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dc.contributor.author
Wadehn, Federico
dc.contributor.supervisor
Loeliger, Hans-Andrea
dc.contributor.supervisor
Heldt, Thomas
dc.contributor.supervisor
Dauwels, Justin
dc.date.accessioned
2019-05-31T06:41:22Z
dc.date.available
2019-05-30T09:42:33Z
dc.date.available
2019-05-31T06:41:22Z
dc.date.issued
2019-06
dc.identifier.isbn
978-3-86628-640-5
en_US
dc.identifier.issn
1616-671X
dc.identifier.uri
http://hdl.handle.net/20.500.11850/344762
dc.identifier.doi
10.3929/ethz-b-000344762
dc.description.abstract
For more than a decade, the model-based approach to signal processing based on state space models (SSMs) and factor graphs is being pursued at the Signal and Information Processing Laboratory of ETH Zurich and other groups around the world. This thesis contributes to the theory and methods of this approach, and showcases some biomedical applications; thereby, further highlighting its usefulness. The proposed models and estimation algorithms, however, are applicable beyond the field of biomedical signal processing. In Part 1 of this thesis we cover modeling, inference, and learning with SSMs and factor graphs. First, we introduce the topic of probabilistic modeling of signals and systems with SSMs and factor graphs. Then, we discuss how to perform inference in linear Gaussian models by Gaussian message passing. When applied to linear SSMs, Gaussian message passing generalizes Kalman filtering and can be used for diverse tasks such as input- and state estimation as well as output smoothing. Using this message passing perspective, two matrix-inversion-free Kalman smoothers are derived (the MBF and BIFM smoothers) and subsequently extended to their respective square root versions. Square root Gaussian message passing is particularly suitable for applications where numerical stability issues arise. After having described inference algorithms, we cover learning algorithms for linear models and SSMs, with a particular focus on learning with sparsity. For this, we rely on variational representations of sparsity-promoting priors called normals with unknown variances (NUV). The NUV representation suggests estimation algorithms based on alternating maximization and expectation maximization (EM). The latter approach commonly requires a round of Gaussian message passing at each EM iteration. Combining SSMs with sparsity opens up many applications, from outlier-robust estimation, to event detection, to signal separation. To handle signals whose variances or sparsity patterns have temporal correlations, a model denoted by state space models with dynamical and sparse variances is proposed. For this model we present approximate inference algorithms based on EM- and variational message passing. The theoretical part of this thesis concludes with a duality perspective on inference and learning in factor graphs. Dual factor graphs represent a dual optimization problem or equivalently a dual estimation problem and are based on the Legendre transformation on factor graphs and the Fenchel duality theorem. Dualizing factor graphs of SSMs results in dual SSMs. These can be used to show that the MBF and BIFM smoothers are dual algorithms. We then proceed to deriving the so called Hamiltonian system using dual SSMs. The Hamiltonian system can be seen as a transformed form of the Karush–Kuhn–Tucker (KKT) conditions of optimality for state estimation in SSMs. The Hamiltonian equations can be solved by iterative algorithms. Algorithms that iteratively solve the Hamiltonian system are alternatives to Kalman smoothing and are a promising approach for estimation in large-scale SSMs, because these primal-dual algorithms do not require the storage of covariance matrices. Finally, the variational NUV representation of sparsity-promoting priors is derived via the Legendre transform on factor graphs. Subsequently, we show how to use Hamiltonian iterations and NUVs for outlier-robust estimation in SSMs. In Part 2, various state space methods are used for analyzing physiological signals and systems. In particular, two cardiovascular signal processing applications are presented. One is an approach for robustly detecting heart beats in photoplethysmogram recordings using autonomous state space models and localized model fitting. In the other, we use Gaussian message passing for input estimation in SSMs to detect heart beats in ballistocardiogram recordings. Finally, we use sparse input estimation in SSMs for estimating neural controller signals and for performing a model-based separation of the different types of eye movements (saccades, smooth pursuit, and fixations) present in free-viewing eye movement recordings.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
ETH Zurich
en_US
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.subject
Biomedical signal processing
en_US
dc.subject
Probabilistic graphical models
en_US
dc.subject
Signal processing
en_US
dc.subject
Optimization
en_US
dc.subject
State space models
en_US
dc.title
State Space Methods with Applications in Biomedical Signal Processing
en_US
dc.type
Doctoral Thesis
dc.rights.license
In Copyright - Non-Commercial Use Permitted
dc.date.published
2019-05-19
ethz.journal.title
Series in Signal and Information Processing
ethz.journal.volume
31
en_US
ethz.size
215 p.
en_US
ethz.code.ddc
DDC - DDC::6 - Technology, medicine and applied sciences::610 - Medical sciences, medicine
ethz.code.ddc
DDC - DDC::5 - Science::510 - Mathematics
ethz.code.ddc
DDC - DDC::6 - Technology, medicine and applied sciences::621.3 - Electric engineering
en_US
ethz.identifier.diss
25926
en_US
ethz.publication.place
Zurich
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02140 - Dep. Inf.technologie und Elektrotechnik / Dep. of Inform.Technol. Electrical Eng.::01209 - Lehre Inf.technologie u. Elektrotechnik::01207 - SR Elektrotechnik und Informationstechn.::01214 - DR Inf.technologie und Elektrotechnik / DR Information Tech.+ Electrical Engin.
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02140 - Dep. Inf.technologie und Elektrotechnik / Dep. of Inform.Technol. Electrical Eng.::02639 - Inst. f. Signal- und Informationsverarb. / Signal and Information Processing Lab.::03568 - Loeliger, Hans-Andrea / Loeliger, Hans-Andrea
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02140 - Dep. Inf.technologie und Elektrotechnik / Dep. of Inform.Technol. Electrical Eng.::02639 - Inst. f. Signal- und Informationsverarb. / Signal and Information Processing Lab.::03568 - Loeliger, Hans-Andrea / Loeliger, Hans-Andrea
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02140 - Dep. Inf.technologie und Elektrotechnik / Dep. of Inform.Technol. Electrical Eng.::02639 - Inst. f. Signal- und Informationsverarb. / Signal and Information Processing Lab.::03568 - Loeliger, Hans-Andrea / Loeliger, Hans-Andrea
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02140 - Dep. Inf.technologie und Elektrotechnik / Dep. of Inform.Technol. Electrical Eng.::02639 - Inst. f. Signal- und Informationsverarb. / Signal and Information Processing Lab.::03568 - Loeliger, Hans-Andrea / Loeliger, Hans-Andrea
ethz.date.deposited
2019-05-30T09:42:41Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2019-05-31T06:41:42Z
ethz.rosetta.lastUpdated
2022-03-28T23:00:16Z
ethz.rosetta.versionExported
true
ethz.COinS
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