Gaussian process based independent analysis for temporal source separation in fMRI

NeuroImage ◽  
2017 ◽  
Vol 152 ◽  
pp. 563-574 ◽  
Author(s):  
Ditte Høvenhoff Hald ◽  
Ricardo Henao ◽  
Ole Winther
2020 ◽  
Author(s):  
Thomas Vandal ◽  
Julien Rameau ◽  
René Doyon

<p>Nearly 15 years of radial velocity (RV) monitoring and direct imaging (DI) enabled the detection oftwo giant planets orbiting the young, nearby star β Pictoris. The δ Scuti pulsations of the star, overwhelming planetary signals, need however to be carefully suppress. In this talk, we propose a new and independent analysis of the system, making use of all available data, including photometric light curve from the ground and space, long term RV and DI monitoring. We demonstrate how all data can be consistently modelled in a Bayesian framework. We show how modern and physically motivated kernels for Gaussian Process can effectively model complex stellar activity. Using further carefull statistical treatment of the data to extend the monitoring, we detect both planets from RV data only for the first time. To characterize the system more accurately, we also perform a joint fit of <br />all available relative astrometry and RV data. We provide precise orbital parameters and discuss the whole system architecture. The inferred dynamical mass measurements for both planets are also compared to mass-luminosity evolutionary tracks. This work opens the path towards a precise characterization of young planetary systems combing photometry, spectroscopy, and astrometry.</p>


2021 ◽  
Vol 7 (2) ◽  
pp. 287-290
Author(s):  
Jannik Prüßmann ◽  
Jan Graßhoff ◽  
Philipp Rostalski

Abstract Gaussian processes are a versatile tool for data processing. Unfortunately, due to storage and runtime requirements, standard Gaussian process (GP) methods are limited to a few thousand data points. Thus, they are infeasible in most biomedical, spatio-temporal problems. The methods treated in this work cover GP inference and hyperparameter optimization, exploiting the Kronecker structure of covariance matrices. To solve regression and source separation problems, two different approaches are presented. The first approach uses efficient matrix-vector-products, whilst the second approach is based on efficient solutions to the eigendecomposition. The latter also enables efficient hyperparameter optimization. In comparison to standard GP methods, the proposed methods can be applied to very large biomedical datasets without any further performance loss and perform substantially faster. The performance is demonstrated on esophageal manometry data, where the cardiac and respiratory signal components are to be inferred by source separation.


Author(s):  
Pengju He ◽  
Mi Qi ◽  
Wenhui Li ◽  
Mengyang Tang ◽  
Ziwei Zhao

Most nonstationary and time-varying mixed source separation algorithms are based on the model of instantaneous mixtures. However, the observation signal is a convolutional mixed source in reverberation environment, such as mobile voice received by indoor microphone arrays. In this paper, a time-varying convolution blind source separation (BSS) algorithm for nonstationary signals is proposed, which can separate both time-varying instantaneous mixtures and time-varying convolution mixtures. We employ the variational Bayesian (VB) inference method with Gaussian process (GP) prior for separating the nonstationary source frame by frame from the time-varying convolution signal, in which the prior information of the mixing matrix and the source signal are obtained by the Gaussian autoregressive method, and the posterior distributions of parameters (source signal and mixing matrix) are obtained by the VB learning. In the learning process, the learned parameters and hyperparameters are propagated to the next frame for VB inference as the prior which is combined with the likelihood function to get the posterior distribution. The experimental results show that the proposed algorithm is effective for separating time-varying mixed speech signals.


This Paper is an attempt to develop the Independent Component Analysis (ICA) based source separation implementation on the speech signals. The blind source separation technique which work on the basis of the Gaussian process is developed and the performance is analyzed. Blind source separation is the process in which the source separation of the main signal and the noise is separated without any reference available. Matlab based implementation is carried out and the results are obtained. The results thus obtained are satisfactory.


2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.


2013 ◽  
Author(s):  
Susanne Mayr ◽  
Gunnar Regenbrecht ◽  
Kathrin Lange ◽  
Albertgeorg Lang ◽  
Axel Buchner

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