• Journal of applied mathematics & informatics
• /
• v.36 no.5_6
• /
• pp.381-396
• /
• 2018

In this paper we have considered a system of mixed generalized variational inequality problems defined on two different domains in a Hilbert space. It has been shown that the solution of a system of mixed generalized variational inequality problems is equivalent to altering point formulation of some mappings. A new parallel S-iteration type process has been considered which converges strongly to the solution of a system of mixed generalized variational inequality problems.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.17 no.10
• /
• pp.2252-2258
• /
• 2013

In this paper, parallel orthogonal matching pursuit (POMP) is proposed to supplement the simultaneous orthogonal matching pursuit (S-OMP) which has been widely used as a greedy algorithm for sparse signal recovery for multiple measurement vector (MMV) problem. The process of POMP is simple but effective: (1) multiple indexes maximally correlated with the observation vector are chosen at the first iteration, (2) the conventional S-OMP process is carried out in parallel for each selected index, (3) the index set which yields the minimum residual is selected for reconstructing the original sparse signal. Empirical simulations show that POMP for MMV outperforms than the conventional S-OMP both in terms of exact recovery ratio (ERR) and mean-squared error (MSE).

• Nuclear Medicine and Molecular Imaging
• /
• v.43 no.5
• /
• pp.443-450
• /
• 2009

Purpose: Conventional image reconstruction uses simplified physical models of projection. However, real physics, for example 3D reconstruction, takes too long time to process all the data in clinic and is unable in a common reconstruction machine because of the large memory for complex physical models. We suggest the realistic distributed memory model of fast-reconstruction using parallel processing on personal computers to enable large-scale technologies. Materials and Methods: The preliminary tests for the possibility on virtual manchines and various performance test on commercial super computer, Tachyon were performed. Expectation maximization algorithm with common 2D projection and realistic 3D line of response were tested. Since the process time was getting slower (max 6 times) after a certain iteration, optimization for compiler was performed to maximize the efficiency of parallelization. Results: Parallel processing of a program on multiple computers was available on Linux with MPICH and NFS. We verified that differences between parallel processed image and single processed image at the same iterations were under the significant digits of floating point number, about 6 bit. Double processors showed good efficiency (1.96 times) of parallel computing. Delay phenomenon was solved by vectorization method using SSE. Conclusion: Through the study, realistic parallel computing system in clinic was established to be able to reconstruct by plenty of memory using the realistic physical models which was impossible to simplify.