• The Journal of the Acoustical Society of Korea
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• 제23권1E호
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• pp.3-9
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• 2004

An important inverse problem in the field of acoustics is that of reconstructing the strengths of a number of sources given a model of transmission paths from the sources to a number of sensors at which measurements are made. In dealing with this kind of the acoustical inverse problem, strengths of the discretised source distribution can be simply deduced from the measured pressure field data and the inversion of corresponding matrix of frequency response functions. However, deducing :he solution of such problems is not straightforward due to the practical difficulty caused by their inherent ill-conditioned behaviour. Therefore, in order to overcome this difficulty associated with the ill-conditioning, the problem is replaced by a nearby well-conditioned problem whose solution approximates the required solution. In this paper a microphone array are identified for which the inverse problem is optimally conditioned, which can be robust to contaminating errors. This involves sampling both source and field in a manner which results in the discrete pressures and source strengths constituting a discrete Fourier transform pair.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.621-638
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• 2009

The linear system Ax = b will have (i) no solution, (ii) only one non-trivial (trivial) solution, or (iii) infinity of solutions. Our focus will be on cases (ii) and (iii). The mathematical models of many real-world problems give rise to (a) ill-conditioned linear systems, (b) singular linear systems (A is singular with all its linearly independent rows are sufficiently linearly independent), or (c) ill-conditioned singular linear systems (A is singular with some or all of its strictly linearly independent rows are near-linearly dependent). This article highlights the scope and need of a randomized algorithm for ill-conditioned/singular systems when a reasonably narrow domain of a solution vector is specified. Further, it stresses that with the increasing computing power, the importance of randomized algorithms is also increasing. It also points out that, for many optimization linear/nonlinear problems, randomized algorithms are increasingly dominating the deterministic approaches and, for some problems such as the traveling salesman problem, randomized algorithms are the only alternatives.

• 대한수학회논문집
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• 제16권3호
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• pp.487-508
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• 2001

We consider the Cauchy problem for Laplacian. Using the single layer representation, we obtain an equivalent system of boundary integral equations. We show the singular values of the ill-posed Cauchy operator decay exponentially, which means that a small error is exponentially amplified in the solution of the Cauchy problem. We show the decaying rate is dependent on the geometry of he domain, which provides the information on the choice of numerically meaningful modes. We suggest a pseudo-inverse regularization method based on singular value decomposition and present various numerical simulations.

• 한국음향학회:학술대회논문집
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• 한국음향학회 2000년도 하계학술발표대회 논문집 제19권 1호
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• pp.337-338
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• 2000

The perceptual filter for speech enhancement was analytically derived where the frequency content of the input noisy signal was made the same as that of the estimated clean signal in auditory domain. However, the analytical derivation should rely on the deconvolution associated with the spreading function in the psychoacoustic model, which results in an ill-conditioned problem. In order to cope with the problem associated with the deconvolution, we propose a novel psychoacoustic model based speech enhancement filter whose principle is the same as the perceptual filter, however the filter is derived by a constrained optimization which provides solutions to the ill-conditioned problem.

• The Journal of the Acoustical Society of Korea
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• 제19권3E호
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• pp.12-18
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• 2000

Psychoacoustic model based methods have recently been introduced in order to enhance speech signals corrupted by ambient noise. In particular, the perceptual filter is analytically derived where the frequency content of the input noisy signal is made the same as that of the estimated clean signal in auditory domain. However, the analytical derivation should rely on the deconvolution associated with the spreading function in the psychoacoustic model, which results in an ill-conditioned problem. In order to cope with the problem associated with the deconvolution, we propose a novel psychoacoustic model based speech enhancement filter whose principle is the same as the perceptual filter, however the filter is derived by a constrained optimization which provides solutions to the ill-conditioned problem. It is demonstrated with artificially generated signals that the proposed filter operates according to the principle. It is shown that superior performance results from the proposed filter over the perceptual filter provided that a clean speech signal is separable from noise.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1998년도 봄 학술발표회 논문집
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• pp.390-397
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• 1998

An approach to identifying input forces is proposed using measured structural dynamic responses and its analytical model. The identification of input forces is a reverse process and ill-conditioned problem. Its solution is unstable and generally case dependent. In this paper, the ill-condition is described considering characteristic matrix which is defined by reduced dynamic stiffness matrix. Special attention is focused on the condition number of a characteristic matrix used in the solution algorithm of this reverse process. Simple example is presented in support of the ill-condition of a reverse process.

