The Tikhonov regularization theory converts ill-posed inverse problems into well-posed problems by putting penalty on the solution sought. Instead of solving an inverse problem, the regularization theory minimizes a weighted sum of "data error" and "penalty" function, and it has been successfully applied to a variety of problems including tomography, inverse scattering, detection of radiation sources and early vision algorithms. Since the function to be minimized is a weighted sum of functions, one should estimate appropriate weights. This is a problem of hyperparameter estimation and a vast literature exists. Another problem is how one should compare a particular penalty function (regularizer) with another. This is a special class of model comparison problems which are generally difficult. A Hierarchical Bayesian scheme is proposed with multiple hyperparameters in order to cope with data containing subsets which consist of different degree of smoothness. The scheme outperforms the previous scheme with single hyperparameter.

Carrier mobilities in poly(3-alkylthiphene) cast films have been studied by means of fabricating a field effect transistor (FET) at the field range of (0.4-1.6)104 V/cm. It is found that the regioregurality is markedly effective to the mobilities than the side chain length. The FET mobilility of the regioregular poly(3-hexylthiophene), PHT is approximately 310-3 cm2/Vs which is larger than that of regiorandom PHT by 3 orders of magnitude. The mobility of regioregular poly(3-dodecylthiophene), PDDT is 810-4 cm2/Vs and is also 3 orders of magnitude larger than that of regiorandom PDDT. The mobilities of regioregular ones decrease, however, those of regiorandom ones increase at higher fields. The FET mobilities are nearly same to the mobilities estimated by the time of flight method. These results have been discussed taking the regularity of the main chain and the length of side chain into consideration.

Triangulations have been one of main research topics in computational geometry and have many applications in computer graphics, finite element methods, mesh generation, etc. This paper surveys properties of triangulations in the two- or higher-dimensional spaces. For triangulations of the planar point set, we have a good triangulation, called the Delaunay triangulation, which satisfies several optimality criteria. Based on Delaunay triangulations, many properties of planar triangulations can be shown, and a graph structure can be constructed for all planar triangulations. On the other hand, triangulations in higher dimensions are much more complicated than in planar cases. However, there does exist a subclass of triangulations, called regular triangulations, with nice structure, which is also touched upon.

An accurate and efficient numerical solution is presented for a two-dimensional electromagnetic wave scattering from a multilayered resistive strip grating embedded in a dielectric slab. Both E- and H-waves are treated. The problem is formulated into a set of integral equations, which is solved by the moment method accompanied by a regularization procedure. The resultant set of linear algebraic equations has the form of the Fredholm second kind, and therefore yields stable and accurate numerical solutions. The power distribution is computed for several grating parameters. Attention is paid to seek a set of parameters that maximizes absorption in the strips. The low frequency approximate formulas are also derived. This analysis would be useful in designing electromagnetic wave absorbers.

We present a symbolic language emptiness check algorithm based on forward state traversal. A verification property is given by a set of error traces written in ω-regular expression and is manipulated explicitly as a non-deterministic state transition graph. State space of the design model is implicitly traversed along the explicit graph. This method has a large amount of flexibility for controlling state traversal on the property space. It should become a good framework of incremental or approximate verification of ω-regular properties.

In this paper, we focus on regularity and set-valued functions. Regularity was first introduced by S. C. Kleene in the propositional operations of his ternary logic. Then, M. Mukaidono investigated some properties of ternary functions, which can be represented by regular operations. He called such ternary functions "regular ternary logic functions". Regular ternary logic functions are useful for representing and analyzing ambiguities such as transient states or initial states in binary logic circuits that Boolean functions cannot cope with. Furthermore, they are also applied to studies of fail-safe systems for binary logic circuits. In this paper, we will discuss an extension of regular ternary logic functions into r-valued set-valued functions, which are defined as mappings on a set of nonempty subsets of the r-valued set {0, 1, . . . , r-1}. First, the paper will show a method by which operations on the r-valued set {0, 1, . . . , r-1} can be expanded into operations on the set of nonempty subsets of {0, 1, . . . , r-1}. These operations will be called regular since this method is identical with the way that Kleene expanded operations of binary logic into his ternary logic. Finally, explicit expressions of set-valued functions monotonic in subset will be presented.

