing solutions of the periodic differential Riccati equation (PRDE) and discrete‐time periodic Riccati equation (DPRE) are proposed. For the numerical solution of PRDEs, a new multiple shooting‐type algorithm is developed to compute the periodic solutions in an arbitrary number of time moments within one period by employing suitable discretizations of the continuous‐time problems. In contrast to single shooting periodic generator methods, the multiple shooting‐type methods have the main advantage of being able to address problems with larger periods. Three methods are discussed to solve DPREs. Two of the methods represent extensions of the periodic QZ algorithm to non‐square periodic pairs, whereas the third method represents an extension of a quotient‐product swapping and collapsing ‘fast’ algorithm. All proposed approaches are completely general, being applicable to periodic Riccati equations with time‐varying dimensions as well as with singular weighting matrices. Copyright © 2008 John Wiley & Sons, Ltd.

New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares

In this paper two new concepts for the classical moving least squares (MLS) approach are presented. The first one is an interpolating weighting function, which leads to MLS shape functions fulfilling the interpolation condition exactly. This enables a direct application of essential boundary conditions in the element-free Galerkin method without additional numerical effort. In contrast to existing approaches using singular weighting functions, this new weighting type leads to regular values of the weights and coefficients matrices in the whole domain even at the support points. The second enhancement is an approach, where the computation of the polynomial coefficient matrices is performed only at the nodes. At the interpolation point then a simple operation leads to the final shape function values. The basis polynomial of each node can be chosen independently which enables the simple realization of a p-adaptive scheme.

SwLORETA: a novel approach to robust source localization and synchronization tomography

Standardized low-resolution brain electromagnetic tomography (sLORETA) is a widely used technique for source localization. However, this technique still has some limitations, especially under realistic noisy conditions and in the case of deep sources. To overcome these problems, we present here swLORETA, an improved version of sLORETA, obtained by incorporating a singular value decomposition-based lead field weighting. We show that the precision of the source localization can further be improved by a tomographic phase synchronization analysis based on swLORETA. The phase synchronization analysis turns out to be superior to a standard linear coherence analysis, since the latter cannot distinguish between real phase locking and signal mixing.

ON SOLVING DISCRETE-TIME PERIODIC RICCATI EQUATIONS

Two numerically reliable algorithms to compute the periodic nonnegative definite stabilizing solution of discrete-time periodic Riccati equations are proposed. The first method represents an extension of the periodic QZ algorithm to non-square periodic pairs, while the second method represents an extension of a quotient-product swapping and collapsing “fast” algorithm. Both approaches are completely general being applicable to periodic Riccati equations with time varying dimensions as well as with singular control weighting. For the “fast” method, reliable software implementation is available in a recently developed PERIODIC SYSTEMS Toolbox.

Point‐source τ‐p transform: A review and comparison of computational methods

The τ‐p transformation of reflection seismic data excited by a point source requires a cylindrical slant stack, which includes compensation for the phase shift and geometrical spreading associated with cylindrical geometry. Using a simple test model, we review and compare the different computational methods used for the cylindrical slant stack. The two major method types are the Bessel‐Fourier transform (BFT) method and a set of methods (TD2D, TDX, TDTC and TDTS) based on time‐domain convolution. The stack integral in each of these approaches can be separated into two parts, with the part corresponding to the contribution of incoming waves being negligible for large ray parameter p. Neglecting the latter term for large p generally avoid a major problem caused by aliasing between time and space domains. The TDTS method introduced here has the advantage of being expressed in terms of a conventional 2-D slant stack (weighted by offset x) plus a correction term. This formulation facilitates a quantitative comparison of the 3-D cylindrical slant stack with a 2-D slant stack. The TDTS method compares favorably with the TD2D method, in which the cylindrical slant stack is expressed as a weighted integral of the 2-D slant stacks. TDTS avoids the singular weighting function needed in the integral for the TD2D method, and therefore has less problems with numerical noise. For all of the methods considered, the accuracy of the map transformation is limited by the spatial and temporal resolution of the test data set. Some corrections to previously published methods are also provided.

A riccati equation approach to the singular LQG problem

The problem of optimal fixed-order dynamic compensation for the singular LQG problem is considered. Necessary conditions characterizing the optimal compensator for the case involving both singular measurement noise and singular control weighting are given. The solution consists of a set of two algebraic Riccati equations and two Lyapunov equations coupled by three projection matrices. One projection is the standard order reduction projection while the other two projections reflect the two types of singularity that exist in the system. The three projections are shown to satisfy disjointness conditions. In addition to order reduction, an advantage of the fixed-structure approach is that differentiation, which is often undersirable from a practical point of view and which may exist in the unconstrained optimal control, can be avoided. It is shown that the fixed-order compensator agrees with the unconstrained solution when the latter possesses the same number of differentiations as are included in the prespecified controller structure and when the order is selected appropriately.

The singular zero-sum differential game with stability usingH ∞ control theory

In this paper we consider the zero-sum, infinite-horizon, linear quadratic differential game. We derive sufficient conditions for the existence of (almost) equilibria as well as necessary conditions. Contrary to all classical references we allow for singular weighting on the minimizing player in the cost criterion. It turns out that this problem has a strong relation with the singularH∞ problem with state feedback, i.e., theH∞ problem where the direct feedthrough matrix from control input to output is not necessarily injective.

The optimal projection equations for static and dynamic output feedback: The singular case

Oblique projections have been shown to arise naturally in both static and dynamic optimal design problems. For static controllers an oblique projection was inherent in the early work of Levine and Athans, while for dynamic controllers an oblique projection was developed by Hyland and Bernstein. This note is motivated by the following natural question: What is the relationship between the oblique projection arising in optimal static output feedback and the oblique projection arising in optimal fixed-order dynamic compensation? We show that in nonstrictly proper optimal output feedback there are, indeed, three distinct oblique projections corresponding to singular measurement noise, singular control weighting, and reduced compensator order. Moreover, we unify the Levine-Athans and Hyland-Bernstein approaches by rederiving the optimal projection equations for combined static/dynamic (nonstrictly proper) output feedback in a form which clearly illustrates the role of the three projections in characterizing the optimal feedback gains. Even when the dynamic component of the nonstrictly proper controller is of full order, the controller is characterized by four matrix equations which generalize the standard LQG result.

A general transfer-function approach to the steady-state linear quadratic Gaussian stochastic control problem

A comprehensive treatment of the steady-state linear quadratic Gaussian stochastic control problem which is based on the transfer-function point of view is presented. The optimal solution is found, for the general multivariable case, by exploiting the properties of the newly defined generalized spectral factors. The exact equivalence between the results found by the time domain and the transfer-function approaches is established, even for the case of unstable systems. The proposed method of solution can easily cope with cases of stationary coloured signals, dynamical operators in the performance index and singular noise autocorrelation and control weighting matrices ; its computational superiority over existing time-domain techniques is demonstrated.

Optimal linear regulators: The discrete-time case

In this paper the optimal discrete-time linear-quadratic regulator problem is carefully presented and the basic results are reviewed. Dynamic programming is used to determine the optimization equations. Special attention is given to problems unique to the discrete-time case; this includes, for example, the possibility of a singular system matrix and a singular control-effort weighting matrix. Some problems associated with sampled-data systems are also summarized, e.g., sensitivity to sampling time, and loss of controllability due to sampling. Computational methods for the solution of the optimization equations are outlined and a simple example is included to illustrate the various computational approaches.