The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform

Simon Daniel Robinson - One of the best experts on this subject based on the ideXlab platform.

  • Phase unwrapping with a rapid opensource minimum Spanning Tree Algorithm (ROMEO).
    Magnetic resonance in medicine, 2020
    Co-Authors: Barbara Dymerska, Korbinian Eckstein, Beata Bachrata, Bernard Siow, Siegfried Trattnig, Karin Shmueli, Simon Daniel Robinson
    Abstract:

    PURPOSE: To develop a rapid and accurate MRI phase-unwrapping technique for challenging phase topographies encountered at high magnetic fields, around metal implants, or postoperative cavities, which is sufficiently fast to be applied to large-group studies including Quantitative Susceptibility Mapping and functional MRI (with phase-based distortion correction). METHODS: The proposed path-following phase-unwrapping Algorithm, ROMEO, estimates the coherence of the signal both in space-using MRI magnitude and phase information-and over time, assuming approximately linear temporal phase evolution. This information is combined to form a quality map that guides the unwrapping along a 3D path through the object using a computationally efficient minimum Spanning Tree Algorithm. ROMEO was tested against the two most commonly used exact phase-unwrapping methods, PRELUDE and BEST PATH, in simulated topographies and at several field strengths: in 3T and 7T in vivo human head images and 9.4T ex vivo rat head images. RESULTS: ROMEO was more reliable than PRELUDE and BEST PATH, yielding unwrapping results with excellent temporal stability for multi-echo or multi-time-point data. It does not require image masking and delivers results within seconds, even in large, highly wrapped multi-echo data sets (eg, 9 seconds for a 7T head data set with 31 echoes and a 208 × 208 × 96 matrix size). CONCLUSION: Overall, ROMEO was both faster and more accurate than PRELUDE and BEST PATH, delivering exact results within seconds, which is well below typical image acquisition times, enabling potential on-console application.

  • Phase Unwrapping with a Rapid Opensource Minimum Spanning Tree Algorithm (ROMEO)
    2020
    Co-Authors: Barbara Dymerska, Korbinian Eckstein, Beata Bachrata, Bernard Siow, Siegfried Trattnig, Karin Shmueli, Simon Daniel Robinson
    Abstract:

    ABSTRACT Purpose To develop a rapid and accurate MRI phase unwrapping technique for challenging phase topographies encountered at high magnetic fields, around metal implants or post-operative cavities, that is sufficiently fast to be applied to large group studies including Quantitative Susceptibility Mapping and functional MRI (with phase-based distortion correction). Methods The proposed path-following phase unwrapping Algorithm, ROMEO, estimates the coherence of the signal both in space - using MRI magnitude and phase information - and over time, assuming approximately linear temporal phase evolution. This information is combined to form a quality map that guides the unwrapping along a three-dimensional path through the object using a computationally efficient minimum Spanning Tree Algorithm. ROMEO was tested against the two most commonly used exact phase unwrapping methods: PRELUDE and BEST PATH in simulated topographies and at several field strengths: in 3 T and 7 T in vivo human head images and 9.4 T ex vivo rat head images. Results ROMEO was more reliable than PRELUDE and BEST PATH, yielding unwrapping results with excellent temporal stability for multi-echo or multi-time-point data. ROMEO does not require image masking and delivers results within seconds even in large, highly wrapped multi-echo datasets (e.g. 9 seconds for a 7 T head dataset with 31 echoes and a 208 x 208 x 96 matrix size). Conclusion Overall, ROMEO was both faster and more accurate than PRELUDE and BEST PATH delivering exact results within seconds, which is well below typical image acquisition times, enabling potential on-console application.

Chip Martel - One of the best experts on this subject based on the ideXlab platform.

  • the expected complexity of prim s minimum Spanning Tree Algorithm
    Information Processing Letters, 2002
    Co-Authors: Chip Martel
    Abstract:

    We study the expected performance of Prim's minimum Spanning Tree (MST) Algorithm implemented using ordinary heaps. We show that this implementation runs in linear or almost linear expected time on a wide range of graphs. This helps to explain why Prim's Algorithm often beats MST Algorithms which have better worst-case run times.Specifically, we show that if we start with any n node m edge graph and randomly permute its edge weights, then Prim's Algorithm runs in expected O(m + nlogn log(2m/n)) time. Note that O(m + nlogn log(2m/n)) = O(m) when m = Ω(n log n log log n).We extend this result to show that the same expected run times apply even when an adversary can select the weights of m/logn edges and the possible weights of the remaining edges (which are then randomly assigned).

