Motion artifact correction in MRI using generalized projections

Hedley, Mark; Yan, Hong; Rosenfeld, Dov

doi:10.1109/42.75609

Cited by 75 publications

(36 citation statements)

References 21 publications

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“…When specialized to the convex feasibility problem (25), the Douglas-Rachford algorithm 104 generates a sequence (x n ), from an arbitrary starting point x 0 , by…”

Section: Fienup's Hybrid Input-output Algorithm and Douglas-rachfomentioning

confidence: 99%

“…Thus the informal use of cyclic projections in the presence of nonconvex sets appears in several places in the literature. [24][25][26][27] In Ref. 28, the error reduction algorithm (loosely called the Gerchberg-Saxton algorithm there) was revealed as such an algorithm, featuring a nonconvex magnitude constraint in the underlying signal space.…”

Section: Introductionmentioning

confidence: 99%

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Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization

2002

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The phase retrieval problem is of paramount importance in various areas of applied physics and engineering. The state of the art for solving this problem in two dimensions relies heavily on the pioneering work of Gerchberg, Saxton, and Fienup. Despite the widespread use of the algorithms proposed by these three researchers, current mathematical theory cannot explain their remarkable success. Nevertheless, great insight can be gained into the behavior, the shortcomings, and the performance of these algorithms from their possible counterparts in convex optimization theory. An important step in this direction was made two decades ago when the error reduction algorithm was identified as a nonconvex alternating projection algorithm. Our purpose is to formulate the phase retrieval problem with mathematical care and to establish new connections between well-established numerical phase retrieval schemes and classical convex optimization methods. Specifically, it is shown that Fienup's basic input-output algorithm corresponds to Dykstra's algorithm and that Fienup's hybrid input-output algorithm can be viewed as an instance of the Douglas-Rachford algorithm. We provide a theoretical framework to better understand and, potentially, to improve existing phase recovery algorithms.

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“…When specialized to the convex feasibility problem (25), the Douglas-Rachford algorithm 104 generates a sequence (x n ), from an arbitrary starting point x 0 , by…”

Section: Fienup's Hybrid Input-output Algorithm and Douglas-rachfomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization

2002

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“…Bei den hier vorgestellten Verfahren wird im Gegensatz zu einer Reihe bisher bekannter Ansätze [1][2][3][4][5][6][7][8][9][10], die Kom- Aus diesem Grund arbeiten die hier vorgestellten Algorithmen direkt auf den in den Tomographen gemessenen Datensätzen, den diskreten Werten der Radon-Transformation. Die bildverbessernden Maßnahmen erfolgen also nicht auf den rekonstruierten Bildern, sondern werden in Form einer effizienten Vorverarbeitungsroutine ausgeführt.…”

Section: Kompensation Von Artefakten In Der Computertomographieunclassified

Aufbereitung medizinischer Bilddaten

Däuber¹,

Haimerl

Hoppe

et al. 1999

Informatik Forsch Entw

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Zusammenfassung. Medizinische Bilddaten durchlaufen von der Datenakquisition bis zur Diagnose beziehungsweiseOperationsplanung die verschiedensten Verarbeitungsschritte. Die frühzeitige Kompensation auftretender Störungen in dieser Verarbeitungskette bietet den anschließend angewandten Algorithmen deutlich verbessertes Datenmaterial. In diesem Zusammenhang werden Verfahren zur Kompensation von Bewegungs-und Metallartefakten in tomographischen Aufnahmen vorgestellt, sowie neue Methoden der modellbasierten Registrierung von Datensätzen unterschiedlicher Modalitäten präsentiert.Abstract. Medical images pass several data processing steps from data acquisition to diagnosis and operation planing. Artifacts which are introduced in this data processing chain should be compensated as early as possible to yield better data sets for the algorithms subsequently performed. In this regard we present new methods for compensation of metal and motion artifacts in computerized tomography and describe a new approach to model based image registration of different image modalities.

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“…When images are reconstructed from these distorted signals, severe ghosting and blurring are often seen [1][2][3][4][5]. Several methods have been proposed to minimize these artifacts [6][7][8][9][10][11][12][13][14][15], but none of these is able to reduce artifacts caused by general motion completely. Therefore, the appearance of motion artifacts remains one of the major drawbacks in MR imaging.…”

Section: Introductionmentioning

confidence: 99%

Two motion-detection algorithms for projection-reconstruction magnetic resonance imaging: Theory and experimental verification

Walle

Lemahieu

Achten

1997

Image Analysis and Processing

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Abstract. In this paper, projection-reconstruction (PR) magnetic resonance (MR) imaging is considered, We present two new quantitative techniques that allow to check when motion was present during a PP~ MR experiment. No a priori information about the motion is required since only the measured MR signals are used in the calculations. Moreover, the proposed methods can be implemented on a standard personal computer or workstation. It is experimentally shown that both methods are able to detect motion intervals with an accuracy of one repetition time.

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Motion artifact correction in MRI using generalized projections

Cited by 75 publications

References 21 publications

Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization

Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization

Aufbereitung medizinischer Bilddaten

Two motion-detection algorithms for projection-reconstruction magnetic resonance imaging: Theory and experimental verification

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