• 한국소음진동공학회논문집
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• 제11권9호
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• pp.431-438
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• 2001

This paper present experimental results of source identification for non-minimum phase system. Generally, a causal linear system may be described by matrix form. The inverse problem is considered as a matrix inversion. Direct inverse method can\`t be applied for a non-minimum phase system, the reason is that the system has ill-conditioning. Therefore, in this study to execute an effective inversion, SVD inverse technique is introduced. In a Non-minimum phase system, its system matrix may be singular or near-singular and has one more very small singular values. These very small singular values have information about a phase of the system and ill-conditioning. Using this property we could solve the ill-conditioned problem of the system and then verified it for the practical system(cantilever beam). The experimental results show that SVD inverse technique works well for non-minimum phase system.

• 한국멀티미디어학회논문지
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• 제8권11호
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• pp.1432-1438
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• 2005

심리음향모델을 기반으로 주파수영역에서 잡음을 형상화하여 오디오 신호에 부가하였을 때 부가된 잡음이 지각되지 않는 방법을 제안하였다. 신호의 마스킹 문턱값으로부터 지각되지 않는 잡음의 준위를 구하는 것은 심리음향모델에서 확산함수와 관련된 디컨버루션을 수반하는데 난제(ill-conditioned Problem)로 알려져 있다. 본 논문에서는 최적화 기법을 적용하여 잡음의 여기준위를 신호의 마스킹 준위에 일치시킴으로써 신호에 부가된 잡음이 청각적으로 지각되지 않는 한도 내에서 최대한의 잡음준위가 되도록 형상화하는 방법을 제시하고 실험적으로 그 타당성을 증명하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권1호
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• pp.85-100
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• 2001

In this paper we propose a block-type parallel preconditioner for solving large sparse nonsymmetric linear systems, which we expect to be scalable. It is Multi-Color Block SOR preconditioner, combined with direct sparse matrix solver. For the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with Multi-Color ordering. Since most of the time is spent on the diagonal inversion, which is done on each processor, we expect it to be a good scalable preconditioner. Finally, due to the blocking effect, it will be effective for ill-conditioned problems. We compared it with four other preconditioners, which are ILU(0)-wavefront ordering, ILU(0)-Multi-Color ordering, SPAI(SParse Approximate Inverse), and SSOR preconditioner. Experiments were conducted for the Finite Difference discretizations of two problems with various meshsizes varying up to 1024 x 1024, and for an ill-conditioned matrix from the shell problem from the Harwell-Boeing collection. CRAY-T3E with 128 nodes was used. MPI library was used for interprocess communications. The results show that Multi-Color Block SOR and ILU(0) with Multi-Color ordering give the best performances for the finite difference matrices and for the shell problem only the Multi-Color Block SOR converges.

• 한국음향학회:학술대회논문집
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• 한국음향학회 2000년도 하계학술발표대회 논문집 제19권 1호
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• pp.335-336
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• 2000

A psychoacoustic model based noise shaping method is proposed, where noise's presence with a host signal will not be perceptually noticeable. The derivation of imperceptible noise levels from the masking thresholds of the signal involves a deconvolution associated with the spreading function in the psychoacoustic model, which results in an ill-conditioned problem. In this paper, the problem is formulated as a constrained optimization, and it is demonstrated that the solution provides noise shaping where the noise excitation level conforms to the masking thresholds of the signal.