a)
Domain decomposition algorithms.
We
study domain decomposition algorithms applied to the image restoration
problem. The problem of recovering an image blurred by a space variant
Point Spread Function is an ill posed problem modelled by a Fredholm integral
equation of the first kind. The discretization of this equation leads to
an ill conditioned linear system of very large size that is solved with
the Thikonov regularization method. Its solution requires hours of
computation on scalar computers. We solve the problem by using a domain
decomposition strategy, that is by partitioning the image domain with suitable
border conditions, and by solving the restoration subproblems in parallel.
This method dramatically lower the computational complexity of the problem.
We tested the application with different domain decompositions on various
parallel architectures, such as transputers, clusters of workstation and
the Cray.
b)
Linear algebra algorithms.
The
basic linear algebra algorithms are used in many different applications
and methods. For this reason, it is important to optimize them when using
parallel architectures.
Since
ten years we've been studying parallel algorithms for the solution
of linear systems on distributed and parallel architectures. We have considered
both direct methods (parallel implementations of LU decompositions and
triangular solvers) and iterative methods of conjugate gradient type. We
first implemented the methods ontransputers
and then we used Cray t3D (64 processors) and Cray t3E (256 processors)
at CINECA.
Publications
·E.Loli
Piccolomini,F. Zama, Parallel Image
Restoration with domain decomposition, Special issue
on Fast-Energy-Minimization-Base Imaging and Vision Techniques on Real--Time
Imaging, 2001.
·A.
Bevilacqua,E.Loli Piccolomini , Parallel
image restoration on parallel and distributed computers, Parallel
Computing, v.26,n.4, pp. 459--506, 2000.
·A.
Baronio,F. Zama, A domain Decomposition technique for spline image
restoration on distributed memory systems , Parallel Computing
,22:101-110 (1996)
·E.
Loli Piccolomini,F. Zama, Parallel Image Restoration on Clusters
of Workstations, Atti del Convegno IASTED Conference Signal and
Image Processing SIP--95, IASTED,1995
·E.
Loli Piccolomini, V. Ruggiero, F. Zama, An Application of the Indirect
Approximation Problem on a Heterogeneous Network of Computing Systems,
Atti del Convegno PARCO95 (Parallel Computing), Elsevier Publishers,1995
·E.
Loli Piccolomini, F. Zama, The Parallel LU Factorization and the
Cray T3D Programming Paradigms, Atti del Convegno PARCO95 (Parallel
Computing), Elsevier Publishers, 1995
·I.
Galligani, E. Loli Piccolomini V. Ruggiero, F. Zama, A substructuring
method for solving the Image Restoration Problem on a Multiprocessor system,
Atti del Convegno SMS TPE 94 (Software for Multiprocessrs and Supercomputers),
IOS Press,1994
·F.
Zama, E. Loli Piccolomini, An Experiment in Image Restoration using
Transputer Networks, Parallel Algorithms and Applications , vol.
6, 1994
·E.
Loli Piccolomini, M. Barulli, Parallel Triangular Solvers on Ring
Transputer Networks, Atti del Convegno Transputer 94, IOS Press,1994
·Loli
Piccolomini, M. Barulli,Parallel Triangular Solvers on Transputer
Network, Atti del Convegno World Transputer Congress IOS Press,1994
·E.
Loli Piccolomini, M. Barulli,Parallel Triangular Solvers on Network
of Transputers, Technical ReportC.N.R. n. 1/186,1993
·E.
Loli Piccolomini, V. Ruggiero, F. Zama, Parallel implementation of
a domain decomposition method for scattered data approximation on multiprocessor
systems , technical ReportC.N.R. n. 1/179,1993.
·E.
Loli Piccolomini, F. Zama, V. Ruggiero, A Domain Decomposition method
for scattered data approximation on a multiprocessor system, Atti
del Convegno Parallel Computing 93(PARCO93) , Elsevier Publishers,1993.
·E.
Loli Piccolomini, V. Ruggiero, F. Zama,Express Performance evaluation
on transputer network, Technical ReportC.N.R. n. 1/98,1992
·E.
Loli Piccolomini, V. Ruggiero, Ricostruzione di immagini su calcolatori
multivettoriali, Technical ReportC.N.R. n. 1/23}, 1990
·Galligani, E. Loli Piccolomini, V. Ruggiero,Numerical solution of the image restoration problem on multivector computer, Parallel Computing: problems, methods and applications (Atti del convegno di Capri, Italy, 3-7 June,1990), P. Messina and A. Murli editors}, Elsevier Publishers, 1990