회절광학소자의 최적 설계를 위한 Iterative Fourier Transform Algorithm의 수렴성에 관한 연구

김휘,양병춘,박진홍,이병호,Kim, Hwi,Yang, Byung-Choon,Park, Jin-Hong,Lee, Byoung-Ho 대한전자공학회 2003 電子工學會論文誌-SD (Semiconductor and devices) Vol.40 No.5

Iterative Fourier transform algorithm, (IFTA) is tile iterative numerical algorithm for the design of the diffractive optical elements (DOE), by which the phase distribution of a DOE converges on a local optimal solution. The convergence of IFTA depends on several factors 3s initial phase distribution, the structure of the degree of freedom on the observation plane, and the values of internal parameters. In this paper, we analyze tile dependence of the convergence of IFTA on an internal parameter of IFTA, the relaxation parameter, and propose a new hybrid scheme of genetic algorithm and IFTA to obtain more accurate solution. Iterative Fourier transform algorithm (IFTA)은 회절광학소자 (DOE)의 위상 분포를 구하기 위한 반복적 수치 해석 알고리즘으로서 회절광학소자의 위상 분포는 반복 과정을 통하여 국소 최적해로 수렴하게 된다. Ink의 수렴은 위상 분포 초기치, 관측면에서의 자유도의 허용 범위 및 알고리즘에 내재된 매개 변수들의 설정 값에 영향을 받는다. 본 논문에서는 IFTA의 내부적 매개 변수인 완화 변수(relaxation parameter)가 IFTA의 수렴에 미치는 영향을 분석하고 이를 토대로 보다 정확한 최적화 해를 얻기 위한 유전 알고리즘과 IFTA의 하이브리드 알고리즘을 제안한다.

터보부호의 계산량 감소를 위한 효율적인 반복중단 알고리즘

정대호,임순자,김환용,Jeong Dae-Ho,Lim Soon-Ja,Kim Hwan-Yong 대한전자공학회 2005 電子工學會論文誌-SD (Semiconductor and devices) Vol.42 No.6

터보부호는 반복복호가 진행됨에 따라서 AWGN 채널 환경에서 BER 성능이 향상된다는 것은 잘 알려진 사실이다. 그러나 다양한 채널 환경하에서 반복복호 횟수가 증가하면 무의미한 반복이 이루어져서 복호하는데 필요한 복호 지연시간과 계산량이 증가하게 되는 단점을 가진다. 따라서 본 논문에서는 터보부호의 계산량과 평균 반복복호 횟수를 크게 감소시킬 수 있는 효율적인 반복중단 알고리즘을 제안한다. 제안된 반복중단 알고리즘은 고정된 반복 횟수 이전에 반복복호를 효율적으로 중단시킬 수 있는 기법으로써 터보복호기의 최종 출력값인 LLR의 분산값을 중단조건으로 이용하여 BER 성능의 손실없이 계산량과 평균 반복복호 횟수를 크게 감소시킬 수 있음을 확인하였다. 모의실험 결과, 제안된 알고리즘의 계산량은 SCR 알고리즘과는 비슷하였으나 CE 알고리즘과 비교하여 약 $40\%$ 정도 줄일 수 있었다. 또한, 제안된 알고리즘의 평균 반복복호 횟수는 HDA 알고리즘이나 SCR 알고리즘과 비교하여 높은 SNR에서 각각 최대 $9.94\%$와 $8.32\%$ 정도의 감소효과를 나타냈으며 CE 알고리즘과 비교하여 약 $2.16\%{\~}7.84\%$ 정도의 감소효과를 나타내었다. It is well blown about the fact that turbo code has better the BER performance as the number of decoding iterations increases in the AWGN channel environment. However, as the number of decoding iterations is increased under the several channel environments, any further iteration results in very little improvement, and it requires much delay and computation in proportion to the number of decoding iterations. In this paper, it proposes the efficient iterative decoding stop criterion algorithm which can largely reduce the computation and the average number of decoding iterations of turbo code. Through simulations, it is verifying that the proposed algorithm can efficiently stop the iterative decoding by using the variance value of LLR and can largely reduce the computation and the average number of decoding iterations without BER performance degradation. As a result of simulation, the computation for the proposed algerian is reduced by about $40\%$ compared to conventional CE algorithm. The average number of decoding iterations for the proposed algorithm is reduced by about $9.94\%$ and $8.32\%$ compared to conventional HDA and SCR algorithm respectively, and by about $2.16\%{\~}7.84\%$ compared to conventional CE algorithm.