This paper considers the problem of generating various calligraphy from some sample fonts. Our method is based on the deformable contour model g-snake. By representing the outline of each stroke of a character with a g-snake, we cast the generation problem into global and local deformation of g-snake under different control parameters, where the local deformation obeys the energy minimization principle of regularization technique. The base values of the control parameters are learned from given sample fonts. The experimental results on alphabet and Japanese characters Hiragana show such processing as a reasonable method for generating calligraphy.

Regular ternary logic functions are one of the most useful special classes of Kleenean functions, and a lot of research has been done on them. However, there has been little work done on incompletely specified regular ternary logic functions. This paper describes the following points: (1) Minimization of incompletely specified regular ternary logic functions. (2) A new definition of incompletely specified fuzzy switching functions and their minimization. (Concretely speaking, minimal disjunctive forms of incompletely specified fuzzy switching functions are represented in formulas of regular ternary logic functions. ) (3) Their application to fuzzy logic circuits such as fuzzy PLAs of AND-OR type.

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 this paper, the authors present general views of computer vision and image processing based on optimization. Relaxation and regularization in both broad and narrow senses are used in various fields and problems of computer vision and image processing, and they are currently being combined with general-purpose optimization algorithms. The principle and case examples of relaxation and regularization are discussed; the application of optimization to shape description that is a particularly important problem in the field is described; and the use of a genetic algorithm (GA) as a method of optimization is introduced.

The paper obtains an algorithm to estimate the irregular sampling in wavelet subspaces. Compared to our former work on the problem, the new estimate is relaxed for some wavelet subspaces.

We introduce a concept of regularization into Genetic Algorithms (GAs). Conventional GAs include no explicit regularizing operations. However, the regularization is very effective in solving ill-posed problems. So, we propose a method of regularization to apply GAs to ill-posed problems. This regularization is a kind of consensus operation among neighboring individuals in GAs, and plays the role of `smoothing the solution. ' Our method is based on the evaluation of macroscopic fitness, which is a new fitness criterion. Conventional fitness of an individual in GAs is defined only from the phenotype of the individual, whereas the macroscopic fitness of an individual is evaluated from the phenotypes of the individual and its neighbors. We tested our regularizing operation by means of experiments with an elastic image mapping problem, and showed the effectiveness of the regularization.

This paper describes a new Vector Sum Excited Linear Prediction (VSELP) coder with very low complexity. The method, called regular pulse VSELP (RP-VSELP), is based on regular pulse basis vectors with mutually orthonormal property. In this Approach, a very efficient vector-sum codebook is constructed from a set of mutually orthonormal regular pulse bassis vectors and enables us to simplify the codebook search without additional degradation of synthesized speech compared with that of the conventional VSELP. The regular pulse basis vectors are explicitly orthonormalized by means of the Gram-Schmidt procedure. To enhance the speech quality of the RP-VSELP speech coder, perceptually weighted distortion measure between the input and the synthesized speech is utilized in an iterative closedloop training process of the regular pulse basis vectors. It is shown that speech quality is improved by the training process. Experimental results demonstrate that the proposed method produces the synthesized speech quality comparable to that of the VSELP scheme at the bit-rate of 4.8 Kbps.

We present a very fast method for calculating an inverse filter for audio reproduction system. The proposed method of FFT-based inverse filter design, which combines the well-known principles of least squares optimization and regularization, can be used for inverting systems comprising any number of inputs and outputs. The method was developed for the purpose of designing digital filters for multi-channel sound reproduction. It is typically several hundred times faster than a conventional steepest descent algorithm implemented in the time domain. A matrix of causal inverse FIR (finite impulse response) filters is calculated by optimizing the performance of the filters at a large number of discrete frequencies. Consequently, this deconvolution method is useful only when it is feasible in practice to use relatively long inverse filters. The circular convolution effect in the time domain is controlled by zeroth-order regularization of the inversion problem. It is necessary to set the regularization parameter β to an appropriate value, but the exact value of β is usually not critical. For single-channel systems, a reliable numerical method for determining β without the need for subjective assessment is given. The deconvolution method is based on the analysis of a matrix of exact least squares inverse filters. The positions of the poles of those filters are shown to be particularly important.

