Parallel image restoration

Cataloged from PDF version of article.In this thesis, we are concerned with the image restoration problem which has been formulated in the literature as a system of linear inequalities. With this formulation, the resulting constraint matrix is an unstructured sparse-matrix and even with small size images we end up with huge matrices. So, to solve the restoration problem, we have used the surrogate constraint methods, that can work efficiently for large size problems and are amenable for parallel implementations. Among the surrogate constraint methods, the basic method considers all of the violated constraints in the system and performs a single block projection in each step. On the other hand, parallel method considers a subset of the constraints, and makes simultaneous block projections. Using several partitioning strategies and adopting different communication models we have realized several parallel implementations of the two methods. We have used the hypergraph partitioning based decomposition methods in order to minimize the communication costs while ensuring load balance among the processors. The implementations are evaluated based on the per iteration performance and on the overall performance. Besides, the effects of different partitioning strategies on the speed of convergence are investigated. The experimental results reveal that the proposed parallelization schemes have practical usage in the restoration problem and in many other real-world applications which can be modeled as a system of linear inequalities.Malas, TahirM.S

Effective preconditioners for iterative solutions of large-scale surface-integral-equation problems

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 2010.Thesis (Ph.D.) -- Bilkent University, 2010.Includes bibliographical references leaves 171-187.A popular method to study electromagnetic scattering and radiation of threedimensional electromagnetics problems is to solve discretized surface integral equations, which give rise to dense linear systems. Iterative solution of such linear systems using Krylov subspace iterative methods and the multilevel fast multipole algorithm (MLFMA) has been a very attractive approach for large problems because of the reduced complexity of the solution. This scheme works well, however, only if the number of iterations required for convergence of the iterative solver is not too high. Unfortunately, this is not the case for many practical problems. In particular, discretizations of open-surface problems and complex real-life targets yield ill-conditioned linear systems. The iterative solutions of such problems are not tractable without preconditioners, which can be roughly defined as easily invertible approximations of the system matrices. In this dissertation, we present our efforts to design effective preconditioners for large-scale surface-integral-equation problems. We first address incomplete LU (ILU) preconditioning, which is the most commonly used and well-established preconditioning method. We show how to use these preconditioners in a blackbox form and safe manner. Despite their important advantages, ILU preconditioners are inherently sequential. Hence, for parallel solutions, a sparseapproximate-inverse (SAI) preconditioner has been developed. We propose a novel load-balancing scheme for SAI, which is crucial for parallel scalability. Then, we improve the performance of the SAI preconditioner by using it for the iterative solution of the near-field matrix system, which is used to precondition the dense linear system in an inner-outer solution scheme. The last preconditioner we develop for perfectly-electric-conductor (PEC) problems uses the same inner-outer solution scheme, but employs an approximate version of MLFMA for inner solutions. In this way, we succeed to solve many complex real-life problems including helicopters and metamaterial structures with moderate iteration counts and short solution times. Finally, we consider preconditioning of linear systems obtained from the discretization of dielectric problems. Unlike the PEC case, those linear systems are in a partitioned structure. We exploit the partitioned structure for preconditioning by employing Schur complement reduction. In this way, we develop effective preconditioners, which render the solution of difficult real-life problems solvable, such as dielectric photonic crystals.Malas, TahirPh.D

INCOMPLETE LU PRECONDITIONING FOR THE ELECTRIC-FIELD INTEGRAL EQUATION

ABSTRACT Linear systems resulting from the electric-field integral equation (EFIE) become ill-conditioned, particularly for large-scale problems. Hence, effective preconditioners should be used to obtain the iterative solution with the multilevel fast multipole algorithm in a reasonable time. In this paper, we show that a threshold-based incomplete LU (ILU) preconditioner, i.e., ILUT, can be used safely for such systems, provided that column pivoting is applied for the stability of the incomplete factors. It is observed that the resulting preconditioner ILUTP reduces the solution times by an order of magnitude, compared to simple Jacobi preconditioner. Moreover, we also use the iterative solution of the nearfield system as a preconditioner, and use ILUTP as the preconditioner for the near-field system. This way, the effectiveness of the ILUTP is further improve

Parallel preconditioners for solutions of dense linear systems with tens of millions of unknowns

