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

Accelerating two projection methods via perturbations with application to Intensity-Modulated Radiation Therapy

Constrained convex optimization problems arise naturally in many real-world applications. One strategy to solve them in an approximate way is to translate them into a sequence of convex feasibility problems via the recently developed level set scheme and then solve each feasibility problem using projection methods. However, if the problem is ill-conditioned, projection methods often show zigzagging behavior and therefore converge slowly. To address this issue, we exploit the bounded perturbation resilience of the projection methods and introduce two new perturbations which avoid zigzagging behavior. The first perturbation is in the spirit of $k$-step methods and uses gradient information from previous iterates. The second uses the approach of surrogate constraint methods combined with relaxed, averaged projections. We apply two different projection methods in the unperturbed version, as well as the two perturbed versions, to linear feasibility problems along with nonlinear optimization problems arising from intensity-modulated radiation therapy (IMRT) treatment planning. We demonstrate that for all the considered problems the perturbations can significantly accelerate the convergence of the projection methods and hence the overall procedure of the level set scheme. For the IMRT optimization problems the perturbed projection methods found an approximate solution up to 4 times faster than the unperturbed methods while at the same time achieving objective function values which were 0.5 to 5.1% lower.Comment: Accepted for publication in Applied Mathematics & Optimizatio

Optimal relay location and power allocation for low SNR broadcast relay channels

We consider the broadcast relay channel (BRC), where a single source transmits to multiple destinations with the help of a relay, in the limit of a large bandwidth. We address the problem of optimal relay positioning and power allocations at source and relay, to maximize the multicast rate from source to all destinations. To solve such a network planning problem, we develop a three-faceted approach based on an underlying information theoretic model, computational geometric aspects, and network optimization tools. Firstly, assuming superposition coding and frequency division between the source and the relay, the information theoretic framework yields a hypergraph model of the wideband BRC, which captures the dependency of achievable rate-tuples on the network topology. As the relay position varies, so does the set of hyperarcs constituting the hypergraph, rendering the combinatorial nature of optimization problem. We show that the convex hull C of all nodes in the 2-D plane can be divided into disjoint regions corresponding to distinct hyperarcs sets. These sets are obtained by superimposing all k-th order Voronoi tessellation of C. We propose an easy and efficient algorithm to compute all hyperarc sets, and prove they are polynomially bounded. Using the switched hypergraph approach, we model the original problem as a continuous yet non-convex network optimization program. Ultimately, availing on the techniques of geometric programming and $p$-norm surrogate approximation, we derive a good convex approximation. We provide a detailed characterization of the problem for collinearly located destinations, and then give a generalization for arbitrarily located destinations. Finally, we show strong gains for the optimal relay positioning compared to seemingly interesting positions.Comment: In Proceedings of INFOCOM 201

New iterative methods for linear inequalities

New iterative methods for solving systems of linear inequalities are presented. Each step in these methods consists of finding the orthogonal projection of the current point onto a hyperplane corresponding to a surrogate constraint which is constructed through a positive combination of a group of violated constraints. Both sequential and parallel implementations are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45240/1/10957_2004_Article_BF00939954.pd

The P-norm surrogate-constraint algorithm for polynomial zero-one programming.

