1,720,995 research outputs found
A variational approach to Gibbs artifacts removal in MRI
Full text linkGibbs ringing is a feature of MR images caused by the finite sampling of the acquisition space (k-space). It manifests itself with ringing patterns around sharp edges which become increasingly significant for low-resolution acquisitions. In this paper, we model the Gibbs artefact removal as a constrained variational problem where the data discrepancy, represented in denoising and convolutive form, is balanced to sparsity-promoting regularization functions such as Total Variation, Total Generalized Variation and L1 norm of the Wavelet transform. The efficacy of such models is evaluated by running a set of numerical experiments both on synthetic data and real acquisitions of brain images. The Total Generalized Variation penalty coupled with the convolutive data discrepancy term yields, in general, the best results both on synthetic and real data
A domain decomposition technique for spline image restoration on distributed memory systems
No full textThe problem of image restoration is considered when the point spread function is Space Variant Non Separable. The algorithm determines a continuous approximation of the original object, following the continuous object-discrete image approach. The image spatial domain is decomposed into subdomains and the local approximants are computed on a distributed memory environment. The continuity of the solution across the image subdomains is obtained by adding a suitable overlapping area to the sides of the subdomains. Numerical experiments have been carried out on a Hypercube Intel iPSC/860 and the most interesting results are reported
The conjugate gradient regularization method in Computed Tomography problems
No full textIn this work we solve inverse problems coming from the area of Computed Tomography by means of regularization methods based on conjugate gradient iterations. We develop a stopping criterion which is efficient for the computation of a regularized solution for the least-squares normal equations. The stopping rule can be suitably applied also to the Tikhonov regularization method. We report computational experiments based on different physical models and with different degrees of noise. We compare the results obtained with those computed by other currently used methods such as Algebraic Reconstruction Techniques (ART) and Backprojection
An experiment in image restoration using transputer networks
No full textThe problem of image restoration, with a blurring function linear, space-variant and nonseparable, has been solved on a transputer network, using primitives of Parasoft express environment and A.C.S. Arnia Library. A domain decomposition strategy has been introduced to split the problem among the processors. Some interesting computational results are reported. © 1995, Taylor & Francis Group, LLC. All rights reserved
Parallel image restoration with domain decomposition
No full textIn this paper we present parallel algorithms to solve the problem of image restoration when the Point Spread Function is Space Variant. The problem has a very high computational complexity and it is very hard to solve it on scalar computers. The algorithms are based on the decomposition of the image spatial domain and on the solution of both constrained and unconstrained restoration subproblems of size smaller than the original. The main results can be summarized as follows: (a) the quality of restorations do not depend on the number of subdomains; (b) the unconstrained restoration is scalable and efficient even with a large number of processors while the constrained restoration is efficient for subdomains of more than 50×50 pixels. The numerical tests have been executed on a Cray T3E with 128 processors and on a network of workstations
An experiment of parallel spect data reconstruction
No full textIn 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
A fast splitting method for efficient Split Bregman iterations
Full text linkIn this paper we propose a new fast splitting algorithm to solve the Weighted Split Bregman minimization problem in the backward step of an accelerated Forward–Backward algorithm. Beside proving the convergence of the method, numerical tests, carried out on different imaging applications, prove the accuracy and computational efficiency of the proposed algorithm
A descent method for computing the Tikhonov regularized solution of linear inverse problems
No full textIn this paper we describe an iterative algorithm, called Descent-TCG, based on truncated Conjugate Gradient iterations to compute Tikhonov regularized solutions of linear ill-posed problems. Suitable termination criteria are built-up to define an inner-outer iteration scheme for the computation of a regularized solution. Numerical experiments are performed to compare the algorithm with other well-established regularization methods. We observe that the best Descent-TCG results occur for highly noised data and we always get fairly reliable solutions, preventing the dangerous error growth often appearing in other well-established regularization methods. Finally, the Descent-TCG method is computationally advantageous especially for large size problems
A method for solving the indirect approximation problem
No full textThis paper presents a regularization method combined with bivariate spline functions for approximating experimental data affected by degradation errors. Some issues concerning the implementation of the method are given. Numerical experiments on two test problems from different fields of application are presented and analized. © Elsevier Science Inc., 1996
Explicit exactly energy-conserving methods for Hamiltonian systems
Full text linkFor Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each time step, or are explicit, but where the exact conservation property depends on the exact evaluation of an integral in continuous time. Under further restrictions, namely that the potential energy contribution to the Hamiltonian is non-negative, newer techniques based on invariant energy quadratisation allow for exact numerical energy conservation and yield linearly implicit updates, requiring only the solution of a linear system at each time step. In this article, it is shown that, for a general class of Hamiltonian systems, and under the non-negativity condition on potential energy, it is possible to arrive at a fully explicit method that exactly conserves numerical energy. Furthermore, such methods are unconditionally stable, and are of comparable computational cost to the very simplest integration methods (such as Störmer-Verlet). A variant of this scheme leading to a conditionally-stable method is also presented, and follows from a splitting of the potential energy. Various numerical results are presented, in the case of the classic test problem of Fermi, Pasta and Ulam and for nonlinear systems of partial differential equations, including those describing high amplitude vibration of strings and plates
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