터보부호의 오류확률 분산값을 이용한 효율적인 반복중단 알고리즘

정대호,심병섭,임순자,김태형,김환용,Jeong Dae ho,Shim Byoung sup,Lim Soon Ja,Kim Tae hyung,Kim Hwan yong 한국통신학회 2004 韓國通信學會論文誌 Vol.29 No.10C

Turbo code, a kind of error correction coding technique, has been used in the field of digital mobile communication systems. And it is well known about the fact that turbo code has better the BER performance as the number of decoding iterations increases in the AWGN channel environment. However, as the number of decoding iterations is increased under the several channel environments, any further iteration results in very little improvement, and it requires much delay, computation and power consumption in proportion to the number of decoding iterations. In this paper, it proposes the efficient iterative decoding stop criterion algorithm which can largely reduce the average number of decoding iterations of turbo code. Through simulations, it is verifying that the proposed algorithm can efficiently stop the iterative decoding by using the variance value of error probability for the soft output value, and can largely reduce the average number of decoding iterations without BER performance degradation. As a result of simulation, the average number of decoding iterations for the proposed algorithm is reduced by about 2.25% ~14.31% and 3.79% ~14.38% respectively compared to conventional schemes, and power consumption is saved in proportion to the number of decoding iterations. 터보부호는 디지별 이동통신 시스템에서 사용되는 오류정정 부호화 기법의 일종으로써 반복복호가 진행됨에 따라서 AWGN 채널 환경에서 BER성능이 향상된다는 것은 잘 알려진 사실이다. 그러나 다양한 채널 환경하에서 반복복호 횟수가 증가하면 무의미한 반복이 이루어져서 복호하는데 필요한 복호 지연시간과 계산량이 증가하게 되고 전력소모 또한 커지게 되는 단점을 가진다. 따라서 본 논문에서는 터보부호의 평균 반복복호 횟수를 크게 감소시킬 수 있는 효율적인 반복중단 알고리즘을 제안한다. 제안된 반복중단 알고리즘은 고정된 반복 횟수 이전에 반복복호를 효율적으로 중단시킬 수 있는 기법으로써 연판정 출력값에 대한 오류확률의 분산값을 중단조건으로 이용하여 BER성능의 손실없이 평균 반복복호 첫수를 크게 감소시킬 수 있음을 확인하였다. 모의실험 결과, 제안된 알고리즘의 평균 반복복호 횟수는 HDA 알고리즘과 비교하여 약 2.25%~14.31% 정도의 감소효과를 나타냈으며 CE 알고리즘과 비교하여 약 3.79%~14.38% 정도의 감소효과를 나타내었다.

Model Based Filtered Backprojection Algorithm: A Tutorial

Gengsheng L. Zeng 대한의용생체공학회 2014 Biomedical Engineering Letters (BMEL) Vol.4 No.1

