Automatic image inspector inspects the quality of printed circuit boards using image-processing technology. In this study, we change an automatic inspection problem into a problem for detecting the signal singularities. Based on the wavelet theory that the wavelet transform can focus on localized signal structures with a zooming procedure, a novel singularity detection and measurement algorithm is proposed. Singularity positions are detected with the local wavelet transform modulus maximum (WTMM) line, and the Lipschitz exponent is estimated at each singularity from the decay of the wavelet transform amplitude along the WTMM line. According to the theoretical analysis and computer simulation results, the proposed algorithm is shown to be successful for solving the automatic inspection problem and calculating the Lipschitz exponents of signals. These Lipschitz exponents successfully characterize singular behavior of signals at singularities.

In this paper, we present our investigation of Latent Semantic Indexing (LSI) on the local query regions for solving the computation restrictions of the LSI on the global information space. Through the experiments with different SVD dimensionality on the local query regions, the results show that low-dimensional LSI can achieve much better precision than VSM and similar precision to global LSI. Such small SVD factors indicate that there is an almost linear surface in the local query regions. The largest or the two largest singular vectors have the ability to capture such a linear surface and benefit the particular query. In spite of the fact that Local LSI analysis needs to perform the Singular Value Decomposition (SVD) computation for each query, the surprisingly small requirements of the SVD dimension resolve the computation restrictions of LSI for large scale IR tasks. Moreover, on the condition that several relevant sample documents are available, application of low dimensional LSI for these documents can obtain comparable precision with the Local RF in a different manner.

The current paper presents an effective deblocking algorithm for block-based coded images using singularity detection in a wavelet transform. Blocking artifacts appear periodically at block boundaries in block-based coded images. The local maxima of a wavelet transform modulus detect all singularities, including blocking artifacts, from multiscale edges. Accordingly, the current study discriminates between a blocking artifact and an edge by estimating the Lipschitz regularity of the local maxima and removing the wavelet transform modulus of a blocking artifact that has a negative Lipschitz regularity exponent. Experimental results showed that the performance of the proposed algorithm was objectively and subjectively superior.

In this paper we analyze an asymptotic stability of nonlinear singularly perturbed systems and propose a composite control with gain scheduling where the fast controller is the gain scheduled controller and the slow state plays a role of slowly varying parameters in gain scheduling. Specifically, the slow controller is designed by the slow manifold to stabilize the reduced slow system. As a result, the slow manifold of the system is the same as the designed manifold.

This paper presents an accurate method for finding the 3D control points of the B-Spline curves. This method can automatically fit a set of data points with piecewise geometrically continuous cubic B-Spline curves. Iterating algorithm has been used for finding the 2D control points. And a new approach for shape reconstruction based on the control points of the curves on the object's surface is proposed. B-Spline patch, the extension of the B-Spline curves to surface, provides recovering the shape of the object in 2D approach. The 3D control points of the cubic B-Spline curves are computed from the factor decomposition of the measurement matrix of 2D control points. The multiple object approach is also proposed to reconstruct the 3D shape of each curves of an object. Some experiments are demonstrated to confirm the effectiveness of our proposed method.

Information geometry is applied to the manifold of neural networks called multilayer perceptrons. It is important to study a total family of networks as a geometrical manifold, because learning is represented by a trajectory in such a space. The manifold of perceptrons has a rich differential-geometrical structure represented by a Riemannian metric and singularities. An efficient learning method is proposed by using it. The parameter space of perceptrons includes a lot of algebraic singularities, which affect trajectories of learning. Such singularities are studied by using simple models. This poses an interesting problem of statistical inference and learning in hierarchical models including singularities.

In this paper, we propose fast bitmap search algorithms to reduce the computational complexity of transform-based vector quantization (VQ) techniques, which achieve better quality in reconstructed images than the ordinary VQ. By removing the unlikely codewords in each step, the bitmap search method, which starts from the most significant bitmap then the successive significant ones, can save more than 90% computation of the ordinary transformed VQ. By applying to the singular value decomposition (SVD) VQ as an example, theoretical analyses and simulation results show that the proposed bitmap search methods dramatically reduce the computation and achieve invisible distortion in the reconstructed images.

