Alexandra Koulouri

Alexandra Koulouri
Tampere University | UTA · Faculty of Information Technology and Communication Sciences

Dipl. Eng. MSc PhD

About

32
Publications
2,601
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55
Citations
Introduction
I graduated (2007) from the Dept. of Electrical and Computer Engineering (EEE), Aristotle University of Thessaloniki (A.U.TH.). I obtained two MSc degrees: in Signal Processing from Imperial College London (2008) and in Medical Image Computing from University College London (2009). I completed my PhD in Brain Imaging and Tomographic Techniques in Imperial College London (2015). My expertise is in inverse problems, Bayesian statistics, optimization techniques and machine learning.
Featured research
Article
Full-text available
In this paper, we focus on the inverse problem of reconstructing distributional brain activity with cortical and weakly detectable deep components in non-invasive Electroencephalography. We consider a recently introduced hybrid reconstruction strategy combining a hierarchical Bayesian model to incorporate a priori information and the advanced randomized multiresolution scanning (RAMUS) source space decomposition approach to reduce modelling errors, respectively. In particular, we aim to generalize the previously extensively used conditionally Gaussian prior (CGP) formalism to achieve distributional reconstructions with higher focality. For this purpose, we introduce as a hierarchical prior, a general exponential distribution, which we refer to as conditionally exponential prior (CEP). The first-degree CEP corresponds to focality enforcing Laplace prior, but it also suffers from strong depth bias, when applied in numerical modelling, making the deep activity unrecoverable. We sample over multiple resolution levels via RAMUS to reduce this bias as it is known to depend on the resolution of the source space. Moreover, we introduce a procedure based on the physiological a priori knowledge of the brain activity to obtain the shape and scale parameters of the gamma hyperprior that steer the CEP. The posterior estimates are calculated using iterative statistical methods, expectation maximization and iterative alternating sequential algorithm, which we show to be algorithmically similar and to have a close resemblance to the iterative $$\ell _1$$ ℓ 1 and $$\ell _2$$ ℓ 2 reweighting methods. The performance of CEP is compared with the recent sampling-based dipole localization method Sequential semi-analytic Monte Carlo estimation (SESAME) in numerical experiments of simulated somatosensory evoked potentials related to the human median nerve stimulation. Our results obtained using synthetic sources suggest that a hybrid of the first-degree CEP and RAMUS can achieve an accuracy comparable to the second-degree case (CGP) while being more focal. Further, the proposed hybrid is shown to be robust to noise effects and compares well with the dipole reconstructions obtained with SESAME.
Article
Full-text available
In this paper, we propose a Bayesian framework to create two dimensional ionospheric images of high spatio-temporal resolution to monitor ionospheric irregularities as measured by the S4 index. Here, we recast the standard Bayesian recursive filtering for a linear Gaussian state-space model, also referred to as the Kalman filter, first by augmenting the (pierce point) observation model with connectivity information stemming from the insight and assumptions/standard modeling about the spatial distribution of the scintillation activity on the ionospheric shell at 350 km altitude. Thus, we achieve to handle the limited spatiotemporal observations. Then, by introducing a set of Kalman filters running in parallel, we mitigate the uncertainty related to a tuning parameter of the proposed augmented model. The output images are a weighted average of the state estimates of the individual filters. We demonstrate our approach by rendering two dimensional real-time ionospheric images of S4 amplitude scintillation at 350 km over South America with temporal resolution of one minute. Furthermore, we employ extra S4 data that was not used in producing these ionospheric images, to check and verify the ability of our images to predict this extra data in particular ionospheric pierce points. Our results show that in areas with a network of ground receivers with a relatively good coverage (e.g. within a couple of kilometers distance) the produced images can provide reliable real-time results. Our proposed algorithmic framework can be readily used to visualize real-time ionospheric images taking as inputs the available scintillation data provided from freely available webservers. Download matlab code: https://github.com/AlexandraKoulouri/real-time-ionospheric-maps-using-Kalman
Preprint
Full-text available
