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

De Michael E. Davies

Apparaît dans les collections : 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, Ecoles de recherche

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.

Informations sur la vidéo

Date de captation 21/11/2018
Date de publication 10/12/2018
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19476703
Citer cette vidéo Davies, Michael E. (21/11/2018). Inexact gradient projection and fast data driven compressed sensing: theory and application. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19476703
URL https://dx.doi.org/10.24350/CIRM.V.19476703

Domaine(s)

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. <arXiv:1809.02506> - 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. <arXiv:1810.01967> - https://arxiv.org/abs/1810.01967
Golbabaee, M., & Davies, M. (2018). Inexact gradient projection and fast data driven compressed sensing. <arXiv:1706.00092> - https://arxiv.org/abs/1706.00092
Golbabaee, M., Chen, Z., Wiaux, Y., & Davies, M. (2018). CoverBLIP: scalable iterative matched filtering for MR Fingerprint recovery. <arXiv:1809.02503> - https://arxiv.org/abs/1809.02503
Golbabaee, M., Chen, Z., Wiaux, Y., & Davies, M. (2017). Cover tree compressed sensing for fast MR fingerprint recovery. <arXiv:1706.07834> - https://arxiv.org/abs/1706.07834

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