A lot of optimum filters have been proposed for an image restoration problem. Parametric filter, such as Parametric Wiener Filter, Parametric Projection Filter, or Parametric Partial Projection Filter, is often used because it requires to calculate a generalized inverse of one operator. These optimum filters are formed by a degradation operator, a covariance operator of noise, and one of original images. In practice, these operators are estimated based on empirical knowledge. Unfortunately, it happens that such operators differ from the true ones. In this paper, we show the unified formulae of inducing them to clarify their common properties. Moreover, we investigate their properties for perturbation of a degradation operator, a covariance operator of noise, and one of original images. Some numerical examples follow to confirm that our description is valid.

The solution of the ordinary kernel ridge regression, based on the squared loss function and the squared norm-based regularizer, can be easily interpreted as a stochastic linear estimator by considering the autocorrelation prior for an unknown true function. As is well known, a stochastic affine estimator is one of the simplest extensions of the stochastic linear estimator. However, its corresponding kernel regression problem is not revealed so far. In this paper, we give a formulation of the kernel regression problem, whose solution is reduced to a stochastic affine estimator, and also give interpretations of the formulation.

In D.O.A. estimation, identification of the signal and the noise subspaces plays an essential role. This identification process was traditionally achieved by the eigenvalue decomposition (EVD) of the spatial correlation matrix of observations or the generalized eigenvalue decomposition (GEVD) of the spatial correlation matrix of observations with respect to that of an observation noise. The framework based on the GEVD is not always an extension of that based on the EVD, since the GEVD is not applicable to the noise-free case which can be resolved by the framework based on the EVD. Moreover, they are not applicable to the case in which the spatial correlation matrix of the noise is singular. Recently, a quotient-singular-value-decomposition-based framework, that can be applied to problems with singular noise correlation matrices, is introduced for noise reduction. However, this framework also can not treat the noise-free case. Thus, we do not have a unified framework of the identification of these subspaces. In this paper, we show that a unified framework of the identification of these subspaces is realized by the concept of proper and improper eigenspaces of the spatial correlation matrix of the noise with respect to that of observations.

This paper aims at improving effectiveness of previously proposed hybrid priority lists, {L*i=LdLsi}, that are applied in nonpreemptive 2-processor scheduling of general acyclic SWITCH-less program nets, where Ld and Lsi are dynamic and static priority lists respectively. Firstly, we investigate the effectiveness of Ld through experiments. According to the experimental results, we reconstruct Ld to propose its improved list L1d. Then analyzing the construction methodology of the static priority lists {Lsi}, we propose a substituted list L2d by taking into account of the factor: remaining firing numbers of nodes. Finally, we combine a part of L1d and L2d to propose a new priority list L**. Through scheduling simulation on 400 program nets, we find the new priority list L** can generate shorter schedules, close to ones of GA (Genetic Algorithm) scheduling that has been shown exceedingly effective but costing much computation time.

The solution of the standard 2-norm-based multiple kernel regression problem and the theoretical limit of the considered model space are discussed in this paper. We prove that 1) The solution of the 2-norm-based multiple kernel regressor constructed by a given training data set does not generally attain the theoretical limit of the considered model space in terms of the generalization errors, even if the training data set is noise-free, 2) The solution of the 2-norm-based multiple kernel regressor is identical to the solution of the single kernel regressor under a noise free setting, in which the adopted single kernel is the sum of the same kernels used in the multiple kernel regressor; and it is also true for a noisy setting with the 2-norm-based regularizer. The first result motivates us to develop a novel framework for the multiple kernel regression problems which yields a better solution close to the theoretical limit, and the second result implies that it is enough to use the single kernel regressors with the sum of given multiple kernels instead of the multiple kernel regressors as long as the 2-norm based criterion is used.