Barbara Dymerska - One of the best experts on this subject based on the ideXlab platform.

  • Phase unwrapping with a rapid opensource minimum Spanning Tree Algorithm (ROMEO).
    Magnetic resonance in medicine, 2020
    Co-Authors: Barbara Dymerska, Korbinian Eckstein, Beata Bachrata, Bernard Siow, Siegfried Trattnig, Karin Shmueli, Simon Daniel Robinson
    Abstract:

    PURPOSE: To develop a rapid and accurate MRI phase-unwrapping technique for challenging phase topographies encountered at high magnetic fields, around metal implants, or postoperative cavities, which is sufficiently fast to be applied to large-group studies including Quantitative Susceptibility Mapping and functional MRI (with phase-based distortion correction). METHODS: The proposed path-following phase-unwrapping Algorithm, ROMEO, estimates the coherence of the signal both in space-using MRI magnitude and phase information-and over time, assuming approximately linear temporal phase evolution. This information is combined to form a quality map that guides the unwrapping along a 3D path through the object using a computationally efficient minimum Spanning Tree Algorithm. ROMEO was tested against the two most commonly used exact phase-unwrapping methods, PRELUDE and BEST PATH, in simulated topographies and at several field strengths: in 3T and 7T in vivo human head images and 9.4T ex vivo rat head images. RESULTS: ROMEO was more reliable than PRELUDE and BEST PATH, yielding unwrapping results with excellent temporal stability for multi-echo or multi-time-point data. It does not require image masking and delivers results within seconds, even in large, highly wrapped multi-echo data sets (eg, 9 seconds for a 7T head data set with 31 echoes and a 208 × 208 × 96 matrix size). CONCLUSION: Overall, ROMEO was both faster and more accurate than PRELUDE and BEST PATH, delivering exact results within seconds, which is well below typical image acquisition times, enabling potential on-console application.

  • Phase Unwrapping with a Rapid Opensource Minimum Spanning Tree Algorithm (ROMEO)
    2020
    Co-Authors: Barbara Dymerska, Korbinian Eckstein, Beata Bachrata, Bernard Siow, Siegfried Trattnig, Karin Shmueli, Simon Daniel Robinson
    Abstract:

    ABSTRACT Purpose To develop a rapid and accurate MRI phase unwrapping technique for challenging phase topographies encountered at high magnetic fields, around metal implants or post-operative cavities, that is sufficiently fast to be applied to large group studies including Quantitative Susceptibility Mapping and functional MRI (with phase-based distortion correction). Methods The proposed path-following phase unwrapping Algorithm, ROMEO, estimates the coherence of the signal both in space - using MRI magnitude and phase information - and over time, assuming approximately linear temporal phase evolution. This information is combined to form a quality map that guides the unwrapping along a three-dimensional path through the object using a computationally efficient minimum Spanning Tree Algorithm. ROMEO was tested against the two most commonly used exact phase unwrapping methods: PRELUDE and BEST PATH in simulated topographies and at several field strengths: in 3 T and 7 T in vivo human head images and 9.4 T ex vivo rat head images. Results ROMEO was more reliable than PRELUDE and BEST PATH, yielding unwrapping results with excellent temporal stability for multi-echo or multi-time-point data. ROMEO does not require image masking and delivers results within seconds even in large, highly wrapped multi-echo datasets (e.g. 9 seconds for a 7 T head dataset with 31 echoes and a 208 x 208 x 96 matrix size). Conclusion Overall, ROMEO was both faster and more accurate than PRELUDE and BEST PATH delivering exact results within seconds, which is well below typical image acquisition times, enabling potential on-console application.

Henning Pagnia - One of the best experts on this subject based on the ideXlab platform.

Walter Guttmann - One of the best experts on this subject based on the ideXlab platform.

  • relation algebraic verification of prim s minimum Spanning Tree Algorithm
    International Colloquium on Theoretical Aspects of Computing, 2016
    Co-Authors: Walter Guttmann
    Abstract:

    We formally prove the correctness of Prim’s Algorithm for computing minimum Spanning Trees. We introduce new generalisations of relation algebras and Kleene algebras, in which most of the proof can be carried out. Only a small part needs additional operations, for which we introduce a new algebraic structure. We instantiate these algebras by matrices over extended reals, which model the weighted graphs used in the Algorithm. Many existing results from relation algebras and Kleene algebras generalise from the relation model to the weighted-graph model with no or small changes. The overall structure of the proof uses Hoare logic. All results are formally verified in Isabelle/HOL heavily using its integrated automated theorem provers.