In this paper, we introduce the following m-layered hard constrained convex feasibility problem HCF(m): Find a point u m, where 0:=H (a real Hilbert space), i: = arg min gi(i-1) and gi(u):=wi,jd 2(u,Ci,j) are defined for (i) nonempty closed convex sets Ci,jH and (ii) weights wi,j > 0 satisfying wi,j=1 (i {1,,m}, j {1,,Mi}. This problem is regarded as a natural extension of the standard convex feasibility problem: find a point u Ci, where Ci H (i {1,, M}) are closed convex sets. Unlike the standard problem, HCF(m) can handle the inconsistent case; i.e., i,j Ci,j = , which unfortunately arises in many signal processing, estimation and design problems. As an application of the hybrid steepest descent method for the asymptotically shrinking nonexpansive mapping, we present an algorithm, based on the use of the metric projections onto Ci,j, which generates a sequence (un) satisfying limn d(un,3) = 0 (for M1 = 1) when at least one of C1,1 or C2,j's is bounded and H is finite dimensional. An application of the proposed algorithm to the pulse shaping problem is given to demonstrate the great flexibility of the method.

The present paper reports a robust projection onto eigenspace that is based on iterative projection. The fundamental method proposed in Shakunaga and Sakaue and involves iterative analysis of relative residual and projection. The present paper refines the projection method by solving linear equations while taking noise ratio into account. The refinement improves both the efficiency and robustness of the projection. Experimental results indicate that the proposed method works well for various kinds of noise, including shadows, reflections and occlusions. The proposed method can be applied to a wide variety of computer vision problems, which include object/face recognition and image-based rendering.

This article describes a new method for converting an arbitrary topology mesh into one having subdivision connectivity. First, a base mesh is produced by applying a sequence of edge collapse operations to the original mesh with irregular connectivity. Then, the base mesh is iteratively subdivided. Each subdivided mesh is optimized to reduce its distance from the original mesh and to improve its global smoothness and compactness. A set of corresponding point pairs, which is required to compute the distance from the original mesh to the subdivided mesh, is determined by combining the initial parameterization and the multi-resolution projection. Experimental results show that the proposed method yields good performance in terms of global smoothness, small distortion, and good compactness, compared with conventional methods.

This paper presents a distinct approach to the robustness stability analysis and design of linear uncertain systems. Based on the extension version of the projection method, the specific stability issue, which ensures the poles within a specific region, can be efficiently analyzed. Furthermore, we derive a simple design scheme for a class of uncertain systems. By the proposed numerical algorithm, some examples are given to demonstrate the validity and effectiveness.

We propose an image generation method for an immersive multi-screen environment that contains a motion ride. To allow a player to look around freely in a virtual world, a method to generate an arbitrary direction image is required, and this technology has already been established. In our environment, displayed images must also be updated according to the movement of the motion ride in order to keep a consistency between the player's viewpoint and the virtual world. In this paper, we indicate that this updating process can be performed by the similar method to generate looking-around images and the same data format can be applicable. Then we discuss the format in terms of the data size and the amount of calculations need to consider the performance in our display environment, and we propose new image formats which improve on the widely-used formats such as the perspective, or the fish-eye format.

The objective of this study was to explore suitable spatial filters for inverse estimation of cortical potentials from the scalp electroencephalogram. The effect of incorporating noise covariance into inverse procedures was examined by computer simulations. The parametric projection filter, which allows inverse estimation with the presence of information on the noise covariance, was applied to an inhomogeneous three-concentric-sphere model under various noise conditions in order to estimate the cortical potentials from the scalp potentials. The present simulation results suggest that incorporation of information on the noise covariance allows better estimation of cortical potentials, than inverse solutions without knowledge about the noise covariance, when the correlation between the signal and noise is low. The method for determining the optimum regularization parameter, which can be applied for parametric inverse techniques, is also discussed.

