12724602
New wavelet preconditioner for solving boundary integral equations over nonsmooth boundaries
Matrices obtained by wavelet discretisation of partial differential equations or boundary integral equations (BIEs) are typically sparse with a finger-like sparsity pattern, in contrast to matrices obtained by traditional single scale discretisation, which are dense. In some cases diagonal preconditioning is sufficient, but there are effective preconditioners that can be used when this is not the case. Here, we consider the particular case of BIEs whose boundary has a geometrical singularity, and propose a new preconditioning strategy based on permutations of the unknowns. The strategy's performance is analysed and compared with related techniques for the double layer equation for Laplace's equation. *E-mail: stuarth@liverpool.ac.uk. Support of a UK EPSRC grant (GR/R22315) is gratefully acknowledged.
122233994
An efficient method for evaluating the integral of a class of highly oscillatory functions
Highly oscillatory integrals require special techniques for their effective evaluation. Various studies have been conducted to find computational methods for evaluating such integrals. In this paper we present an efficient numerical method to evaluate a class of generalised Fourier integrals (on a line or a square) with integrands of the form f(x)e^i^k^g^(^x^), under the assumption that in the domain of integration, both f and g are sufficiently smooth and that g does not have any stationary/critical points. Numerical analysis and results are given to illustrate the effectiveness of our method for computing generalised Fourier integrals.
15785287
A Nonlinear Multigrid Method for Total Variation Minimization from Image Restoration
Abstract
Image restoration has been an active research topic and variational formulations are particularly effective in high quality recovery. Although there exist many modelling and theoretical results, available iterative solvers are not yet robust in solving such modeling equations. Recent attempts on developing optimisation multigrid methods have been based on first order conditions. Different from this idea, this paper proposes to use piecewise linear function spanned subspace correction to design a multilevel method for directly solving the total variation minimisation. Our method appears to be more robust than the primal-dual method (Chan et al., SIAM J. Sci. Comput. 20(6), 1964–1977, 1999) previously found reliable. Supporting numerical results are presented.

3879090
On A Recursive Schur Preconditioner For Iterative Solution Of A Class Of Dense Matrix Problems
There are currently several distinct preconditioning methods for dense matrices based on applying a wavelet transform to obtain a matrix with a large number of small entries. A sparse preconditioner for this transformed matrix can be formed by setting to zero entries that are assumed to be unimportant. The effectiveness of the preconditioner depends on retaining the most important entries and on ensuring that they are positioned conveniently within the transformed matrix. In this paper we present a new, recursive preconditioning strategy that takes into account more of the significant entries without greatly increasing cost and outperforms existing methods in certain cases.
12726286
Fast Multilevel Algorithm for a Minimization Problem in Impulse Noise Removal
An effective 2-phase method for removing impulse noise was recently proposed. Its phase 1 identifies noisy pixel candidates by using median-type filters. Then in phase $2$, it restores only the noisy pixel candidates by some variational methods. The resulting method can handle salt-and-pepper noise and random-valued impulse noise at a level as high as 90% and 60%, respectively. The aim of this paper is to generalize a fast multilevel method for Gaussian denoising to solving the minimization problem arising in phase $2$ of the 2-phase method. The multilevel algorithm gives better images than standard optimization methods such as the Newton method or the conjugate gradient method. Also it can handle more general regularization functionals than the smooth ones previously considered. Supporting numerical experiments on two-dimensional gray-scale images are presented.
205413619
An efficient preconditioned iterative solver for solving a coupled fluid structure interaction problem
Modelling the interaction of an acoustic field in a fluid and an elastic structure submerged in the fluid leads to a system of complex linear equations with a complicated sparsity structure and, for higher wavenumbers and adequate modelling, the systems are very large. Direct methods are not practical. Preconditioned iterative methods, which are suitable for single operator equations, are not immediately applicable to the coupled case. This article proposes a block diagonal preconditioner of the sparse approximate inverse (SPAI) type that can accelerate the convergence of Krylov iterative solvers for the coupled system. Moreover, the proposed preconditioner can properly and implicitly scale the coupled matrix. Some numerical results are presented to demonstrate the effectiveness of the new method.
