Riccati-regularized precision matrices for neuroimaging

Nicolas Honnorat, Christos Davatzikos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The introduction of graph theory in neuroimaging has provided invaluable tools for the study of brain connectivity. These methods require the definition of a graph, which is typically derived by estimating the effective connectivity between brain regions through the optimization of an ill-posed inverse problem. Considerable efforts have been devoted to the development of methods extracting sparse connectivity graphs. The present paper aims at highlighting the benefits of an alternative approach.We investigate low-rank L2 regularized matrices recently introduced under the denomination of Riccati regularized precision matrices. We demonstrate their benefits for the analysis of cortical thickness map and the extraction of functional biomarkers from resting state fMRI scans. In addition, we explain how speed and result quality can be further improved with random projections. The promising results obtained using the Human Connectome Project dataset, as well as, the numerous possible extensions and applications suggest that Riccati precision matrices might usefully complement current sparse approaches.

Original languageEnglish (US)
Title of host publicationInformation Processing in Medical Imaging - 25th International Conference, IPMI 2017, Proceedings
PublisherSpringer Verlag
Pages275-286
Number of pages12
Volume10265 LNCS
ISBN (Print)9783319590493
DOIs
StatePublished - 2017
Externally publishedYes
Event25th International Conference on Information Processing in Medical Imaging, IPMI 2017 - Boone, United States
Duration: Jun 25 2017Jun 30 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10265 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other25th International Conference on Information Processing in Medical Imaging, IPMI 2017
CountryUnited States
CityBoone
Period6/25/176/30/17

Fingerprint

Neuroimaging
Brain
Connectivity
Graph Connectivity
Random Projection
Functional Magnetic Resonance Imaging
Graph theory
Biomarkers
Ill-posed Problem
Inverse problems
Inverse Problem
Complement
Optimization
Alternatives
Graph in graph theory
Demonstrate

Keywords

  • Precision
  • rs-fMRI
  • Sparse inverse covariance

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Honnorat, N., & Davatzikos, C. (2017). Riccati-regularized precision matrices for neuroimaging. In Information Processing in Medical Imaging - 25th International Conference, IPMI 2017, Proceedings (Vol. 10265 LNCS, pp. 275-286). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10265 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-59050-9_22

Riccati-regularized precision matrices for neuroimaging. / Honnorat, Nicolas; Davatzikos, Christos.

Information Processing in Medical Imaging - 25th International Conference, IPMI 2017, Proceedings. Vol. 10265 LNCS Springer Verlag, 2017. p. 275-286 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10265 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Honnorat, N & Davatzikos, C 2017, Riccati-regularized precision matrices for neuroimaging. in Information Processing in Medical Imaging - 25th International Conference, IPMI 2017, Proceedings. vol. 10265 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10265 LNCS, Springer Verlag, pp. 275-286, 25th International Conference on Information Processing in Medical Imaging, IPMI 2017, Boone, United States, 6/25/17. https://doi.org/10.1007/978-3-319-59050-9_22
Honnorat N, Davatzikos C. Riccati-regularized precision matrices for neuroimaging. In Information Processing in Medical Imaging - 25th International Conference, IPMI 2017, Proceedings. Vol. 10265 LNCS. Springer Verlag. 2017. p. 275-286. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-59050-9_22
Honnorat, Nicolas ; Davatzikos, Christos. / Riccati-regularized precision matrices for neuroimaging. Information Processing in Medical Imaging - 25th International Conference, IPMI 2017, Proceedings. Vol. 10265 LNCS Springer Verlag, 2017. pp. 275-286 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{1db2d86090ac41e7851f820f64294a72,
title = "Riccati-regularized precision matrices for neuroimaging",
abstract = "The introduction of graph theory in neuroimaging has provided invaluable tools for the study of brain connectivity. These methods require the definition of a graph, which is typically derived by estimating the effective connectivity between brain regions through the optimization of an ill-posed inverse problem. Considerable efforts have been devoted to the development of methods extracting sparse connectivity graphs. The present paper aims at highlighting the benefits of an alternative approach.We investigate low-rank L2 regularized matrices recently introduced under the denomination of Riccati regularized precision matrices. We demonstrate their benefits for the analysis of cortical thickness map and the extraction of functional biomarkers from resting state fMRI scans. In addition, we explain how speed and result quality can be further improved with random projections. The promising results obtained using the Human Connectome Project dataset, as well as, the numerous possible extensions and applications suggest that Riccati precision matrices might usefully complement current sparse approaches.",
keywords = "Precision, rs-fMRI, Sparse inverse covariance",
author = "Nicolas Honnorat and Christos Davatzikos",
year = "2017",
doi = "10.1007/978-3-319-59050-9_22",
language = "English (US)",
isbn = "9783319590493",
volume = "10265 LNCS",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "275--286",
booktitle = "Information Processing in Medical Imaging - 25th International Conference, IPMI 2017, Proceedings",

}

TY - GEN

T1 - Riccati-regularized precision matrices for neuroimaging

AU - Honnorat, Nicolas

AU - Davatzikos, Christos

PY - 2017

Y1 - 2017

N2 - The introduction of graph theory in neuroimaging has provided invaluable tools for the study of brain connectivity. These methods require the definition of a graph, which is typically derived by estimating the effective connectivity between brain regions through the optimization of an ill-posed inverse problem. Considerable efforts have been devoted to the development of methods extracting sparse connectivity graphs. The present paper aims at highlighting the benefits of an alternative approach.We investigate low-rank L2 regularized matrices recently introduced under the denomination of Riccati regularized precision matrices. We demonstrate their benefits for the analysis of cortical thickness map and the extraction of functional biomarkers from resting state fMRI scans. In addition, we explain how speed and result quality can be further improved with random projections. The promising results obtained using the Human Connectome Project dataset, as well as, the numerous possible extensions and applications suggest that Riccati precision matrices might usefully complement current sparse approaches.

AB - The introduction of graph theory in neuroimaging has provided invaluable tools for the study of brain connectivity. These methods require the definition of a graph, which is typically derived by estimating the effective connectivity between brain regions through the optimization of an ill-posed inverse problem. Considerable efforts have been devoted to the development of methods extracting sparse connectivity graphs. The present paper aims at highlighting the benefits of an alternative approach.We investigate low-rank L2 regularized matrices recently introduced under the denomination of Riccati regularized precision matrices. We demonstrate their benefits for the analysis of cortical thickness map and the extraction of functional biomarkers from resting state fMRI scans. In addition, we explain how speed and result quality can be further improved with random projections. The promising results obtained using the Human Connectome Project dataset, as well as, the numerous possible extensions and applications suggest that Riccati precision matrices might usefully complement current sparse approaches.

KW - Precision

KW - rs-fMRI

KW - Sparse inverse covariance

UR - http://www.scopus.com/inward/record.url?scp=85020505910&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85020505910&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-59050-9_22

DO - 10.1007/978-3-319-59050-9_22

M3 - Conference contribution

C2 - 29503515

AN - SCOPUS:85020505910

SN - 9783319590493

VL - 10265 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 275

EP - 286

BT - Information Processing in Medical Imaging - 25th International Conference, IPMI 2017, Proceedings

PB - Springer Verlag

ER -