For the last few decades, learning with multiple kernels, represented by the ensemble kernel regressor and the multiple kernel regressor, has attracted much attention in the field of kernel-based machine learning. Although their efficacy was investigated numerically in many works, their theoretical ground is not investigated sufficiently, since we do not have a theoretical framework to evaluate them. In this paper, we introduce a unified framework for evaluating kernel regressors with multiple kernels. On the basis of the framework, we analyze the generalization errors of the ensemble kernel regressor and the multiple kernel regressor, and give a sufficient condition for the ensemble kernel regressor to outperform the multiple kernel regressor in terms of the generalization error in noise-free case. We also show that each kernel regressor can be better than the other without the sufficient condition by giving examples, which supports the importance of the sufficient condition.

A fast cross-validation algorithm for model selection in kernel ridge regression problems is proposed, which is aiming to further reduce the computational cost of the algorithm proposed by An et al. by eigenvalue decomposition of a Gram matrix.

A parametric linear filter for a linear observation model usually requires a parameter selection process so that the filter achieves a better filtering performance. Generally, criteria for the parameter selection need not only the filtered solution but also the filter itself with each candidate of the parameter. Obtaining the filter usually costs a large amount of calculations. Thus, an efficient algorithm for the parameter selection is required. In this paper, we propose a fast parameter selection algorithm for linear parametric filters that utilizes a joint diagonalization of two non-negative definite Hermitian matrices.

This paper presents a formal approach for generating train timetables in a mesoscopic level that is more concrete than the macroscopic level, where each station is simply expressed in a black-box, and more abstract than the microscopic level, where the infrastructure in each station-area is expressed in detail. The accuracy of generated timetable and the computational effort for the generation is a trade-off. In this paper, we design a formal mesoscopic modeling language by analyzing real railways, for example Tazawako-line as the first step of this work. Then, we define the constraint formulae for generating train timetables with the help of SMT (Satisfiability Module Theories)-Solver, and explain our tool RW-Solver that is an implementation of the constraint formulae. Finally, we demonstrate how RW-Solver with the help of SMT-Solver can be used for generating timetables in a case study of Tazawako-line.

Binary sparse representation based on arbitrary quality metrics and its applications are presented in this paper. The novelties of the proposed method are twofold. First, the proposed method newly derives sparse representation for which representation coefficients are binary values, and this enables selection of arbitrary image quality metrics. This new sparse representation can generate quality metric-independent subspaces with simplification of the calculation procedures. Second, visual saliency is used in the proposed method for pooling the quality values obtained for all of the parts within target images. This approach enables visually pleasant approximation of the target images more successfully. By introducing the above two novel approaches, successful image approximation considering human perception becomes feasible. Since the proposed method can provide lower-dimensional subspaces that are obtained by better image quality metrics, realization of several image reconstruction tasks can be expected. Experimental results showed high performance of the proposed method in terms of two image reconstruction tasks, image inpainting and super-resolution.

Practical image restoration filters usually include a parameter that controls regularizability, trade-off between fidelity of a restored image and smoothness of it, and so on. Many criteria for choosing such a parameter have been proposed. However, the relation between these criteria and the squared error of a restored image, which is usually used to evaluate the restoration performance, has not been theoretically substantiated. Sugiyama and Ogawa proposed the subspace information criterion (SIC) for model selection of supervised learning problems and showed that the SIC is an unbiased estimator of the expected squared error between the unknown model function and an estimated one. They also applied it to restoration of images. However, we need an unbiased estimator of the unknown original image to construct the criterion, so it can not be used for general situations. In this paper, we present a modified version of the SIC as a new criterion for choosing a parameter of image restoration filters. Some numerical examples are also shown to verify the efficacy of the proposed criterion.

In this paper, we propose a novel multi-frame image denoising technique, which achieves the minimum variance of noise. Zero-mean and unknown variance white noise with an arbitrary distribution is considered in this paper. The proposed method consists of two parts. The first one is the estimation of the variance of noise for each image by considering the differences of all pairs of images. The second one is an actual denoising process in which the convex combination of all images with weight coefficients determined by the estimated variances is constructed. We also give an efficient algorithm by which we can obtain the same result by successive convex combinations. The efficacy of the proposed method is confirmed by computer simulations.

