Browsing by Subject "Linear feasibility"

Now showing 1 - 3 of 3

Unknown
Algorithms for linear and convex feasibility problems: A brief study of iterative projection, localization and subgradient methods
(1998) Özaktaş, Hakan
Several algorithms for the feasibility problem are investigated. For linear systems, a number of different block projections approaches have been implemented and compared. The parallel algorithm of Yang and Murty is observed to be much slower than its sequential counterpart. Modification of the step size has allowed us to obtain a much better algorithm, exhibiting considerable speedup when compared to the sequential algorithm. For the convex feasibility problem an approach combining rectangular cutting planes and subgradients is developed. Theoretical convergence results are established for both ca^es. Two broad classes of image recovery problems are formulated as linear feasibility problems and successfully solved with the algorithms developed.
Unknown
Parallel algorithms for the solution of large sparse inequality systems on distributed memory architectures
(1998) Turna, Esma
In this thesis, several parallel algorithms are proposed and utilized for the solution of large sparse linear inequality systems. The parallelization schemes are developed from the coarse-grain parallel formulation of the surrogate constraint method, based on the partitioning strategy: 1D partitioning and 2D partitioning. Furthermore, a third parallelization scheme is developed for the explicit minimization of the communication overhead in 1D partitioning, by using hypergraph partitioning. Utilizing the hypergraph model, the communication overhead is maintained via a global communication scheme and a local communication scheme. In addition, new algorithms that use the bin packing heuristic are investigated for efficient load balancing in uniform rowwise stripped and checkerboard partitioning. A general class of image recovery problems is formulated as a linear inequality system. The restoration of images blurred by so called point spread functions arising from effects such as misfocus of the photographic device, atmospheric turbulence, etc. is successfully provided with the developed parallel algorithms.
Open Access
Restoration of space-variant global blurs caused by severe camera movements and coordinate distortions
(IOP Science, 1998) Özaktaş, H.; Pınar, M. Ç.; Akgül, M.
We show that a broad class of image recovery problems where an object undergoing an arbitrary two-dimensional, time- and space-variant, non-separable, nonlinear global coordinate distortion, is imaged for a certain duration, can be formulated as a system of linear inequalities. Since the system of inequalities arising in this context can be solved efficiently, our approach yields an effective method for solving this class of image recovery problems. A novel step size policy is introduced to accelerate the parallel surrogate constraint algorithm employed. The approach is illustrated by recovering an image severely blurred by the combined effects of translational and rotational motion and elliptic scaling.