Computational methods in single molecule localization microscopy Abstract Fluorescence microscopy is one of the chief tools used in biomedical research as it is a non invasive, non destructive, and highly specific imaging method. Unfortunately, an optical microscope is a diffraction limited system. Maximum achievable spatial resolution is approximately 250 nm laterally and 500 nm axially. Since most of the structures in cells researchers are interested in are smaller than that, increasing resolution is of prime importance. In recent years, several methods for imaging beyond the diffraction barrier have been developed. One of them is single molecule localization microscopy, a powerful method reported to resolve details as small as 5 nm. This approach to fluorescence microscopy is very computationally intensive. Developing methods to analyze single molecule data and to obtain super-resolution images are the topics of this thesis. In localization microscopy, a super-resolution image is reconstructed from a long sequence of conventional images of sparsely distributed single photoswitchable molecules that need to be sys- tematically localized with sub-diffraction precision. We designed, implemented, and experimentally verified a set of methods for automated processing, analysis and visualization of data acquired...

The recent emergence of time-of-flight cameras has opened up new possibilities in the world of computer vision. These compact sensors, capable of recording the depth of a scene in real-time, are very advantageous in many applications, such as scene or object reconstruction. This thesis first addresses the problem of fusing depth data with color images. A complete process to combine a time-of-flight camera with a color camera is described and its accuracy is evaluated. The results show that a satisfying precision is reached and that the step of calibration is very important. The second part of the work consists of applying super-resolution techniques to the time-of-flight camera in order to improve its low resolution. Different types of super-resolution algorithms exist but this thesis focuses on the combination of multiple shifted depth maps. The proposed framework is made of two steps: registration and reconstruction. Different methods for each step are tested and compared according to the improvements reached in term of level of details, sharpness and noise reduction. The results obtained show that Lucas-Kanade performs the best for the registration and that a non-uniform interpolation gives the best results in term of reconstruction. Finally, a few suggestions are made about future work and extensions for our solutions.

Les méthodes de microscopie de super-résolution (SRM) telles que la microscopie PALM (photoactivated localization microscopy), STORM (stochastic optical reconstruction microscopy), BALM (binding-activated localization microscopy) et le DNA-PAINT, représentent un nouvel ensemble de techniques de microscopie optique qui permettent de surpasser la limite de diffraction ( > 200 nm dans le spectre visible). Ces méthodes sont basées sur la localisation de la fluorescence de molécules uniques, et peuvent atteindre des résolutions de l'ordre du nanomètres (~20 nm latéralement et 50 nm axialement). Les techniques SRM ont un large spectre d'applications dans les domaines de la biologie et de la biophysique, rendant possible l'accès à l'information tant dynamique que structurale de structures connues ou non, in vivo et in vitro. Beaucoup d'efforts ont été fournis durant la dernière décennie afin d'élargir le potentiel de ces méthodes en développant des méthodes de localisation à la fois plus précise et plus rapide, d'améliorer la photophysique des fluorophores, de développer des algorithmes pour obtenir une information quantitative et augmenter la précision de localisation, etc. Cependant, très peu de méthodes ont été développées pour examiner l'hétérogénéité des images et extraire les informations statistiquement pertinent à partir de plusieurs milliers d'images individuelles super-résolues. Dans mon travail de thèse, je me suis spécifiquement attaquée à ces limitations en: (1) construisant des objets de dimensions nanométriques et de structures bien définies, avec la possibilité d'être adaptés aux besoins. Ces objets sont basés sur les origamis d'ADN. (2) développant des approches de marquage afin d'acquérir des images homogènes de ces objets. (3) implémentant des outils statistiques dans le but d'améliorer l'analyse et la validation d'images. Ces outils se basent sur des méthodes de reconstruction de molécules uniques communément appliquées aux reconstructions d'images de microscopie électronique. J'ai spécifiquement appliqué ces développements à la reconstruction de formes 3D de deux origamis d'ADN modèles (en une et trois dimensions). Je montre comment ces méthodes permettent la dissection de l'hétérogénéité de l'échantillon, et la combinaison d'images similaires afin d'améliorer le rapport signal sur bruit. La combinaison de différentes classes moyennes ont permis la reconstruction des formes tridimensionnelles des origamis d'ADN. Particulièrement, car cette méthode utilise la projection 2D de différentes vues d'une même structure, elle