Purpose People have been wandering for a long timewhether a filtered backprojection (FBP) algorithm is able toincorporate measurement noise in image reconstruction. Thepurpose of this tutorial is to develop such an FBP algorithmthat is able to minimize an objective function with anembedded noise model. Methods An objective function is first set up to modelmeasurement noise and to enforce some constraints so thatthe resultant image has some pre-specified properties. Aniterative algorithm is used to minimize the objective function,and then the result of the iterative algorithm is converted intothe Fourier domain, which in turn leads to an FBP algorithm. The model based FBP algorithm is almost the same as theconventional FBP algorithm, except for the filtering step. Results The model based FBP algorithm has been applied tolow-dose x-ray CT, nuclear medicine, and real-time MRIapplications. Compared with the conventional FBP algorithm,the model based FBP algorithm is more effective in reducingnoise. Even though an iterative algorithm can achieve thesame noise-reducing performance, the model based FBPalgorithm is much more computationally efficient. Conclusions The model based FBP algorithm is an efficientand effective image reconstruction tool. In many applications,it can replace the state-of-the-art iterative algorithms, whichusually have a heavy computational cost. The model basedFBP algorithm is linear and it has advantages over a nonlineariterative algorithm in parametric image reconstruction andnoise analysis.

Optimal Viewpoint Extraction of 3D Model Based on AdaBoost Iterative Algorithm

Dong Tao 보안공학연구지원센터 2016 International Journal of Multimedia and Ubiquitous Vol.11 No.1

According to the limitations of a single measurement algorithm in the current 3D models’ viewpoint extraction, this essay puts forward a viewpoint extraction algorithm based on AdaBoost iterative algorithm, which can make the features adaptive automatically. It, firstly, extracts 3D models’ feature descriptor and feature vector in the model library and adopts AdaBoost iterative algorithm to establish rules about classification and matching from geometric features and various viewpoint extraction algorithm; then, it constructs decision classifier in order to extract optimal viewpoint. In query process, the model obtains viewpoint extraction algorithm which can suit its geometric feature through decision classifier and then gets its best view by calculation. The experimental result shows this algorithm extraction effect is superior to the one by a single measurement algorithm.

A Preconditioner for the LSQR algorithm

Saeed Karimi,Davod Khojasteh Salkuyeh,Faezeh Toutounian 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.1

Iterative methods are often suitable for solving least squares problems min∥Ax − b∥₂, where A ∈ Rm×n is large and sparse. The well known LSQR algorithm is among the iterative methods for solving these problems. A good preconditioner is often needed to speedup the LSQR convergence. In this paper we present the numerical experiments of applying a well known preconditioner for the LSQR algorithm. The preconditioner is based on the ATA-orthogonalization process which furnishes an incomplete upper-lower factorization of the inverse of the normal matrix ATA. The main advantage of this preconditioner is that we apply only one of the factors as a right preconditioner for the LSQR algorithm applied to the least squares problem min∥Ax − b∥₂. The preconditioner needs only the sparse matrix-vector product operations and significantly reduces the solution time compared to the unpreconditioned iteration. Finally, some numerical experiments on test matrices from Harwell-Boeing collection are presented to show the robustness and efficiency of this preconditioner. Iterative methods are often suitable for solving least squares problems min∥Ax − b∥₂, where A ∈ Rm×n is large and sparse. The well known LSQR algorithm is among the iterative methods for solving these problems. A good preconditioner is often needed to speedup the LSQR convergence. In this paper we present the numerical experiments of applying a well known preconditioner for the LSQR algorithm. The preconditioner is based on the ATA-orthogonalization process which furnishes an incomplete upper-lower factorization of the inverse of the normal matrix ATA. The main advantage of this preconditioner is that we apply only one of the factors as a right preconditioner for the LSQR algorithm applied to the least squares problem min∥Ax − b∥₂. The preconditioner needs only the sparse matrix-vector product operations and significantly reduces the solution time compared to the unpreconditioned iteration. Finally, some numerical experiments on test matrices from Harwell-Boeing collection are presented to show the robustness and efficiency of this preconditioner.