618005
Online conflict-free coloring for halfplanes, congruent disks, and axis-parallel rectangles
We present randomized algorithms for online conflict-free coloring (CF in short) of points in the plane, with respect to halfplanes, congruent disks, and nearly-equal axis-parallel rectangles. In all three cases, the coloring algorithms use O(log n) colors, with high probability.
 We also present a deterministic algorithm for online CF coloring of points in the plane with respect to nearly-equal axis-parallel rectangles, using O(log3n) colors. This is the first efficient (i.e, using polylog(n) colors) deterministic online CF coloring algorithm for this problem.
9877808
On the use of different speech representations for speaker modeling
Numerous speech representations have been reported to be useful in speaker recognition. However, there is much less agreement on which speech representation provides a perfect representation of speaker-specific information conveyed in a speech signal. Unlike previous work, we propose an alternative approach to speaker modeling by the simultaneous use of different speech representations in an optimal way. Inspired by our previous empirical studies, we present a soft competition scheme on different speech representations to exploit different speech representations in encoding speaker-specific information. On the basis of this soft competition scheme, we present a parametric statistical model, generalized Gaussian mixture model (GGMM), to characterize a speaker identity based on different speech representations. Moreover, we develop an expectation-maximization algorithm for parameter estimation in the GGMM. The proposed speaker modeling approach has been applied to text-independent speaker recognition and comparative results on the KING speech corpus demonstrate its effectiveness.
18568401
Capture inter-speaker information with a neural network for speaker identification
Many speaker identification systems are created by model-based approaches, where a statistical model is used to characterize a speaker's voice and no inter-speaker information is used in parameter estimation. It is well known that inter-speaker information is very helpful in discrimination of different speakers. We propose a method for the use of inter-speaker information to improve performance of a model-based speaker identification system. A neural network is employed to capture inter-speaker information from output space of those statistical models. In order to sufficiently utilize inter-speaker information, a rival penalized encoding rule is proposed to design supervised learning pairs for training the neural network. Comparative results in the KING speech corpus show that our method leads to a considerable improvement for a model-based speaker identification system.
5841267
The Data Mining Technology Based on CIMS and its Application on Automotive Remanufacturing
Nowadays, with the development of computer technology, data mining has been widely used in various fields. This paper describes a CIMSMINER that combines the data mining with CIMS (computer integrated manufacturing system) and instructs its objectives, model, physical architecture and methods. Considering the characteristics of remanufacturing of automotive products in China, the CIMSMINER is used to get the information concourse together and obtain the data mining results to help the improvement of products. The application in automotive remanufacturing is a reform to make the automotive product information chain be not only an information carrier, but also an information miner. Currently, the government strongly emphasizes energy saving and emission reducing, which is closely related to the sustainable development of China. Obviously, CIMSMINER is an effective tool to support the implementation of this policy.
15908834
Ensemble Learning with Active Data Selection for Semi-Supervised Pattern Classification
Unlike traditional pattern classification, semi-supervised learning provides a novel technique to make use of both labeled and unlabeled data for improving the performance of classification. In general, there are two critical issues for semi-supervised learning of discriminative classifiers; i.e., how to create an initial classifier of a good generalization capability with the limited labeled data and the how to make an effective use of unlabeled data without degradation of the established classifier. To tackle two aforementioned problems, we propose an ensemble learning approach based on a recent active data selection strategy, where ensemble learning would yield good generalization and active data selection tends to choose the unlabeled data more likely resulting in an improvement during semi-supervised learning. By using an ensemble of K-NN classifiers, we demonstrate the effectiveness of our approach on a synthetic data classification and a facial expression recognition tasks.