permet la récupération de résolutions isotropes en trois dimensions. Des fonctions spécifiques ont été adaptées à partir de méthodologies existantes afin de quantifier la fiabilité des reconstructions et de leur résolution. A l'avenir, ces développements seront utiles pour la reconstruction 3D de tous types d'objets biologiques pouvant être observés à haute résolution par des méthodologies dérivées de PALM, STORM ou PAINT. / Super resolution microscopy (SRM) methods such as photoactivated localization microscopy (PALM), stochastic optical reconstruction microscopy (STORM), binding-activated localization microscopy (BALM) and DNA-PAINT represent a new collection of light microscopy techniques that allow to overpass the diffraction limit barrier ( > 200 nm in the visible spectrum). These methods are based on the localization of bursts of fluorescence from single fluorophores, and can reach nanometer resolutions (~20 nm in lateral and 50 nm in axial direction, respectively). SRM techniques have a broad spectrum of applications in the field of biology and biophysics, allowing access to structural and dynamical information of known and unknown biological structures in vivo and in vitro. Many efforts have been made over the last decade to increase the potential of these methods by developing more precise and faster localization techniques, to improve fluorophore photophysics, to develop algorithms to obtain quantitative information and increase localization precision, etc. However, very few methods have been developed to dissect image heterogeneity and to extract statistically relevant information from thousands of individual super-resolved images. In my thesis, I specifically tackled these limitations by: (1) constructing objects with nanometer dimensions and well-defined structures with the possibility of be tailored to any need. These objects are based on DNA origami. (2) developing labeling approaches to homogeneously image these objects. These approaches are based on adaptations of BALM and DNA-PAINT microscopies. (3) implemented statistical tools to improve image analysis and validation. These tools are based on single-particle reconstruction methods commonly applied to image reconstruction in electron microscopy.I specifically applied these developments to reconstruct the 3D shape of two model DNA origami (in one and three dimensions). I show how this method permits the dissection of sample heterogeneity, and the combination of similar images in order to improve the signal-to-noise ratio. The combination of different average classes permitted the reconstruction of the three dimensional shape of DNA origami. Notably, because this method uses the 2D projections of different views of the same structure, it permits the recovery of isotropic resolutions in three dimensions. Specific functions were adapted from previous methodologies to quantify the reliability of the reconstructions and their resolution.In future, these developments will be helpful for the 3D reconstruction of any biological object that can be imaged at super resolution by PALM, STORM or PAINT-derived methodologies.

Synapse is the fundamental unit of synaptic transmission. Learning, memory and neurodegenerative diseases of the brain are attributed to the maintenance and alteration in synaptic connections. The efficiency for synaptic transmission depends on how well the post synapse receives the signals from the presynapse; this in turn depends on the receptors present in the post synaptic density (PSD). PSD is present in the post synapse right opposite to the neurotransmitter release site in presynapse (active zone) is an indispensable part of the synapse. The PSD is comprised of receptors and scaffold proteins, which is ultimately supported by the actin cytoskeleton of the dendritic spines. Cytoskeletal dynamics is shown to influence the structural plasticity of spine and also PSD, but how it regulates the dynamicity of the synaptic transmission is not completely understood. Here we studied the influence of actin depolymerisation on sub synaptic organization of an excitatory synapse. In order to study the organization of the synapse at molecular resolution, the conventional microscopy cannot be employed due to the limit of diffraction. Super resolution microscopy circumvents this diffraction limitation. In this study we have used custom built fluorescence microscope with Total Internal Reflection Fluorescence (TIRF) modality to observe the nanometre sized structures inside spines of mouse hippocampal primary neurons. The setup was integrated with Metamorph imaging software for both operating the microscope and imaging acquisition purpose with a separate appropriate laser system. This setup was successful in achieving the lateral resolution of ~30nm and axial resolution of ~51nm. Over all we were able to observe the loss of spines and significant reduction in area of nanometer sized protein clusters in postsynaptic density with in the spines of latrunculin A treated mouse hippocampal primary neurons compared to the native neurons. Along with the morphological alterations in neurons we also observed the changes in nanoscale organization of few key molecules in the postsynaptic density.