A new algorithm of abstracting numeric image outline

Xiao-Feng Shang,Xue-Heng Tao,Xin Zhao,Jin-Shi Lu 한국멀티미디어학회 2006 한국멀티미디어학회 국제학술대회 Vol.2006 No.-

A new algorithm based on iterative-dynamic algorithm and edge detection algorithm has been formulated in this paper. In the experiment, the binary image was first introduced by iterative-dynamic threshold algorithm, which had a good performance in restraining noise. Gauss filter was then applied to the binary image in order to eliminate some false edge pixels; statistic and differential coefficient methods were used for calculating the grads-in-image of scope and direction. The object edge was hereby detected and abstracted by using double threshold. Compared with traditional edge abstraction algorithm, the algorithm is advanced in solving the main problem that traditional edge abstraction was in the face of. By reason of using iterative-dynamic algorithm in the first step, it has perfect quality in restraining variety of disturbing factor, like random noise, optic distortion, light intensity and so on. Due to the application of statistic and differential coefficient, the perfect outcome was realized. The results of experiments have indicated that the edge of complex image can be precisely abstracted and the drawbacks of traditional edge detection algorithm can be thoroughly overcome by means of this method.

Fast division algorithm and its architecture over GF(2m)

Min-Sup Kang 보안공학연구지원센터(JSE) 2017 보안공학연구논문지 Vol.14 No.4

In this paper, a hardware algorithm is first proposed for executing fast division over GF(2m), and then new hardware architecture is presented based on the algorithm. The algorithm is based on the existing Extended binary GCD algorithm using standard basis representation. However, the proposed method adopts a technique which uses only two 1-bit flags for comparing the magnitude of S and R while the existing methods use m-bit comparator. From implementation results, the proposed algorithm is shown to achieve the best performance in both area and speed aspects over the existing algorithms. The designed 163- bit iterative divider operates at a clock frequency of about 359 MHz on Xilinx FPGA with Virtex4-xc4vlx15 target device.

ONE NEW TYPE OF INTERLEAVED ITERATIVE ALGORITHM FOR H-MATRICES

Qing Tuo,Jianzhou Liu 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.1

In the theory and the applications of Numerical Linear Al- gebra, the class of H-matrices is very important. In recent years, many appeared works have proposed iterative criterion for H-matrices. In this paper, we provide a new type of interleaved iterative algorithm, which is always convergent in finite steps for H-matrices and needs fewer iterations than those proposed in the related works, and a corresponding algorithm for general matrix, which eliminates the redundant computations when the given matrix is not an H-matrix. Finally, several numerical examples are presented to show the effectiveness of the proposed algorithms. In the theory and the applications of Numerical Linear Al- gebra, the class of H-matrices is very important. In recent years, many appeared works have proposed iterative criterion for H-matrices. In this paper, we provide a new type of interleaved iterative algorithm, which is always convergent in finite steps for H-matrices and needs fewer iterations than those proposed in the related works, and a corresponding algorithm for general matrix, which eliminates the redundant computations when the given matrix is not an H-matrix. Finally, several numerical examples are presented to show the effectiveness of the proposed algorithms.

Improved Iterative Closest Point Algorithm using Truncated Signed Distance Function

Hanjun Kim,H. K. Hong,B. H. Lee 제어로봇시스템학회 2018 제어로봇시스템학회 국제학술대회 논문집 Vol.2018 No.10

Truncated signed distance is one of the methods to represent 3D spatial information by using the distance from the surface of an object, and is mainly used for 3D dense reconstruction. When using truncated signed distance value for 3D reconstruction, iterative closest point algorithm is generally used for matching two point clouds. However, iterative closest point algorithm for 3D reconstruction uses only the geometric information of point clouds themselves. Due to lack of information in the surface structure, it is possible to fall in the local minimum or occur convergence failure in iteration process. To solve these problems, we use additional information from truncated signed distance function values. As we optimize the joint objective function composed of the geometric information and the truncated signed distance function information, it is possible to register two point clouds to be more robust in iterative closest point algorithm. Experimental results demonstrate that the proposed method outperforms the conventional method using only a geometric information.