Multicore Performance of Block Algebraic Iterative Reconstruction Methods

Sørensen, Henrik Rokkjær; Hansen, Per Christian

doi:10.1137/130920642

Cited by 27 publications

(15 citation statements)

References 39 publications

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“…All the iterative methods can include constraints that can be formulated as a projection on a convex set; we provide box constraints which include, as a special case, nonnegativity constraints. Our package does not include implementations of any block versions [39] of the above methods; such methods are highly suitable for large-scale problems but MATLAB is not the right platform for such software.…”

Section: Introductionmentioning

confidence: 99%

AIR Tools II: algebraic iterative reconstruction methods, improved implementation

2017

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Section: Introductionmentioning

confidence: 99%

AIR Tools II: algebraic iterative reconstruction methods, improved implementation

2017

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“…In a practical sense this amounts to ordering the projection data so that the achieved by a randomised ordering scheme [21]. …”

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confidence: 99%

Limited view X-ray tomography for dimensional measurements

Jones

Huthwaite

2018

NDT & E International

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6The growing use of complex and irregularly shaped components for safetycritical applications has increasingly led to the adoption of X-ray CT as an NDE inspection tool. Standard X-ray CT methods require thousands of projections, each regularly distributed evenly through 360• to produce an accurate image. The time consuming acquisition of thousands of projections can lead to significant bottlenecks. Recent developments in medical imaging driven by both increasing computational power and the desire to reduce patient X-ray exposure have led to the development of a number of limited view CT methodologies.Thus far these limited view algorithms have been applied to basic synthetic data derived from simple medical phantoms. Here, we use experimental data to rigorously test the capability of limited view algorithms to accurately reconstruct and precisely measure the dimensional features of an additive manufactured sample and a turbine blade. Our findings highlight the importance of prior information in producing accurate reconstructions capable of significantly reducing X-ray projections by at least an order of magnitude. In the turbine blade example a dramatic reduction in projections from 5000 to 24 was observed while still demonstrating the same level of accuracy as standard CT methods. The findings of the study also suggest the importance of sample complexity and the presence of sparsity in the X-ray projections in order to maximise the capabilities of these limited algorithms. With the ever increasing computational power limited view CT algorithms offer a method for reducing data acquisition time and alleviating manufacturing throughput bottlenecks without compromising

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“…A proper directed graph depends to the problem (application), how to implement the algorithm and what are the objects of running the algorithm (reducing time, getting a regularized solution, controlling semi‐convergence, ⋯) and so on. However, the paper deals with some special combination of operators. They tested those combinations in single and parallel processors and suggest using sequential block algorithms among full simultaneous, full sequential and simultaneous block algorithms (simple kind of string‐averaging methods).…”

Section: Patternmentioning

confidence: 99%

Perturbed fixed point iterative methods based on pattern structure

Nikazad

Abbasi

2018

Math Methods in App Sciences

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We introduce a new idea of algorithmic structure, called assigning algorithm, using a finite collection of a subclass of strictly quasi‐nonexpansive operators. This new algorithm allows the iteration vectors to take steps on a pattern which is based on a connected directed acyclic graph. The sequential, simultaneous, and string‐averaging methods for solving convex feasibility problems are the special cases of the new algorithm which may be used to reduce idle time of processors in parallel implementations. We give a convergence analysis for such algorithmic structure with perturbation. Also, we extend some existence results of the split common fixed point problem based on the new algorithm. The performance of the new algorithm is illustrated with numerical examples from computed tomography.

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Multicore Performance of Block Algebraic Iterative Reconstruction Methods

Cited by 27 publications

References 39 publications

AIR Tools II: algebraic iterative reconstruction methods, improved implementation

AIR Tools II: algebraic iterative reconstruction methods, improved implementation

Limited view X-ray tomography for dimensional measurements

Perturbed fixed point iterative methods based on pattern structure

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