Le cerveau est formé d’un réseau complexe de neurones responsables de nos fonctions cognitives et de nos comportements. Les neurones reçoivent via des contacts spécialisés nommés « synapses », des signaux d’autres neurones.[...] Le mécanisme par lequel les neurones reçoivent, intègrent et transmettent ces informations est très complexe et n'est toujours pas parfaitement compris. Dans les synapses excitatrices, les récepteurs AMPA (AMPARs) sont responsables de la transmission synaptique rapide. Les récents développements en microscopie de super résolution ont permis à la communauté scientifique de changer la vision de la transmission synaptique. Une première avancée fait suite à l’observation que les AMPARs ne sont pas distribués de façon homogène dans les synapses, mais sont organisés en nanodomaines de ~ 80 nm de diamètre contenant ~ 20 récepteurs. Ce contenu est un facteur important pour déterminer l'amplitude de la réponse synaptique. En raison de la basse affinité des AMPARs pour le glutamate, un AMPAR ne peut être activé que lorsqu'il est situé dans une zone de ~ 150 nm en face du site de libération des neurotransmetteurs. Récemment, il a été montré que les nanodomaines d’AMPARs sont situés en face de ces sites de libération, formant des nano-colonnes trans-synaptiques à l'état basal. Cette organisation précise à l’échelle nanométrique semble être un facteur clé dans l'efficacité de la transmission synaptique. Une autre avancée a été l'observation que les AMPARs diffusent à la surface des neurones et sont immobilisés à la synapse pour participer à la transmission synaptique. L'échange dynamique entre le pool diffusif d’AMPARs et les récepteurs immobilisés dans les nanodomaines participe au maintien de l’efficacité de la réponse synaptique lors de stimulations à hautes fréquences. L'objectif de ma thèse a été de déterminer le rôle des paramètres indiqués ci-dessus sur les propriétés de la transmission synaptique, à l'état basal et au cours de phénomènes dits de plasticité synaptique. Tout d'abord, nous avons identifié le rôle crucial de la Neuroligine dans l'alignement des nanodomaines d’AMPARs avec les sites de libération du glutamate. En plus de cela, nous avons mis en évidence l’impact de cet alignement sur l’efficacité de la transmission synaptique en perturbant celui-ci. En parallèle, nous avons démontré que les AMPARs désensibilisés sont plus mobiles à la membrane plasmatique que les récepteurs ouverts ou fermés, et ce, en raison d'une diminution de leur affinité pour les sites d’immobilisation synaptiques. Nous avons montré que ce mécanisme permettait aux synapses de récupérer plus rapidement de la désensibilisation et d'assurer la fidélité de la transmission synaptique lors de stimulations à hautes fréquences. Enfin, les synapses peuvent moduler leurs intensités de réponse grâce à des mécanismes de plasticité synaptique à long terme, et plus particulièrement, la dépression à long terme (LTD) qui correspond à un affaiblissement durable de ce poids synaptique. [...] À la suite des découvertes précédentes concernant le rôle de la nano-organisation dynamique des AMPARs pour réguler le poids et la fiabilité de la transmission synaptique, j'ai décidé d'étudier leur rôle dans l'affaiblissement et la sélection des synapses. J'ai découvert que la quantité d’AMPAR par nanodomaine diminue rapidement et durablement. Cette première phase semble due à une augmentation de l’internalisation des AMPARs. Dans un deuxième temps, la mobilité des AMPARs augmente suite à une réorganisation moléculaire de la synapse. Ce changement de mobilité des AMPARs permet aux synapses déprimées de maintenir leur capacité à répondre aux signaux neuronaux à hautes fréquences. Ainsi, nous proposons que l'augmentation de la mobilité des AMPARs au cours de la LTD permet de transmettre une réponse fidèle dans les synapses stimulées à hautes fréquences et donc de sélectivement les maintenir tout en éliminant les synapses inactives. / The brain is a complex network of interconnected neurons responsible for all our cognitive functions and behaviors. Neurons receive inputs at specialized contact zones named synapses which convert an all or none electrical signal to a chemical one, through the release of neurotransmitters. This chemical signal is then turned back in a tunable electrical signal by receptors to neurotransmitters. However, a single neuron receives thousands of inputs coming from several neurons in a spatial- and temporal-dependent manner. The precise mechanism by which neurons receive, integrate and transmit this synaptic inputs is highly complex and is still not perfectly understood. At excitatory synapses, AMPA receptors (AMPARs) are responsible for the fast synaptic transmission. With the recent developments in super-resolution microscopy, the community has changed its vision of synaptic transmission. One breakthrough was the discovery that