The problem we consider in this paper is whether the Menezes-Okamoto-Vanstone (MOV) reduction for attacking elliptic curve cryptosystems can be realized for genera elliptic curves. In realizing the MOV reduction, the base field Fq is extended so that the reduction to the discrete logarithm problem in a finite field is possible. Recent results by Balasubramanian and Koblitz suggest that, if l q-1, such a minimum extension degree is the minimum k such that l|qk-1, which is equivalent to the condition under which the Frey-Ruck (FR) reduction can be applied, where l is the order of the group in the elliptic curve discrete logarithm problem. Our point is that the problem of finding an l-torsion point required in evaluating the Weil pairing should be considered as well from an algorithmic point of view. In this paper, we actually propose a method which leads to a solution of the problem. In addition, our contribution allows us to draw the conclusion that the MOV reduction is indeed as powerful as the FR reduction under l q-1 not only from the viewpoint of the minimum extension degrees but also from that of the effectiveness of algorithms.

A nonlinear multiple complex sinusoidal estimator (NMSE) is proposed, as an extended and improved version with system noise of the single sinusoidal estimator previously presented by the author, for extracting multiple complex sinusoids in white noise. This estimator is derived by applying an extended complex Kalman filter (ECKF) to a noisy multiple complex sinusoidal model with state-representation, where the model becomes a nonlinear stochastic system. Proof of the stability is given by using a structure of the state-space signal model and Lyapunov techniques. Also, computer simulations demonstrate the effectiveness of the NMSE from various points of view.

Heartbeat interval time series is an example of natural signals with 1/f characteristics. The exponent α of the 1/fα spectrum has some clinical significance. But sometimes the 1/f components is superimposed by some sinusoid components in the signal. To estimate the slope accurately, the 1/f component must be extracted from the signal. The singular spectrum analysis (SSA) method is recruited here to perform the task. Experimental results on data from real patients are satisfactory.

A procedure for radar target discrimination is presented in this paper. The scheme includes an enhancement of late-time noisy scattering data based on a proposed signal processing algorithm and a decision procedure using previously known resonance annihilation filters. The signal processing stage is specifically adapted to scattering signals and makes use of the results of the singularity expansion method. It is based on a signal reconstruction using the SVD of a data matrix with a suitable choice of the number of singular vectors employed. To justify the inclusion of this stage, this procedure is shown to maintain the signal characteristics necessary to identify the scattered response. Simulation results clearly reveal a significant improvement due to the inclusion of the proposed stage. This improvement becomes especially important when the noise level is high or the targets to be discriminated (five regular polygonal loops) have a similar geometry.

A new concept of "an imperfect singular solution" is defined as an approximate solution which becomes a singular solution by adding a suitable small perturbation to the original equations. A numerical method is presented for proving the existence of imperfect singular solutions of nonlinear equations with guaranteed accuracy. A few numerical examples are also presented for illustration.

Recently, Miura introduced a construction method of one-point algebraic geometry codes on singular curves, which is regarded as a generalization of one on nonsingular curves, and enables us to construct codes on wider class of algebraic curves. However, it is still not clear whether there really exist singular curves on which we can construct good codes that are never obtained from nonsingular curves. In this paper, we show that for fixed designed minimum distance in a wide range, the dimension of codes on a singular curve is smaller than or equal to that of the codes on its normalization, and the number of check symbols of the former codes is larger than that of the latter codes. This implies the optimality of nonsingular curves for code construction.

In this paper, we analyze the inverse scattering problem by a new deterministic method called "Source and Radiation Field Solution," which has the merit that both the source and the radiation field can be treated at the same time, the effect of which has already shown in ordinary scattering problems.

A new method is proposed for estimating a single complex sinusoid and its parameters (frequency and amplitude) from measurements corrupted by white noise. This method is called the ECKF-SVD method, which is derived by applying an extended complex Kalman filter (ECKF) to a nonlinear stochastic system whose state variables consist of the AR coefficient (a function of frequency) and a sample of the original signal. Proof of the stability is given in the case of a single sinusoid. Simulations demonstrate that the proposed ECKF-SVD method is effective for estimating a single complex sinusoid and its frequency under a low signal-to-noise ratio (SNR). In addition, the amplitude estimation by means of the ECKF-SVD method is also discussed.

In the conventional sound field reproduction system with control of the transfer functions from the source to both ears of a listener, a slight shift of the ears caused by movement of the listener inevitably results in sound localization being different from that expected. In this paper, a method for reproducing a sound field by controlling the transfer function from the source to multiple points (called the "method of multiple-points control" hereafter) is applied to a sound reproduction system with the aim of expanding the area which can be controlled. The system is controlled so that the transfer functions from the input of the system to the multiple points adjacent to the original receiving points have the same desired transfer function. By placing the control points at appropriate intervals, a "zone of equalization" is formed. Based on a computer simulation, the intervals between control points is discussed. The configuration of the loundspeakers for sound reproduction is also discussed.

