Thesis title: A Bayesian approach for periodic components estimation for chronobiological signals
Thesis abstract: The toxicity and efficacy of more than 30 anticancer agents presents very high variations, depending on the dosing time. Therefore the biologists studying the circadian rhythm require a very precise method for estimating the Periodic Components (PC) vector of chronobiological signals. Moreover, in recent developments not only the dominant period or the PC vector present a crucial interest, but also their stability or variability. In cancer treatment experiments the recorded signals corresponding to different phases of treatment are short, from seven days for the synchronization segment to two or three days for the after treatment segment. When studying the stability of the dominant period we have to consider very short length signals relative to the prior knowledge of the dominant period, placed in the circadian domain. The classical approaches, based on Fourier Transform (FT) methods are inefficient (i.e. lack of precision) considering the particularities of the data (i.e. the short length). Another particularity of the signals considered in such experiments is the level of noise: such signals are very noisy and establishing the periodic components that are associated with the biological phenomena and distinguish them from the ones associated with the noise is a difficult task. In this thesis we propose a new method for the estimation of the PC vector of biomedical signals, using the biological prior informations and considering a model that accounts for the noise. The experiments developed in the cancer treatment context are recording signals expressing a limited number of periods. This is a prior information that can be translated as the sparsity of the PC vector. The proposed method considers the PC vector estimation as an Inverse Problem (IP) using the general Bayesian inference in order to infer all the unknowns of our model, i.e. the PC vector but also the hyperparameters. The sparsity prior information is modelled using a sparsity enforcing prior law. In this thesis we propose a Student-t distribution, viewed as the marginal distribution of a bivariate Normal - Inverse Gamma distribution. In fact, when the equality between the shape and scale parameters corresponding to the Inverse Gamma distribution is not imposed, the marginal of the Normal-Inverse Gamma distribution is a generalization of the Student-t distribution. We build a general Infinite Gaussian Scale Mixture (IGSM) hierarchical model where we also assign prior distributions for the hyperparameters. The expression of the joint posterior law of the unknown PC vector and the hyperparameters is obtained via the Bayes rule and then the unknowns are estimated via Joint Maximum A Posteriori (JMAP) or Posterior Mean (PM). For the PM estimator, the expression of the posterior distribution is approximated by a separable one, via Variational Bayesian Approximation (VBA), using the Kullback-Leibler (KL) divergence. Two possibilities are considered: an approximation with partially separable distributions and an approximation with a fully separable one. The algorithms are presented in detail and are compared with the ones corresponding to the Gaussian model. We examine the practical convergency of the algorithms and give simulation results to compare their performances. Finally we show simulation results on synthetic and real data in cancer treatment applications. The real data considered in this thesis examines the rest-activity patterns and gene expressions of KI/KI Per2::luc mouse, aged 10 weeks, singly housed in RT-BIO. Keywords : Periodic Components (PC) vector estimation, Sparsity enforcing, Bayesian parameter estimation, Variational Bayesian Approximation (VBA), Kullback-Leibler (KL) divergence, Infinite Gaussian Scale Mixture (IGSM), Normal - Inverse Gamma, Inverse problem, Joint Maximum A Posteriori (JMAP), Posterior Mean (PM), Chronobiology, Circadian rhythm, Cancer treatment.. Citation: Mircea Dumitru. A Bayesian approach for periodic components estimation for chronobiological signals. Probability [math.PR]. Université Paris-Saclay, 2016. English. <NNT : 2016SACLS104>. <tel-01318048> @phdthesis{dumitru:tel-01318048, TITLE = {{A Bayesian approach for periodic components estimation for chronobiological signals}}, AUTHOR = {Dumitru, Mircea}, URL = {https://tel.archives-ouvertes.fr/tel-01318048}, NUMBER = {2016SACLS104}, SCHOOL = {{Universit{\'e} Paris-Saclay}}, YEAR = {2016}, MONTH = Mar, KEYWORDS = {Bayesian approach ; Sparsity enforcing ; Chronobiology ; Hierarchical model ; Periodic Components vector estimation ; Inverse problem ; Approches bay{\'e}siennes ; Renforcement de parcimonie ; Chronobiologie ; Mod{\`e}le hi{\'e}rarchique ; Estimation de composantes p{\'e}riodiques ; Probl{\`e}mes inverses}, TYPE = {Theses}, PDF = {https://tel.archives-ouvertes.fr/tel-01318048/file/76211_DUMITRU_2016_diffusion.pdf}, HAL_ID = {tel-01318048}, HAL_VERSION = {v1}, }

2018

Journal articles

titre
Bayesian 3D X-ray Computed Tomography with a Hierarchical Prior model for Sparsity in Haar Transform domain
auteur
Li Wang, Ali Mohammad-Djafari, Nicolas Gac, Mircea Dumitru
article
Entropy, MDPI, 2018, Special Issue "Probabilistic Methods for Inverse Problems", ⟨10.3390/e20120977⟩
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Conference papers

titre
Bayesian Inference with Error Variable Splitting and Sparsity Enforcing Priors for Linear Inverse Problems
auteur
Ali Mohammad-Djafari, Mircea Dumitru, Camille Chapdelaine, Nicolas Gac
article
26th European Signal Processing Conference (EUSIPCO 2018), Sep 2018, Rome, Italy
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https://hal.archives-ouvertes.fr/hal-01837986/file/PID5428005.pdf BibTex

Software

titre
iterTomoGPI-GPL - Ref CNRS du pré-dépôt APP 11562-02 (num IDDN prochainement disponible)
auteur
Mircea Dumitru, Li Wang, Nicolas Gac, Ali Mohammad-Djafari
article
2018
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2017