AMPARs are not randomly distributed at synapses but are organized in nanodomains of ~80 nm of diameter containing ~20 receptors. This content is an important factor since it will determine the intensity of the synaptic response. Due to their mM affinity for glutamate, AMPARs can only be activated when located in an area of ~150 nm in front of the neurotransmitter release site. Recently, AMPAR nanodomains have been shown to be located in front of glutamate release sites and to form trans-synaptic nanocolumns at basal state. Thus, the nanoscale organization of AMPARs regarding release sites seems to be a key parameter for the efficiency of synaptic transmission. Another breakthrough in the field was the observation that AMPARs diffuse at the cell surface and are immobilized at synapses to participate to synaptic transmission. The dynamic exchange between AMPAR diffusive pool and the receptors immobilized into the nanodomains participates to maintain the efficiency of synaptic response upon high-frequency stimulation.The overall aim of my PhD has been to determine the role of each above listed parameters on the intimate properties of synaptic transmission both at basal state and during synaptic plasticity. First, we identified the crucial role of Neuroligin in the alignment of AMPAR nanodomains with glutamate release sites. In addition, we managed to break this alignment to understand its impact on synaptic transmission properties. In parallel, we demonstrated that, due to a decrease in their affinity for synaptic traps, desensitized AMPARs diffuse more at the plasma membrane than opened or closed receptors. This mechanism allows synapses to recover faster from desensitization and ensure the fidelity of synaptic transmission upon high-frequency release of glutamate. Finally, synapses can modulate their strength through long-term synaptic plasticity, in particular, Long-Term Depression (LTD) corresponds to a long-lasting weakening of synaptic strength and is thought to be important in some cognitive processes and behavioral flexibility through synapse selective elimination. Following the previous discoveries about the impact of AMPAR dynamic nano-organization at synapses on the regulation of the synaptic transmission strength and reliability, I decided to investigate their role in the weakening of synapses. I found that AMPAR nanodomain content drops down rapidly and this depletion last several minutes to hours. The initial phase seems due to an increase of endocytosis events, but in a second phase, AMPAR mobility is increased following a reorganization of the post-synaptic density. This change in mobility allows depressed synapses to maintain their capacity to answer to high-frequency inputs. Thus, we propose that LTD-induced increase in AMPAR mobility allows to conduct a reliable response in synapses under high-frequency stimulation and thus to selectively maintain them while eliminating the inactive ones.

Approximate Nearest-Neighbour Field (ANNF\ maps between two related images are commonly used by computer vision and graphics community for image editing, completion, retargetting and denoising. In this work we generalize ANNF computation to unrelated image pairs. For accurate ANNF map computation we propose Feature Match, in which the low-dimensional features approximate image patches along with global colour adaptation. Unlike existing approaches, the proposed algorithm does not assume any relation between image pairs and thus generalises ANNF maps to any unrelated image pairs. This generalization enables ANNF approach to handle a wider range of vision applications more efficiently. The following is a brief description of the applications developed using the proposed Feature Match framework. The first application addresses the problem of detecting the optic disk from retinal images. The combination of ANNF maps and salient properties of optic disks leads to an efficient optic disk detector that does not require tedious training or parameter tuning. The proposed approach is evaluated on many publicly available datasets and an average detection accuracy of 99% is achieved with computation time of 0.2s per image. The second application aims to super-resolve a given synthetic image using a single source image as dictionary, avoiding the expensive training involved in conventional approaches. In the third application, we make use of ANNF maps to accurately propagate labels across video for segmenting video objects. The proposed approach outperforms the state-of-the-art on the widely used benchmark SegTrack dataset. In the fourth application, ANNF maps obtained between two consecutive frames of video are enhanced for estimating sub-pixel accurate optical flow, a critical step in many vision applications. Finally a summary of the framework for various possible applications like image encryption, scene segmentation etc. is provided.