A useful optimization problem to help solve various base station layout problems in multihop wireless networks is formulated. By solving the proposed generalized formula, the relation between the permissible largest number of hops and the minimum base station density necessary to cover an entire service area while guaranteeing a specified QoS is easily calculated. Our formula is extendable to other allocation problems by replacing parameters. The energy-cost transformation and scope of the multihop effect are also presented.

A Wiener-based inpainting quality prediction method is presented in this paper. The proposed method is the first method that can predict inpainting quality both before and after the intensities have become missing even if their inpainting methods are unknown. Thus, when the target image does not include any missing areas, the proposed method estimates the importance of intensities for all pixels, and then we can know which areas should not be removed. Interestingly, since this measure can be also derived in the same manner for its corrupted image already including missing areas, the expected difficulty in reconstruction of these missing pixels is predicted, i.e., we can know which missing areas can be successfully reconstructed. The proposed method focuses on expected errors derived from the Wiener filter, which enables least-squares reconstruction, to predict the inpainting quality. The greatest advantage of the proposed method is that the same inpainting quality prediction scheme can be used in the above two different situations, and their results have common trends. Experimental results show that the inpainting quality predicted by the proposed method can be successfully used as a universal quality measure.

A QoS support technique for easily minimizing delay in multihop wireless networks is proposed. Using a priority queue operation that reduces delays overall, the proposed technique, Reduced Congestion Queuing (RCQ), solves problems peculiar to multihops. By adding RCQ to a multihop system, base station or access point density and cost can be more effectively curtailed than by simply applying multihops to a cellular network or wireless LAN because RCQ expands the multihop service area. Due to its simplicity, the proposed technique can be used in a wide range of applications, including VoIP.

This letter proposes a compact multi-layered bandpass filter exhibiting left-handed and right-handed behaviors in its passband. This filter has a greatly expanded passband from 1.61 GHz to 4.16 GHz (88.4% bandwidth) with a maximum ripple of 1.2 dB and well-suppressed out-of-passbands with transmission zeros at 1.15 GHz and 4.52 GHz. The physical mechanisms are studied with FEM-based full-wave simulations, equivalent circuit analysis and careful experiments.

Optimum filters for an image restoration are formed by a degradation operator, a covariance operator of original images, and one of noise. However, in a practical image restoration problem, the degradation operator and the covariance operators are estimated on the basis of empirical knowledge. Thus, it appears that they differ from the true ones. When we restore a degraded image by an optimum filter belonging to the family of Projection Filters and Parametric Projection Filters, it is shown that small deviations in the degradation operator and the covariance matrix can cause a large deviation in a restored image. In this paper, we propose new optimum filters based on the regularization method called the family of Regularized Projection Filters, and show that they are stable to deviations in operators. Moreover, some numerical examples follow to confirm that our description is valid.

In terms of the formulation of the optimality, image restoration filters can be divided into two streams. One is formulated as an optimization problem in which the fidelity of a restored image is indirectly evaluated, and the other is formulated as an optimization problem based on a direct evaluation. Originally, the formulation of the optimality and the solutions derived from the formulation are identical each other. However in many studies adopting the former stream, an arbitrary choice of a solution without a mathematical ground passes unremarked. In this paper, we discuss the relation between the formulation of the optimality and the solution derived from the formulation from a mathematical point of view, and investigate the relation between a direct style formulation and an indirect one. Through these analyses, we show that the both formulations yield the identical filter in practical situations.

In signal restoration problems, we expect to improve the restoration performance with a priori information about unknown target signals. In this paper, the parametric Wiener filter with linear constraints for unknown target signals is discussed. Since the parametric Wiener filter is usually defined as the minimizer of the criterion not for the unknown target signal but for the filter, it is difficult to impose constraints for the unknown target signal in the criterion. To overcome this difficulty, we introduce a criterion for the parametric Wiener filter defined for the unknown target signal whose minimizer is equivalent to the solution obtained by the original formulation. On the basis of the newly obtained criterion, we derive a closed-form solution for the parametric Wiener filter with linear constraints.