Conference papers

titre
Performance comparison of Bayesian iterative algorithms for three classes of sparsity enforcing priors with application in computed tomography
auteur
Mircea Dumitru, Wang Li, Nicolas Gac, Ali Mohammad-Djafari
article
2017 IEEE International Conference on Image Processing, Sep 2017, Beijing, China
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https://hal.archives-ouvertes.fr/hal-01568337/file/ICIP2017.pdf BibTex
titre
Comparaison des performances d’algorithmes itératifs bayésiens basés sur trois classes de modèles a priori parcimonieux appliqués à la reconstruction tomographique
auteur
Mircea Dumitru, Li Wang, Nicolas Gac, Ali Mohammad-Djafari
article
26eme Colloque GRETSI Traitement du Signal & des Images, GRETSI 2017, Sep 2017, Juans-Les-Pins, France
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https://hal.archives-ouvertes.fr/hal-01569349/file/Gretsi2017_Mircea.pdf BibTex
titre
Model selection in the sparsity context for inverse problems in Bayesian framework
auteur
Mircea Dumitru, Li Wang, Ali Mohammad-Djafari, Nicolas Gac
article
37th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Jul 2017, Jarinu, Brazil
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https://hal.archives-ouvertes.fr/hal-01568318/file/Dumitru_MaxEnt2017.pdf BibTex
titre
Unsupervised sparsity enforcing iterative algorithms for 3D image reconstruction in X-ray computed tomography
auteur
Mircea Dumitru, Nicolas Gac, Li Wang, Ali Mohammad-Djafari
article
The 2017 International Conference on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, Jun 2017, Xi'an, China. pp.359-362
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https://hal.archives-ouvertes.fr/hal-01568325/file/Fully3D2017.pdf BibTex
titre
3D X-ray Computed Tomography reconstruction using sparsity enforcing Hierarchical Model based on Haar Transformation
auteur
Li Wang, Ali Mohammad-Djafari, Nicolas Gac, Mircea Dumitru
article
The 2017 International Conference on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, Jun 2017, Xi'an, China. pp.295-298
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https://hal.archives-ouvertes.fr/hal-01490554/file/Fully3D_LW_AMD_NG_MD.pdf BibTex

2016

Journal articles

titre
Precise periodic components estimation for chronobiological signals through Bayesian Inference with sparsity enforcing prior
auteur
Mircea Dumitru, Ali Mohammad-Djafari, Simona Sain
article
EURASIP Journal on Bioinformatics and Systems Biology, SpringerOpen, 2016, 1, pp.548 - 548. ⟨10.1186/s13637-015-0033-6⟩
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https://hal.archives-ouvertes.fr/hal-01475255/file/2016_Dumitru_Djafari_Baghai%20-%20EURASIP.pdf BibTex

Conference papers

titre
Computed tomography reconstruction based on a hierarchical model and variational Bayesian method
auteur
Li Wang, Ali Mohammad-Djafari, Nicolas Gac, Mircea Dumitru
article
IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Mar 2016, Shanghai, China. pp.883-887, ⟨10.1109/ICASSP.2016.7471802⟩
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https://hal.archives-ouvertes.fr/hal-01403784/file/ICASSP_Wang_Final.pdf BibTex

Theses

titre
A Bayesian approach for periodic components estimation for chronobiological signals
auteur
Mircea Dumitru
article
Probability [math.PR]. Université Paris-Saclay, 2016. English. ⟨NNT : 2016SACLS104⟩
Accès au texte intégral et bibtex
https://tel.archives-ouvertes.fr/tel-01318048/file/76211_DUMITRU_2016_diffusion.pdf BibTex

2015

Journal articles

titre
Bayesian sparse solutions to linear inverse problems with non-stationary noise with Student-t priors
auteur
Ali Mohammad-Djafari, Mircea Dumitru
article
Digital Signal Processing, Elsevier, 2015, 47, pp.128 - 156. ⟨10.1016/j.dsp.2015.08.005⟩
Accès au texte intégral et bibtex
https://hal.archives-ouvertes.fr/hal-01475262/file/2015_Djafari_Dumitru%20-%20Digital%20Signal%20Processing.pdf BibTex

Conference papers

titre
Estimating the periodic components of a biomedical signal through inverse problem modelling and Bayesian inference with sparsity enforcing prior
auteur
Mircea Dumitru, Ali Mohammad-Djafari
article
AIP Conference, Sep 2014, Amboise, France. pp.548-555, ⟨10.1063/1.4906021 ⟩
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titre
Periodic components estimation in chronobiological time series via a Bayesian approach
auteur
Mircea Dumitru, Ali Mohammad-Djafari
article
23rd European Signal Processing Conference (EUSIPCO 2015), Aug 2015, Nice, France. ⟨10.1109/EUSIPCO.2015.7362784⟩
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https://hal.archives-ouvertes.fr/hal-01588968/file/Eusipco215_MDumitru_A-MDjafariV3.pdf BibTex

2013

Journal articles

titre
A circadian clock transcription model for the personalization of cancer chronotherapy.
auteur
Xiao-Mei Li, Ali Mohammad-Djafari, Mircea Dumitru, Sandrine Dulong, Elisabeth Filipski, Sandrine Siffroi-Fernandez, Ali Mteyrek, Francesco Scaglione, Catherine Guettier, Franck Delaunay, Francis Lévi
article
Cancer Research, American Association for Cancer Research, 2013, 73 (24), pp.7176-88. ⟨10.1158/0008-5472.CAN-13-1528⟩
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2012

Conference papers

titre
Bayesian variational approximation implementation for linear inverse problem with infinite Gaussian mixture model
auteur
Mohammad-Djafari Ali, Leila Gharsalli, Mircea Dumitru
article
Journée GDR ISIS: Résolution de problèmes inverses : optimisation et parallélisation, Jun 2012, Paris, France
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