A deterministic pushdown automaton (dpda) having just one stack symbol is called a deterministic restricted one-counter automaton (droca). A deterministic one-counter automaton (doca) is a dpda having only one stack symbol, with the exception of a bottom-of-stack market. The class of languages accepted by droca's is a proper subclass of the class of languages accepted by doca's. Valiant has shown that the regularity problem for doca's is decidable in a single exponential worst-case time complexity. In this paper, we prove that the class of languages accepted by droca's which accept by final state is incomparable with the class of languages accepted by droca's which accept by empty stack (strict droca's), and that the intersection of them is equal to the class of strict regular languages. In addition, we present a new direct branching algorithm for checking the regularity for not only a strict droca but also a real-time droca which accepts by final state. Then we show that the worst-case time complexity of our algorithm is polynomial in the size of each droca.

In this communication we propose to solve the problem of reconstruction from limited data using a statistical regularization method based on a Bayesian information criterion. The minimization of the Bayesian information criterion, which is used here as an objective index to measure the goodness of an estimate, gives the optimum value of the smoothing parameter. By doing so, we could reduce the inversion problem to a simple minimization of a one-variable nonlinear function. The application of such a technique overcomes the nonuniqueness of the solution of the ill-posed problem and all shortcomings of many iterative methods. In the light of simulation and application to real data, we propose a slight modification to the Bayesian information criterion to reconstruct the wave energy distribution at the ionospheric base from the observation of radio wave electromagnetic field on the ground. The achieved results in both the inversion problem and the wave direction finding are very promising and may support other works so far suggested the use of Bayesian methods in the inversion of ill-posed problems to benefit from the valuable information brought by the a priori knowledge.

In identification of a finite impulse response (FIR) model using noise-corrupted input and output data, the least squares type of estimation schemes such as the ordinary least squares (LS), the corrected least squares (CLS) and the total least squares (TLS) method become often numerically unstable, when the true input signal to the system is strongly correlated. To overcome this ill-conditioned problem, we propose a regularized CLS estimation method by introducing multiple regularization parameters to minimize the mean squares error (MSE) of the regularized CLS estimate of the FIR model. The asymptotic MSE can be evaluated by considering the third and fourth order cross moments of the input and output measurement noises, and an analytical expression of the optimal regularization parameters minimizing the MSE is also clarified. Furthermore, an effective regularization algorithm is given by using the only accessible input-output data without using any true unknown parameters. The effectiveness of the proposed data-based regularization algorithm is demonstrated and compared with the ordinary LS, CLS and TLS estimates through numerical examples.

This paper proposes a distributed built-in self-test (BIST) technique and its test design platform for VLSIs. This BIST has lower hardware overhead pattern generators, compressors and controller. The platform cuts down on the number of complicated operations needed for the BIST insertion and evaluation, so the BIST implementation turn-around-time (TAT) is dramatically reduced. Experimental results for the 110 k-gate arithmetic execution blocks of an image-processing LSI show that using this BIST structure and platform enables the entire BIST implementation within five days. The implemented BIST has a 1% hardware overhead and 96% fault coverage. This platform will significantly reduce testing costs for time-to-market and mass-produced LSIs.

This letter addresses stability problems of interval matrices stemming from robustness issues in control theory. A quick overview is first made pertaining to methods to obtain stability conditions of interval matrices, putting particular emphasis upon one of them, regularity condition approach. Then, making use of this approach, several new stability criteria, for both Hurwitz and Schur stability, are derived.

This paper describes an advanced rule-embedded neural network (RENN+) that has an extended framework for achieving a very tight integration of learning-based neural networks and rule-bases of existing if-then rules. The RENN+ is effective in pattern recognition with ill-posed conditions. It is basically composed of several component RENNs and an output RENN, which are three-layer back-propagation (BP) networks except for the input layer. Each RENN can be pre-organized by embedding the if-then rules through translation of the rules into logic functions in a disjunctive normal form, and can be trainded to acquire adaptive rules as required. A weight-modification-reduced learning algorithm (WMR) capable of standard regularization is used for the post-training to suppress excessive modification of the weights for the embedded rules. To estimate the effectiveness of the proposed RENN+, it was used for pattern recognition in a radar system for detection of buried pipes. This trial showed that a RENN+ with two component RENNs had good recognition capability, whereas a conventional BP network was ineffective.