The objective of this paper is to find a parametric representation for the vocal-tract log-area function that is directly and simply related to basic acoustic characteristics of the human vocal-tract. The importance of this representation is associated with the solution of the articulatory-to-acoustic inverse problem, where a simple mapping from the articulatory space onto the acoustic space can be very useful. The method is as follows: Firstly, given a corpus of log-area functions, a parametric model is derived following a factor analysis technique. After that, the articulatory space, defined by the parametric model, is filled with approximately uniformly distributed points, and the corresponding first three formant frequencies are calculated. These formants define an acoustic space onto which the articulatory space maps. In the next step, an independent component analysis technique is used to determine acoustic and articulatory coordinate systems whose components are as independent as possible. Finally, using singular value decomposition, acoustic and articulatory coordinate systems are rotated so that each of the first three components of the articulatory space has major influence on one, and only one, component of the acoustic space. An example showing how the proposed model can be applied to the solution of the articulatory-to-acoustic inverse problem is given at the end of the paper.

This paper describes a finite element method to obtain an accurate solution of the scalar Helmholtz equation with field singularities. It is known that the spatial derivatives of the eigenfunction of the scalar Helmholtz equation become infinite under certain conditions. These field singularities under mine the accuracy of the numerical solutions obtained by conventional finite element methods based on piecewise polynomials. In this paper, a regularized eigenfunction is introduced by subtracting the field singularities from the original eigenfunction. The finite element method formulated in terms of the regularized eigenfunction is expected to improve the accuracy and convergence of the numerical solutions. The finite element matrices for the present method can be easily evaluated since they do not involve any singular integrands. Moreover, the Dirichlet-type boundary conditions are explicitly imposed on the variables using a transform matrix while the Neumann-type boundary conditions are implicitly imposed in the functional. The numerical results for three test problems show that the present method clearly improves the accuracy of the numerical solutions.

If a general Petri net N = (S, T, F, Mo) is transition-live under Mo, it is evident that each maximal structural deadlock SDL(D) in N as well as each minimal structural deadlock MSDL (ND) in each D is also transition-live under Mo. However, since the converse of the latter of the above is not always true, it is important to obtain the conditions for this converse to be true if we want to have a useful necessary and sufficient "initial-marking-based" or "structural" liveness condition for N. Up to now, usefull and well-known structural or initial-marking-based necessary and sufficient liveness conditions of Petri nets have only been those of an asymmetric choice (AC) net and its subclasses such as an EFC net, an FC net, an FCF net, MG, and SM. However, all the above subclasses are activated only by real or virtual deadlock-trap properties which are local liveness for each minimal deadlocks; in other words, the above topics of this paper are unconditionally satisfied in those subclasses because of their special structure of nets. In this paper, a necessary and sufficient structural liveness condition for a general Petri net N with globally structural live minimal structural deadlocks is presented as follows: The next () or () is satisfied. () N has no SDL D. () If N has at least one SDL D, () or () is satisfied under the condition that each MSDL ND in N is transition-live under Mo. () N has no singular MSDL (α) (i.e., (α-) and (α-)). () If N has at least one singular MSDL (α-)((α-), resp.), every semi-MDSL ()((), resp.) NDS = (SDS, TDS, FDS, MoDS with respect to each singular MSDL (α-)((α-), resp.), is transition-live under the MoDS under the condition of "the condition (**)", where the locally structural liveness for this NDS means (1) or (2)((3), resp.) of Lemma 4-4 and "the condition (**)" is defined in Lemma 4-7 of this paper. The relationship between the above results and the liveness problem for N is also shown.

The analytic structure of the governing equation for a 2nd order Phase–Locked Loops (PLL) is studied in the complex time plane. By a local reduction of the PLL equation to the Ricatti equation, the PLL equation is analytically shown to have singularities which form a fractal structure in the complex time plane. Such a fractal structure of complex time singularities is known to be characteristic for nonintegrable, especially chaotic systems. On the other hand, a direct numerical detection of the complex time singularities is performed to verify the fractal structure. The numerical results show the reality of complex time singularities and the fractal structure of singularities on a curve.