We propose novel parallel preconditioning schemes for the iterative solution of integral equation methods. In particular, we try to improve convergence rate of the ill-conditioned linear systems formulated by the electric-field integral equation, which is the only integral-equation formulation for targets having open surfaces. For moderate-size problems, iterative solution of the neat-field system enables much faster convergence compared to the widely used sparse approximate inverse preconditioner. For larger systems, we propose an approximation strategy to the multilevel fast multipole algorithm (MLFMA) to be used as a preconditioner. Our numerical experiments reveal that this scheme significantly outperforms other preconditioners. With the combined effort of effective preconditioners and an efficiently parallelized MLFMA, we are able to solve targets with tens of millions of unknowns, which are the largest problems ever reported in computational electromagnetics

Approximate MLFMA as an efficient preconditioner

In this work, we propose a preconditioner that approximates the dense system operator. For this purpose, we develop an approximate multilevel fast multipole algorithm (AMLFMA), which performs a much faster matrix-vector multiplication with some relative error compared to the original MLFMA. We use AMLFMA to solve a closely related system, which makes up the preconditioner. Then, this solution is embedded in the main solution that uses MLFMA. By taking into account the far-field elements wisely, this preconditioner proves to be much more effective compared to the near-field preconditioners

Sequential and parallel preconditioners for Large-scale integral-equation problems

For efficient solutions of integral-equation methods via the multilevel fast multipole algorithm (MLFMA), effective preconditioners are required. In this paper we review appropriate preconditioners that have been used for sparse systems and developed specially in the context of MLFMA. First we review the ILU-type preconditioners that are suitable for sequential implementations. We can make these preconditioners robust and efficient for integral-equation methods by making appropriate selections and by employing pivoting to suppress the instability problem. For parallel implementations, the sparse approximate inverse or the iterative solution of the near-field system enables fast convergence up to certain problem sizes. However, for very large problems, the near-field matrix itself becomes insufficient to approximate the dense system matrix and preconditioners generated from the near-field interactions cannot be effective. Therefore, we propose an approximation strategy to MLFMA to be used as an effective preconditioner. Our numerical experiments reveal that this scheme significantly outperforms other preconditioners. With the combined effort of effective preconditioners and an efficiently parallelized MLFMA, we are able to solve problems with tens of millions of unknowns in a few hours. We report the solution of integral-equation problems that are among the largest in their classes

Preconditioning iterative MLFMA solutions of integral equations

The multilevel fast multipole algorithm (MLFMA) is a powerful method that enables iterative solutions of electromagnetics problems with low complexity. Iterative solvers, however, are not robust for three-dimensional complex reallife problems unless suitable preconditioners are used. In this paper, we present our efforts to devise effective preconditioners for MLFMA solutions of difficult electromagnetics problems involving both conductors and dielectrics

Efficient preconditioning strategies for the multilevel fast multipole algorithm

For the iterative solutions of the integral equation methods employing the multilevel fast multipole algorithm (MLFMA), effective preconditioning techniques should be developed for robustness and efficiency. Preconditioning techniques for such problems can be broadly classified as fixed preconditioners that are generated from the sparse near-field matrix and variable ones that can make use of MLFMA with the help of the flexible solvers. Among fixed preconditioners, we show that an incomplete LU preconditioner depending on threshold (ILUT) is very successful in sequential implementations, provided that pivoting is applied whenever the incomplete factors become unstable. For parallel preconditioners, sparse approximate inverses (SAI) can be used; however, they are not as successful as ILUT for the electric-field integral equation. For a remedy, we employ variable preconditioning, and we iteratively solve the neax-field system in each major iteration. However, for very large systems, neither of these methods succeeds to reduce the iteration counts as desired because of the thinning of the near-field matrices for increasing problem sizes. Considering this fact, we develop a preconditioner using MLFMA, with which we solve an approximate system. Respective advantages of these different preconditioners are demonstrated on a variety of problems ranging in both geometry and size

Analysis of Dielectric Photonic-Crystal Problems With MLFMA and Schur-Complement Preconditioners

We present rigorous solutions of electromagnetics problems involving 3-D dielectric photonic crystals (PhCs). Problems are formulated with recently developed surface integral equations and solved iteratively using the multilevel fast multipole algorithm (MLFMA). For efficient solutions, iterations are accelerated via robust Schur-complement preconditioners. We show that complicated PhC structures can be analyzed with unprecedented efficiency and accuracy by an effective solver based on the combined tangential formulation, MLFMA, and Schur-complement preconditioners