This paper develops mathematical methods for localizing focal sources at different depths based on the non-invasive electro-/magnetoencephalography measurements. In the context of hierarchical Bayesian modelling, we introduce a conditionally exponential prior (CEP) which extends the concept of the conditionally Gaussian prior (CGP) and has been proposed to be advantageous in reconstructing far-field activity, in particular, when coupled with randomized multiresolution scanning (RAMUS). An approach to obtain the shape and scale parameter of the gamma hyperprior steering the CEP is derived from the physiological a priori knowledge of the brain activity. The core concept of this study is to show that the first-degree CEP will yield and improve the focality compared to the second-order case. The results of the present numerical experiments suggest that sources reconstructed via a combination of the first-degree CEP and RAMUS achieve an accuracy comparable to the second-degree case while being more focal for numerically simulated originators of human somatosensory evoked potentials (SEPs) related to human median nerve stimulation, including simultaneous thalamic and cortical activity, as well as for a sub-thalamic dipolar and quadrupolar source configuration.
Preprint
Full-text available
In this paper, we propose a Bayesian framework to create two dimensional ionospheric images of high spatio-temporal resolution to monitor ionospheric irregularities as measured by the S4 index. Here, we recast the standard Bayesian recursive filtering for a linear Gaussian state-space model, also referred to as the Kalman filter, first by augmenting the (pierce point) observation model with connectivity information stemming from the insight and assumptions/standard modeling about the spatial distribution of the scintillation activity on the ionospheric shell at 350 km altitude. Thus, we achieve to handle the limited spatio-temporal observations. Then, by introducing a set of Kalman filters running in parallel, we mitigate the uncertainty related to a tuning parameter of the proposed augmented model. The output images are a weighted average of the state estimates of the individual filters. We demonstrate our approach by rendering two dimensional real-time ionospheric images of S4 amplitude scintillation at 350 km over South America with temporal resolution of one minute. Furthermore, we employ extra S4 data that was not used in producing these ionospheric images, to check and verify the ability of our images to predict this extra data in particular ionospheric pierce points. Our results show that in areas with a network of ground receivers with a relatively good coverage (e.g. within a couple of kilometers distance) the produced images can provide reliable real-time results. Our proposed algorithmic framework can be readily used to visualize real-time ionospheric images taking as inputs the available scintillation data provided from freely available web-servers.
Article
Full-text available
The aim of this paper is to investigate superresolution in deconvolution driven by sparsity priors. The observed signal is a convolution of an original signal with a continuous kernel. With the prior knowledge that the original signal can be considered as a sparse combination of Dirac delta peaks, we seek to estimate the positions and amplitudes of these peaks by solving a finite dimensional convex problem on a computational grid. Because the support of the original signal may or may not be on this grid, by studying the discrete de-convolution of sparse peaks using L1-norm sparsity prior, we confirm recent observations that canonically the discrete reconstructions will result in multiple peaks at grid points adjacent to the location of the true peak. Owning to the complexity of this problem, we analyse carefully the de-convolution of single peaks on a grid and gain a strong insight about the dependence of the reconstructed magnitudes on the exact peak location. This in turn allows us to infer further information on recovering the location of the exact peaks i.e. to perform super-resolution. We analyze in detail the possible cases that can appear and based on our theoretical findings, we propose an self-driven adaptive grid approach that allows to perform superresolution in one-dimensional and multidimensional spaces. With the view that the current study can contribute in the development of more robust algorithms for the detection of single molecules in fluorescence microscopy or identification of characteristic frequencies in spectral analysis, we demonstrate how the proposed approach can recover sparse peaks using simulated signals of low-resolution in one and two-dimensional spaces.
Additional affiliations
October 2018 - October 2021
Tampere University
Position
  • PostDoc Position
Description
  • My research work is titled ''Super-resolution driven by sparsity priors in linear inverse problems with application in microscopy and neuroimaging''
May 2018 - November 2018
University of Bath
Position
  • Researcher
Description
  • Researcher in the Ionospheric imaging group. My work was focused on developing computational tools for the visualization of the ionospheric scintillation activity.
November 2016 - October 2017
Aristotle University of Thessaloniki
Position
  • Research Associate
Description
  • Research fellow in the group of Bioelectromagentism, School of Physics, Aristotle University of Thessaloniki, Greece, Nov. 2016 – Oct. 2017 My work was focused on electric brain imaging and electrical impedance tomography for the identification of the brain conductivity patterns.
Education
September 2010 - August 2015
Imperial College London
Field of study
  • Tomography and Electric Brain Imaging
September 2007 - September 2008
Imperial College London
Field of study
  • Communications and Signal Processing
September 2002 - September 2007
Aristotle University of Thessaloniki
Field of study
  • Electrical engineering