The existing methods for the reconstruction of a super-resolution image from a sequence of undersampled and subpixel shifted images have to solve a large ill-condition equation group by approximately finding the pseudo-inverse matrix or performing many iterations to approach the solution. The former leads to a big burden of computation, and the latter causes the artifacts or noise to be stressed. In order to solve these problems, in this paper, we consider applying pyramid structure to the super-resolution of the image sequence and present a suitable pyramid framework, called Super-Resolution Image Pyramid (SRIP). Based on the imaging process of the image sequence, the proposed method divides a big back-projection into a series of different levels of small back-projections, thereby avoiding the above problems. As an example, the Iterative Back-Projection (IBP) suggested by Peleg is included in this pyramid framework. Computer simulations and error analyses are conducted and the effectiveness of the proposed framework is demonstrated. The image resolution can be improved better even in the case of severely undersampled images. In addition, the other general super-resolution methods can be easily included in this framework and done in parallel so as to meet the need of real-time processing.

A robust adaptive filtering algorithm was established recently (I. Yamada, K. Slavakis, K. Yamada 2002) based on the interactive use of statistical noise information and the ideas developed originally for efficient algorithmic solutions to the convex feasibility problems. The algorithm is computationally efficient and robust to noise because it requires only an iterative parallel projection onto a series of closed half spaces highly expected to contain the unknown system to be identified and is free from the computational load of solving a system of linear equations. In this letter, we show the potential applicability of the adaptive algorithm to the identification problem for the second order Volterra systems. The numerical examples demonstrate that a straightforward application of the algorithm to the problem soundly realizes fast and stable convergence for highly colored excited speech like input signals in possibly noisy environments.

The existing methods for reconstruction of a super-resolution image from undersampled and shubpixel shifted image sequence have two disadvantages. One is that most of them have to perform a lot of computations which lead to taking a lot of time and cannot meet the need of realtime processing. Another is that they cannot achieve satisfactory results in the case that the undersampling rate is too low. This paper considers applying a pyramid structure method to the super-resolution of the image sequence since it has some iterative optimization and parallel processing abilities. Based on the Iterative Back-Projection proposed by Peleg, a practical implementation, called Pyramid Iterative Back-Projection, is presented. The experiments and the error analysis show the effectiveness of this method. The image resolution can be improved better even in the case of severely undersampled images. In addition, the proposed method can be done in parallel and meet the need of real-time processing. The implementation framework of the method can be easily extended to the other general super-resolution methods.

In many practical situations in NN learning, training examples tend to be supplied one by one. In such situations, incremental learning seems more natural than batch learning in view of the learning methods of human beings. In this paper, we propose an incremental learning method in neural networks under the projection learning criterion. Although projection learning is a linear learning method, achieving the above goal is not straightforward since it involves redundant expressions of functions with over-complete bases, which is essentially related to pseudo biorthogonal bases (or frames). The proposed method provides exactly the same learning result as that obtained by batch learning. It is theoretically shown that the proposed method is more efficient in computation than batch learning.

It is widely known that the family of projection filters includes the generalized inverse filter, and that the family of parametric projection filters includes parametric generalized projection filters. However, relations between the family of parametric projection filters and constrained least squares filters are not sufficiently clarified. In this paper, we consider relations between parameter estimation and image restoration by these families. As a result, we show that the restored image by the family of parametric projection filters is a maximum penalized likelihood estimator, and that it agrees with the restored image by constrained least squares filter under some suitable conditions.

In this letter, we propose a spatially adaptive image restoration algorithm, using local statistics. The local variance, mean and maximum value are utilized to constrain the solution space. These parameters are computed at each iteration step using partially restored image. A parameter defined by the user determines the degree of local smoothness imposed on the solution. The resulting iterative algorithm exhibits increased convergence speed when compared with the non-adaptive algorithm. In addition, a smooth solution with a controlled degree of smoothness is obtained. Experimental results demonstrate the capability of the proposed algorithm.

In this paper, we propose a projection based design of near perfect reconstruction QMF banks. An advantage of this method is that additional design specifications are easily implemented by defining new convex sets. To apply convex projection technique, the main difficulty is how to approximate the design specifications by some closed convex sets. In this paper, introducing a notion of Magnitude Product Space where a pair of magnitude responses of analysis filters is expressed as a point, we approximate design requirements of QMF banks by multiple closed convex sets in this space. The proposed method iteratively applies a convex projection technique, Hybrid Steepest Descent Method, to find a point corresponding to the optimal analysis filters at each stage, where the closed convex sets are dynamically improved. Design examples show that the proposed design method leads to significant improvement over conventional design methods.

