• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.207-220
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• 2004

Necessary and sufficient conditions are given for the regularity of block triangular fuzzy matrices. This leads to characterization of idem-potency of a class of triangular Toeplitz matrices. As an application, the existence of group inverse of a block triangular fuzzy matrix is discussed. Equivalent conditions for a regular block triangular fuzzy matrix to be expressed as a sum of regular block fuzzy matrices is derived. Further, fuzzy relational equations consistency is studied.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.137-149
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• 2018

In this paper, under the assumption of the symmetry point spread function, antireflective boundary conditions(AR-BCs) are considered in connection with the fast truncated Lagrange(FTL) method. The FTL method is proposed as an image restoration method for large-scale ill-conditioned BTTB(block Toeplitz with Toeplitz block) and BTHHTB(block Toeplitz-plus-Hankel matrix with Toeplitz-plus-Hankel blocks) linear systems([13, 17]). The implementation and efficiency of the FTL method in the AR-BCs are further illustrated. Especially, by employing the AR-BCs, both the continuity of the image and the continuity of its normal derivative are preserved at the boundary. A reconstructed image with less artifacts at the boundary is obtained as a result.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.5
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• pp.3-10
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• 2014

In this paper we review the typical Toeplitz matrices and block circulant matrices, and propose the a circulant Hadamard matrix which is consisted of +1 and -1, but its structure is different from typical Hadamard matrix. The proposed circulant Hadamard matrix decreases computational complexities to $Nlog_2N$ additions through high speed algorithm compare to original one. This matrix is able to be applied to Massive MIMO channel estimation, FIR filter design, amd signal processing.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.237-252
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• 2014

In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators $T_{\Phi}$, where ${\Phi}$ = $F+G^*$, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space $L^2_a(\mathbb{D},\mathbb{C}^n)$. We also show some necessary conditions for the hyponormality of $T_{F+G^*}$ with $F+G^*{\in}h^{\infty}{\otimes}M_{n{\times}n}$ on $L^2_a(\mathbb{D},\mathbb{C}^n)$.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.197-205
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• 2018

In this note we give a relationship between the degree and coprime-ness of matrix-valued rational functions.

• The Journal of the Acoustical Society of Korea
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• v.8 no.4
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• pp.39-43
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• 1989

In this paper, the concept of ultrasonic transmission imaging system with crossed -arrays is Introduced. The crossed-array system is simulated by angular spectrum method In the operating frequency of 12MHz. A theoritical development of a system transfer function matrix 1M is presented. Using this matrix, a priori knowledge on the physical properties of the system is understood. It proves to be a block Toeplitz matrix with Toeplitz entries. Using the Inversion procedure, the spatial degradations of the measured image can be removed.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.151-164
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• 2005

The regularized structured total least norm (RSTLN) method finds an approximate solution x and error matrix E to the overdetermined linear system (H + E)x $\approx$ b, preserving structure of H. A new separation scheme by parts of variables for the regularized structured total least norm on blind deconvolution problem is suggested. A method combining the regularized structured total least norm method with a separation by parts of variables can be obtain a better approximated solution and a smaller residual. Computational results for the practical problem with Block Toeplitz with Toeplitz Block structure show the new method ensures more efficiency on image restoration.

• Journal of Industrial Technology
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• v.14
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• pp.19-28
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• 1994

We can get a tridiagonal block Toeplitz linear system by the finite difference approximation of 2-D Poisson equation. To exploit the nice property of this linear equation, we transform the equation into a Lyapunov equation and apply DST (discrete sine transform) to get diagonal matrix based Lyapunov equation. DST can be performed using FFT, which enables high-speed computaion. All the computations are performed on an SIMD parallel computer, the MasPar MP-2 with 4,096 processing elements. In this paper, parallel algorithm, mapping method of the algorithm onto the MP-2, and timing results are presented.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.8C
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• pp.786-794
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• 2006

We proposed a novel preconditioner based PCG(Preconditioned Conjugate Gradient) method for super resolution image reconstruction. Compared with the conventional block circulant type preconditioner, the proposed preconditioner can be more effectively applied for objective functions that include roughness penalty functions. The effectiveness of the proposed method was shown by simulations and experiments.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10a
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• pp.172-177
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• 1988

In this paper, a new fast algorithm of FIR least squares filter with linear phase is presented. The general unknown statistics case is considered, whereby only sample records of the data are available. Taking advantage of the near-to-Toeplitz+Hankel structure of the resulting normal equation, a fast algorithm which gurantees the linear phase constraint, is developed that recursively produces the filter coefficient of linear phase FIR filter for a single block of data.