A parallel multisplitting solution of the least squares problem

Renaut, Rosemary A.

doi:10.1002/(sici)1099-1506(199801/02)5:1<11::aid-nla123>3.0.co;2-f

Cited by 33 publications

(6 citation statements)

References 13 publications

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“…A selection strategy, denoted by "Sel" in the results indicating Selection, is also tested in which at each step the update chosen is that which gives the greatest reduction in the objective function when chosen from the local solutions Y i , the BJ update z (k) and the convex update given by (2.13). This is consistent with the approach presented for the convex cases in [17], [15], and permits evaluation of whether the optimal update is necessary for obtaining a good solution.…”

Section: Evaluation Of the Pvdtls Algorithmssupporting

confidence: 81%

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Parallel variable distribution for total least squares

Guo

Renaut

2005

Numer. Linear Algebra Appl.

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SUMMARYA novel parallel method for determining an approximate total least squares (TLS) solution is introduced. Based on domain distribution, the global TLS problem is partitioned into several dependent TLS subproblems. A convergent algorithm using the parallel variable distribution technique (Ferris and Mangasarian, 1994) is presented. Numerical results support the development and analysis of the algorithms.

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Section: Evaluation Of the Pvdtls Algorithmssupporting

confidence: 81%

“…This approach is suitable for both sparse and dense data structures. The specialization of PVD to the linear least squares problem was presented in [15], [16] and a more general approach was presented in [17].…”

Section: Introductionmentioning

confidence: 99%

Parallel variable distribution for total least squares

Guo

Renaut

2005

Numer. Linear Algebra Appl.

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“…Another method of acceleration is to combine the iterative algorithms with parallel computing schemes. One example would be partitioning the projection data, pixels, or system matrix, relating the former two, and then operating on subsets, which would allow parallel computation (Renaut 1998, Jiang et al 2013, Lu and Xiao 2015, Gao and Blumensath 2018. Decomposing the optimization problem into several sub-problems is also an effective way to enable parallelization, such as what occurs in the alternating direction method of multipliers (ADMM) for convex problems (Boyd et al 2011, Parikh and Boyd 2014, Deng et al 2017.…”

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confidence: 99%

A fast regularized iterative algorithm for fan-beam CT reconstruction

et al. 2019

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We propose a fast iterative image reconstruction algorithm for normal, short-scan, and super-short-scan fan-beam computed tomography (CT), which aims at iterative reconstruction for low-dose and few-view CT by minimizing a data-fidelity term regularized with a total variation (TV) penalty. The derivation of the algorithm can be outlined as follows. First, the original minimization problem is formulated into a saddle-point (primal-dual) problem by using the Lagrangian duality, to which we apply the alternating projection proximal (APP) algorithm, which belongs to a class of first-order primal-dual methods. Second, we precondition the iterative formula using the modified ramp filter of the filtered back-projection (FBP) reconstruction algorithm in such a way that the solution to this preconditioned iteration perfectly coincides with the solution to the original problem. The resulting algorithm converges quickly to the minimizer of the cost function. To demonstrate the advantages of our method, we perform reconstruction experiments using projection data from both numerical phantoms and real CT data. Both qualitative and quantitative results are presented.

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“…To parallelize the stationary iterative methods, space decomposition methods are employed to partition matrix A into blocks (block Jacobi or block SOR) as well as the original problem into smaller local problems (Frommer & Renaut, 1999). Renaut (1998) also proposed a parallel multi-splitting solution of the least-squares problem where the solutions to the local problems are recombined using weighting matrices.…”

Section: Distributed Tomography Algorithmsmentioning

confidence: 99%