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In this work we use a massively parallel architecture for solving the problem of reconstructing human brain sections from experimental data obtained from a Gamma camera equipped with parallel-hole collimators. We compute least-squares regularized solutions by means of weighted conjugate gradient iterations coupled with a suitable stopping rule. The computations are distributed to the CRAY T3E parallel processors following two different decomposition strategies obtaining high speed up values. This decomposition strategy can be easily extended to a wide family of iterative reconstruction algebraic methods. [ABSTRACT FROM AUTHOR]

In this work we consider an inverse ill-posed problem coming from the area of dynamic magnetic resonance imaging (MRI), where high resolution images must be reconstructed from incomplete data sets collected in the Fourier domain. The reduced-encoding imaging by generalized-series reconstruction (RIGR) method used leads to ill-conditioned linear systems with Hermitian Toeplitz matrix and noisy right-hand side. We analyze the behavior of some regularization methods such as the truncated singular value decomposition (TSVD), the Lavrent''yev regularization method and conjugate gradients (CG) type iterative methods. For what concerns the choice of the regularization parameter, we use some known methods and we propose new heuristic criteria for iterative regularization methods. The simulations are carried on test problems obtained from real data acquired on a 1.5 T Phillips system. [Copyright &y& Elsevier]

Medical images obtained with emission processes are corrupted by noise of Poisson type. In the paper the denoising problem is modeled in a Bayesian statistical setting by a nonnegatively constrained minimization problem, where the objective function is constituted by a data fitting term, the Kullback-Leibler divergence, plus a regularization term, the Total Variation function, weighted by a regularization parameter. Aim of the paper is to propose an efficient numerical method for the solution of the constrained problem. The method is a Newton projection method, where the inner system is solved by the Conjugate Gradient method, preconditioned and implemented in an efficient way for this specific application. The numerical results on simulated and real medical images prove the effectiveness of the method, both for the accuracy and the computational cost., (Copyright © 2011 Elsevier Ltd. All rights reserved.)