Publications

Publications (32)
Article
Full-text available
In this paper, we focus on the inverse problem of reconstructing distributional brain activity with cortical and weakly detectable deep components in non-invasive Electroencephalography. We consider a recently introduced hybrid reconstruction strategy combining a hierarchical Bayesian model to incorporate a priori information and the advanced rando...
Article
Full-text available
In this paper, we propose a Bayesian framework to create two dimensional ionospheric images of high spatio-temporal resolution to monitor ionospheric irregularities as measured by the S4 index. Here, we recast the standard Bayesian recursive filtering for a linear Gaussian state-space model, also referred to as the Kalman filter, first by augmentin...
Article
This study concerns reconstructing brain activity at various depths based on non-invasive EEG (electroencephalography) scalp measurements. We aimed at demonstrating the potential of the RAMUS (randomized multiresolution scanning) technique in localizing weakly distinguishable far-field sources in combination with coninciding cortical activity. As w...
Preprint
Full-text available
This paper develops mathematical methods for localizing focal sources at different depths based on the non-invasive electro-/magnetoencephalography measurements. In the context of hierarchical Bayesian modelling, we introduce a conditionally exponential prior (CEP) which extends the concept of the conditionally Gaussian prior (CGP) and has been pro...
Preprint
Full-text available
In this paper, we propose a Bayesian framework to create two dimensional ionospheric images of high spatio-temporal resolution to monitor ionospheric irregularities as measured by the S4 index. Here, we recast the standard Bayesian recursive filtering for a linear Gaussian state-space model, also referred to as the Kalman filter, first by augmentin...
Chapter
Unknown electric conductivities of human tissues is a common issue in medical engineering. Electrical impedance tomography (EIT) is an imaging modality that can be used to determine these conductivities in vivo from boundary measurements. In this paper, we demonstrate that local conductivity values of different skull segments can be solved from EIT...
Chapter
The electroencephalography (EEG) source imaging problem is very sensitive to the electrical modelling of the skull of the patient under examination. Unfortunately, the currently available EEG devices and their embedded software do not take this into account; instead, it is common to use a literature-based skull conductivity parameter. In this paper...
Article
Full-text available
The aim of this paper is to investigate superresolution in deconvolution driven by sparsity priors. The observed signal is a convolution of an original signal with a continuous kernel. With the prior knowledge that the original signal can be considered as a sparse combination of Dirac delta peaks, we seek to estimate the positions and amplitudes of...
Preprint
Full-text available
The aim of this paper is to investigate superresolution in deconvolution driven by sparsity priors. The observed signal is a convolution of an original signal with a continuous kernel.With the prior knowledge that the original signal can be considered as a sparse combination of Dirac delta peaks, we seek to estimate the positions and amplitudes of...
Article
Full-text available
We focus on electro-/magnetoencephalography imaging of the neural activity and, in particular, finding a robust estimate for the primary current distribution via the hierarchical Bayesian model (HBM). Our aim is to develop a reasonably fast maximum a posteriori (MAP) estimation technique which would be applicable for both superficial and deep areas...
Preprint
Full-text available
We focus on electromagnetoencephalography imaging of the neural activity and, in particular, finding a robust estimate for the primary current distribution via the hierarchical Bayesian model (HBM). Our aim is to develop a reasonably fast maximum a posteriori (MAP) estimation technique which would be applicable for both superficial and deep areas w...
Article
Full-text available
Satellite-based communications, navigation systems and many scientific instruments rely on observations of trans-ionospheric signals. The quality of these signals can be deteriorated by ionospheric scintillation which can have detrimental effects on the mentioned applications. Therefore, monitoring of ionospheric scintillation and quantifying its e...
Preprint
Unknown electric conductivities of human tissues is a common issue in medical engineering. Electrical impedance tomography (EIT) is an imaging modality that can be used to determine these conductivities in vivo from boundary measurements. In this paper, we demonstrate that local conductivity values of different skull segments can be solved from EIT...
Preprint
The electroencephalography (EEG) source imaging problem is very sensitive to the electrical modelling of the skull of the patient under examination. Unfortunately, the currently available EEG devices and their embedded software do not take this into account; instead, it is common to use a literature-based skull conductivity parameter. In this paper...
Preprint
Full-text available
The expected position error in many cases is far from feasible to be estimated experimentally using real satellite measurements which makes the model-based position dilution of precision (PDOP) crucial in positioning and navigation applications. In the following text we derive the relationship between PDOP and position error and we explain that thi...
Preprint
Satellite-based communications, navigation systems and many scientific instruments rely on observations of trans-ionospheric signals. The quality of these signals can be deteriorated by ionospheric scintillation which can have detrimental effects on the mentioned applications. Therefore, monitoring of ionospheric scintillation and quantifying its e...