by Wang Jun.Thesis (M.Phil.)--Chinese University of Hong Kong, 1999.Includes bibliographical references (leaves 82-86).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Background --- p.1Chapter 1.2 --- The polynomial zero-one programming problem --- p.2Chapter 1.3 --- Motivation --- p.3Chapter 1.4 --- Thesis outline --- p.4Chapter 2 --- Literature Survey --- p.6Chapter 2.1 --- Lawler and Bell's method --- p.7Chapter 2.2 --- The covering relaxation algorithm for polynomial zero-one pro- gramming --- p.8Chapter 2.3 --- The method of reducing polynomial integer problems to linear zero- one problems --- p.9Chapter 2.4 --- Pseudo-boolean programming --- p.11Chapter 2.5 --- The Balasian-based algorithm for polynomial zero-one programming --- p.12Chapter 2.6 --- The hybrid algorithm for polynomial zero-one programming --- p.12Chapter 3 --- The Balasian-based Algorithm --- p.14Chapter 3.1 --- The additive algorithm for linear zero-one programming --- p.15Chapter 3.2 --- Some notations and definitions referred to the Balasian-based al- gorithm --- p.17Chapter 3.3 --- Identification of all the feasible solutions to the master problem --- p.18Chapter 3.4 --- Consistency check of the feasible partial solutions --- p.19Chapter 4 --- The p-norm Surrogate Constraint Method --- p.21Chapter 4.1 --- Introduction --- p.21Chapter 4.2 --- Numerical example --- p.23Chapter 5 --- The P-norm Surrogate-constraint Algorithm --- p.26Chapter 5.1 --- Main ideas --- p.26Chapter 5.2 --- The standard form of the polynomial zero-one programming problem --- p.27Chapter 5.3 --- Definitions and notations --- p.29Chapter 5.3.1 --- Partial solution in x --- p.29Chapter 5.3.2 --- Free term --- p.29Chapter 5.3.3 --- Completion --- p.29Chapter 5.3.4 --- Feasible partial solution --- p.30Chapter 5.3.5 --- Consistent partial solution --- p.30Chapter 5.3.6 --- Partial solution in y --- p.30Chapter 5.3.7 --- Free variable --- p.31Chapter 5.3.8 --- Augmented solution in x --- p.31Chapter 5.4 --- Solution concepts --- p.33Chapter 5.4.1 --- Fathoming --- p.33Chapter 5.4.2 --- Backtracks --- p.41Chapter 5.4.3 --- Determination of the optimal solution in y --- p.42Chapter 5.5 --- Solution algorithm --- p.42Chapter 6 --- Numerical Examples --- p.46Chapter 6.1 --- Solution process by the new algorithm --- p.46Chapter 6.1.1 --- Example 5 --- p.46Chapter 6.1.2 --- Example 6 --- p.57Chapter 6.2 --- Solution process by the Balasian-based algorithm --- p.61Chapter 6.3 --- Comparison between the p-norm surrogate constraint algorithm and the Balasian-based algorithm --- p.71Chapter 7 --- Application to the Set Covering Problem --- p.74Chapter 7.1 --- The set covering problem --- p.74Chapter 7.2 --- Solving the set covering problem by using the new algorithm . .。 --- p.75Chapter 8 --- Conclusions and Future Work --- p.80Bibliography --- p.8

Convergent surrogate-constraint dynamic programming.

Wang Qing.Thesis (M.Phil.)--Chinese University of Hong Kong, 2006.Includes bibliographical references (leaves 72-74).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Literature survey --- p.2Chapter 1.2 --- Research carried out in this thesis --- p.4Chapter 2 --- Conventional Dynamic Programming --- p.7Chapter 2.1 --- Principle of optimality and decomposition --- p.7Chapter 2.2 --- Backward dynamic programming --- p.12Chapter 2.3 --- Forward dynamic programming --- p.15Chapter 2.4 --- Curse of dimensionality --- p.19Chapter 2.5 --- Singly constrained case --- p.21Chapter 3 --- Surrogate Constraint Formulation --- p.24Chapter 3.1 --- Conventional surrogate constraint formulation --- p.24Chapter 3.2 --- Surrogate dual search --- p.26Chapter 3.3 --- Nonlinear surrogate constraint formulation --- p.30Chapter 4 --- Convergent Surrogate Constraint Dynamic Programming: Objective Level Cut --- p.38Chapter 5 --- Convergent Surrogate Constraint Dynamic Programming: Domain Cut --- p.44Chapter 6 --- Computational Results and Analysis --- p.60Chapter 6.1 --- Sample problems --- p.61Chapter 7 --- Conclusions --- p.7

Parallel algorithms for the solution of large sparse inequality systems on distributed memory architectures

Ankara : Department of Computer Engineering and Information Science and the Institute of Engineering and Science of Bilkent University, 1998.Thesis (Master's) -- Bilkent University, 1998.Includes bibliographical references leaves 101-104.Turna, EsmaM.S