This paper has two parts. In the first part of the paper, we note the property that under the para perspective camera projection model of a camera, the set of 2D images produced by a 3D point can be optimally represented by two lines in the affine space (α-β space). The slope of these two lines are same, and we observe that this constraint is exactly the same as the epipolar line constraint. Using this constraint, the equation of the epipolar line can be derived. In the second part of the paper, we use the "same slope" property of the lines in the α-β space to derive the affine structure of the human face. The input to the algorithm is not limited to an image sequence of a human head under rigid motion. It can be snapshots of the human face taken by the same or different cameras, over different periods of time. Since the depth variation of the human face is not very large, we use the para perspective camera projection model. Using this property, we reformulate the (human) face structure reconstruction problem in terms of the much familiar multiple baseline stereo matching problem. Apart from the face modeling aspect, we also show how we use the results for reprojecting human faces in identification tasks.

This paper proposes a scheme which combines the conventional technique with a multi-level structure of Thai sentences for detection and segmentation for touching Thai printed characters. The proposed scheme solves problems of both horizontally and vertically touching characters. The complexity of a multi-level structure is employed to classify characters into three zones. The edge detection technique is applied to separate overlapping characters. Then, the horizontal touching characters are determined by using a statistical width of characters. The segmentation point of horizontal touching characters is determined using vertical projection combined with a statistical width of characters. The vertical touching characters are determined by considering the overlapping area of character boundary between zones. The height of line is used to separate the segment of vertical touching characters. Ambiguities are handle by using distinctive features of Thai characters. The effectiveness of the proposed scheme is tested with data from both newspapers and printed documents. The accuracy of 97 and 98 percents are obtained for newspaper and printed documents respectively.

There are the following three targets to be achieved in a software project from the three viewpoints of process management (or progress management), cost management, and quality management for software project to be successful: (a) drafting a software development plan based on accurate estimation, (b) early detection of risks that the project includes based on correct situation appraisal, (c) early avoidance of risks that the project includes. In this paper, the authors propose a method and facilities to project risks in a software project through Kepner-Tregoe program, and propose schedule re-planning by using genetic algorithm for avoiding the projected risks. Furthermore the authors show, from the results of execution of the system, that the system is effective in early avoidance of risks that the software project includes.

Recently, Kundur and Hatzinakos showed that a linear restoration filter designed by using the almost obvious a priori knowledge on the original image, such as (i) nonnegativity of the true image and (ii) the smallest rectangle encompassing the original object, can realize a remarkable performance for a blind image deconvolution problem. In this paper, we propose a new set-theoretic blind image deconvolution scheme based on a recently developed convex projection technique called Hybrid Steepest Descent Method (HSDM), where some partial information can be utilized set-theoretically by parallel projections onto convex sets while the others are incorporated in a cost function to be minimized by a steepest descent method. Numerical comparisons with the standard set-theoretic scheme based on POCS illustrate the effectiveness of the proposed scheme.

This paper presents a new method for image interpolation based on truncated projections onto convex sets (POCS). By using the convergence property to properly defined convex sets, the proposed algorithm can restore high frequency details in the original high resolution image. In order to apply the POCS method to the interpolation procedure, we first present a two-dimensional separable image degradation model for a low resolution imaging system. According to the model, we propose a truncated POCS-based spatial interpolation algorithm for image sequences. Experimental results with synthetic and real image sequence show that the proposed algorithm gives indiscernible interpolation performance compared with the conventional POCS-base algorithm, while it significantly reduces computational complexity and is suitable for processing image sequences.

The transfer function of IIR all-pass filters is a rational function of ω. However, the optimization of such a rational function using the successive projections method, which has a wider range of application than the Remez algorithm, has not been presented. In this paper, we propose designing IIR all-pass filters using the successive projections method.

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.