Single-molecule localisation microscopy (SMLM) allows imaging of fluorescently-tagged proteins in live cells with a precision well below that of the diffraction limit. As a single-molecule technique, it has also introduced a new quantitative approach to fluorescence microscopy. In the Part A of this thesis, the design and building of three SMLM instruments, the implementation of a custom-developed image analysis package and the characterisation of the photo-physical properties of the photo-activable fluorescent protein used in this thesis (mEos), are discussed. Then, a new post-processing method for SMLM analysis is characterised: axial optical sectioning of SMLM images is demonstrated by thresholding fitted localisations using their fitted width and amplitude to reject fluorophores that emit from above or below a virtual ?light-sheet?, a thin volume centred on the focal plane of the microscope. This method provides qualitative and quantitative improvements to SMLM. In the Part B of this thesis, SMLM is applied to study T cell activation. Although the T cell receptor plays a key role in immunity, its stoichiometry in the membrane of resting T cells is still a matter of debate. Here, single-molecule counting methods are implemented to compare the stoichiometry of TCRs fused with mEos2 in resting T cells to monomeric and dimeric controls. However, because of the stochasticity of mEos2 photo-physics, results are inconclusive and new counting techniques based on structural imaging are discussed. In addition to TCR triggering, T cells require the co-stimulatory triggering of the CD28 transmembrane receptor to become fully activated. However, some immobilised anti-CD28 antibodies, referred to as super-agonists (SA), can directly activate T cells without triggering the TCR. In this thesis, single-molecule tracking techniques are used to investigate the molecular mechanism of CD28 super-agonism in live T cells. The results indicate that the diffusion of CD28 is slowed by SA binding. This effect is further discussed in light of the kinetic-segregation model proposed for TCR triggering. Quantitative SMLM as implemented and further developed in this work offers new tools to investigate the molecular mechanisms initiating T cell activation, ultimately facilitating the discovery of novel approaches to target these pathways for therapeutic purposes.

La thèse explore trois questions méthodologiques en imagerie de diffusion (DTI) clinique du cerveau, dans le contexte d’une étude sur le VIH. La première question est comment améliorer la résolution du DTI. Le deuxième problème est comment créer un atlas multimodal spécifique à la population. La troisième question porte sur le calcul des statistiques pour comparer les zones de matière blanche entre les contrôles et patients. Les DTI cliniques ont une résolution spatiale et un rapport signal sur bruit faibles, ce qui rend difficile le calcul de statistiques significatives. Nous proposons un algorithme de super-résolution pour améliorer la résolution qui utilise un a priori spatial anisotrope. Cette méthode démontre une amélioration de l’anisotropie fractionnelle et de la tractographie. Pour normaliser spatialement les images du cerveau dans un système de coordonnées commun, nous proposons ensuite de construire un atlas multimodal spécifique á la population. Ceci permet de créer un atlas probabiliste de la matière blanche qui est consistant avec l’atlas anatomique. Cet atlas peut être utilisé pour des statistiques basées sur des régions d’intérêt ou pour le raffinement d’une segmentation. Enfin, nous améliorons les résultats de la méthode TBSS (Tract-Based Spatial Statistics) en utilisant le recalage des images DTI. Contrairement á la méthode TBSS traditionnelle, nous utilisons ici des statistiques multivariées. Nous montrons que ceci permet de détecter des différences dans les régions de matière blanche qui étaient non significatives auparavant, et de les corréler avec les scores des tests neuropsychologiques. / The thesis explores three major methodological questions in clinical brain DTI, in the context of a clinical study on HIV. The first question is how to improve the DTI resolution. The second problem addressed in the thesis is how to create a multimodal population specific atlas. The third question is on the computation of statistics to compare white matter (WM) regions among controls and HIV patients. Clinical DTIs have low spatial resolution and signal-to-noise ratio making it difficult to compute meaningful statistics. We propose a super-resolution (SRR) algorithm for improving DTI resolution. The SRR is achieved using anisotropic regularization prior. This method demonstrates improved fractional anisotropy and tractography. In order to spatially normalize all images in a consistent coordinate system, we create a multimodal population specific brain atlas using the T1 and DTI images from a HIV dataset. We also transfer WM labels from an existing white matter parcellation map to create probabilistic WM atlas. This atlas can be used for region of interest based statistics and refining manual segmentation. On the statistical analysis side, we improve the existing tract based spatial statistics (TBSS) by using DTI based registration for spatial normalization. Contrary to traditional TBSS routines, we use multivariate statistics for detecting changes in WM tracts. With the improved method it is possible to detect differences in WM regions and correlate it with the neuropschylogical test scores of the subjects.

