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Inexact gradient projection and fast data driven compressed sensing: theory and application

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Post-edited
Auteurs : Davies, Michael E. (Auteur de la Conférence)
CIRM (Editeur )

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compressed sensing inverse problems motivating example: magnetic resonance fingerprinting inexact iterative projected gradient theory numerical experiments magnetic resonance fingerprinting results questions from the audience
Résumé : We consider the convergence of the iterative projected gradient (IPG) algorithm for arbitrary (typically nonconvex) sets and when both the gradient and projection oracles are only computed approximately. We consider different notions of approximation of which we show that the Progressive Fixed Precision (PFP) and (1+epsilon) optimal oracles can achieve the same accuracy as for the exact IPG algorithm. We also show that the former scheme is also able to maintain the (linear) rate of convergence of the exact algorithm, under the same embedding assumption, while the latter requires a stronger embedding condition, moderate compression ratios and typically exhibits slower convergence. We apply our results to accelerate solving a class of data driven compressed sensing problems, where we replace iterative exhaustive searches over large datasets by fast approximate nearest neighbour search strategies based on the cover tree data structure. Finally, if there is time we will give examples of this theory applied in practice for rapid enhanced solutions to an emerging MRI protocol called magnetic resonance fingerprinting for quantitative MRI.

Keywords : compressed sensing; magnetic resonance fingerprinting; random pulse excitation; subsampling strategy

Codes MSC :
62D05 - Sampling theory, sample surveys
 65C60 - Computational problems in statistics
 94A12 - Signal theory (characterization, reconstruction, filtering, etc.)
    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 10/12/2018
    Date de captation : 21/11/2018
    Sous collection : Research School
    arXiv category : Statistics Theory ; Numerical Analysis
    Domaine : Numerical Analysis & Scientific Computing ; Probability & Statistics
    Format : MP4 (.mp4) - HD
    Durée : 00:59:19
    Audience : Researchers ; Graduate Students
    Download : https://videos.cirm-math.fr/2018-11-21_Davies.mp4
Informations sur la Rencontre

Nom de la rencontre : International traveling workshop on interactions between low-complexity data models and sensing techniques / Colloque international et itinérant sur les interactions entre modèles de faible complexité et acquis
Organisateurs de la rencontre : Anthoine, Sandrine ; Boursier, Yannick ; Jacques, Laurent
Dates : 19/11/2018 - 23/11/2018
Année de la rencontre : 2018
URL Congrès : https://conferences.cirm-math.fr/1865.html

Données de citation

DOI : 10.24350/CIRM.V.19476703
Citer cette vidéo: Davies, Michael E. (2018). Inexact gradient projection and fast data driven compressed sensing: theory and application. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19476703
URI : http://dx.doi.org/10.24350/CIRM.V.19476703

Voir aussi

Bibliographie

  • Benjamin, A.J.V., Gómez, P.A., Golbabaee, M., Sprenger, T., Menzel, M.I., Davies, M., & Marshall, I. (2018). Balanced multi-shot EPI for accelerated Cartesian MRF: An alternative to spiral MRF. - https://arxiv.org/abs/1809.02506

  • Davies, M., Puy, G., Vandergheynst, P., & Wiaux, Y. (2014). A compressed sensing framework for magnetic resonance fingerprinting. SIAM Journal on Imaging Sciences, 7(4), 2623-2656 - https://doi.org/10.1137/130947246

  • Golbabaee, M., Chen, Z., Wiaux, Y., & Davies, M. (2018). CoverBLIP: accelerated and scalable iterative matched-filtering for Magnetic Resonance Fingerprint reconstruction. - https://arxiv.org/abs/1810.01967

  • Golbabaee, M., & Davies, M. (2018). Inexact gradient projection and fast data driven compressed sensing. - https://arxiv.org/abs/1706.00092

  • Golbabaee, M., Chen, Z., Wiaux, Y., & Davies, M. (2018). CoverBLIP: scalable iterative matched filtering for MR Fingerprint recovery. - https://arxiv.org/abs/1809.02503

  • Golbabaee, M., Chen, Z., Wiaux, Y., & Davies, M. (2017). Cover tree compressed sensing for fast MR fingerprint recovery. - https://arxiv.org/abs/1706.07834


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