Article
Electroencephalography (EEG) source imaging is an ill-posed inverse problem that requires accurate conductivity modelling of the head tissues, especially the skull. Unfortunately, the conductivity values are difficult to determine in vivo. In this paper, we show that the exact knowledge of the skull conductivity is not always necessary when the Bay...
Conference Paper
Knowing the correct skull conductivity is crucial for the accuracy of EEG source imaging, but unfortunately, its true value, which is inter- and intra-individually varying, is difficult to determine. In this paper, we propose a statistical method based on the Bayesian approximation error approach to compensate for source imaging errors related to e...
Conference Paper
In electroencephalography (EEG) source imaging, the inverse source estimates are depth biased in such a way that their maxima are often close to the sensors. This depth bias can be quantified by inspecting the statistics (mean and covariance) of these estimates. In this paper, we find weighting factors within a Bayesian framework for the used \(\el...
Article
Vector tomography methods intend to reconstruct and visualize vector fields in restricted domains by measuring line integrals of projections of these vector fields. Here, we deal with the reconstruction of irrotational vector functions from boundary measurements. As the majority of inverse problems, vector field recovery is an ill posed in the cont...
Article
Knowing the correct skull conductivity is crucial for the accuracy of EEG source imaging, but unfortunately, its true value, which is inter- and intra-individually varying, is difficult to determine. In this paper, we propose a statistical method based on the Bayesian approximation error approach to compensate for source imaging errors related to e...
Article
Full-text available
In electroencephalography (EEG) source imaging, the inverse source estimates are depth biased in such a way that their maxima are often close to the sensors. This depth bias can be quantified by inspecting the statistics (mean and co-variance) of these estimates. In this paper, we find weighting factors within a Bayesian framework for the used L1/L...
Article
In vector tomography (VT), the aim is to reconstruct an unknown multi-dimensional vector field using line integral data. In the case of a 2-dimensional VT, two types of line integral data are usually required. These data correspond to integration of the parallel and perpendicular projection of the vector field along the integration lines and are ca...
Article
In the inverse source problem of the Poisson equation, measurements on the domain boundaries are used to reconstruct sources inside the domain. The problem is an ill-posed inverse problem and it is sensitive to modelling errors of the domain. These errors can be boundary, structure and material property errors, for example. In this paper, we invest...
Technical Report
Full-text available
In this paper, we show that the estimation of an irrotational vector field employing the longitudinal ray transform in the discrete domain is tractable, despite the fact that this problem cannot be solved in the continuous domain using the same formulation. We derive a set of algebraic equations and solve the ill conditioned inverse problem by dire...
Article
We revisit the problem of the reconstruction of an irrotational vector field by solving a set of line integral equations in the discrete domain. We show that the continuous inverse Radon formulation fails to reconstruct an irrotational vector field while the approximate solution of the problem in the digital domain is feasible, overcoming the intri...
Thesis
Full-text available
In the present project, the final goal is the implementation of a different approach for the EEG (Electroencephalography) analysis employing the proposed vector field method. Rather than estimating strengths or locations of the electric sources inside the brain, which is a very complicated task, a reconstruction of the corresponding static bioelect...
Thesis
Full-text available
We present a novel method for the automatic segmentation of the thoracic cavity and the detection of human lungs and the major thoracic organs, as a necessary pre-processing step for a subsequent deformable registration scheme. Our method is divided into two parts. In the first stage, a coarse separation of the body into two subregions, one with th...
Thesis
Full-text available
We present a method for the segmentation and the detection of human Abdominal Aortia in CT images. Our method is divided into two parts. In the first part we estimate the position and the dimension of the aortic lumen using state-of-the-art object tracking techniques. The second part employs curve fitting methods in order to detect the boundaries o...

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Project (1)
Project
My current work deals with super-resolution in de-convolution driven by L1 sparsity prior. The observed signal is a convolution of an underlying signal with a kernel (e.g. Gaussian). Considering that the original signal is a sparse sequence of Dirac-delta functions (distinctive peaks), our aim is to estimate the positions and amplitudes of these peaks by solving a finite dimensional convex problem on a discrete grid. The support of the original signal may or may not be on this grid. By studying the de-convolution of a single peak, we confirm the recent observations that the discrete reconstruction gives multiple peaks at grid points adjacent to the location of the actual peak. Furthermore, we show that with these adjacent peaks and appropriately chosen approximation techniques we can estimate the location of the original peak i.e. perform super-resolution. Finally, based on these theoretical findings we propose an adaptive scheme in which we perform local refinements on the grid in order to automatically separate and detect the underlying peaks.