Les propriétés optiques de nanotubes de carbone sont décrites idéalement parla physique d’un objet unidimensionnel, donnant lieu notamment à l’apparition des excitons pour décrire les transitions optiques de ces objets. Les expériences d’optique(émission, absorption) réalisées sur ces objets à température ambiante et sur des ensemble d’objets ont permis de confirmer les prédictions théoriques basées sur la physique des objets 1D. Mais à température cryogénique et à l’échelle de l’objet unique,les propriétés optiques observées expérimentalement sont systématiquement très éloignées de celles d’un objet 1D. On peut notamment citer l’apparition de propriétés comme l’émission de photons uniques, qui a largement contribué à l’intensification de la recherche sur ces objets pour des applications en photonique quantique. Ces propriétés sont attribuées à la localisation des excitons le long de l’axe des nanotubes dans des puits de potentiel créés aléatoirement par l’interaction des nanotubes avec leur environnement. Les propriétés optiques sont alors proches de celles des objets0D, et sont fortement modulées par l’environnement. Les mécanismes et l’origine de la localisation et la connaissance physique de ces puits sont encore très limités. Ce travail montre d’une part le développement d’une technique d’absorption sur objet individuel et la caractérisation de sa sensibilité, et d’autre part l’étude statistique de l’émission de nanotubes à température cryogénique. Les résultats obtenus par une technique de super-résolution couplée à une imagerie hyper-spectrale montrent les grandeurs caractéristiques des puits de potentiels au sein de nanotubes individuels.Un dispositif expérimental de photoluminescence résolue en excitation implémenté au cours de ce travail a également montré une modification de l’état excitonique fondamental par l’environnement, avec l’apparition d’une discrétisation spatiale et spectrale de l’état fondamental délocalisé en une multitude d’états localisés. / The optical properties of carbon nanotubes are ideally described by the physicsof a one-dimensional object, giving rise in particular to the emergence of excitons todescribe the optical transitions of these objects. The optical experiments (emission,absorption) carried out on these objects at ambient temperature and on ensemblesconfirm the theoretical predictions based on the physics of 1D objects. But atcryogenic temperature and at the single emitter scale, the optical properties observedexperimentally are systematically different from those of a 1D object. One can citethe emergence of properties such as photon antibunching, which largely contributed tothe intensification of research on these objects for applications in quantum photonics.These properties are attributed to the localization of excitons along the nanotube axisin local potential wells (traps) created randomly by the interaction of nanotubes withtheir environment. The optical properties are then close to those of 0D objects, andare strongly modulated by the environment. The mechanisms and the origin of thelocalization and the physical knowledge of these traps are still very limited. This workshows on the one hand the development of an absorption setup on individual objectand the characterization of its sensitivity, and on the other hand the statistical studyof the emission of nanotubes at cryogenic temperature in a micro-photoluminescencesetup. The results obtained in the later setup by a super-resolution technique coupledwith hyper-spectral imaging show the characteristic quantities of potential wellswithin individual nanotubes. An experimental excitation-resolved photoluminescencesetup implemented during this work also showed a modification of the fundamentalexcitonic state by the environment, with the emergence of a spatial and spectraldiscretization of the delocalized ground state in a multitude of localized states.

Les différentes modalités d’imagerie par ondes présentent chacune des limitations en termes de résolution ou de contraste. Dans ce travail, nous modélisons l’imagerie ultrasonore ultrarapide et présentons des méthodes de reconstruction qui améliorent la précision de l’imagerie ultrasonore. Nous introduisons deux méthodes qui permettent d’augmenter le contraste et de mesurer la position super-résolue et la vitesse dans les vaisseaux sanguins. Nous présentons aussi une méthode de reconstruction des paramètres microscopiques en tomographie d’impédance électrique en utilisant des mesures multifréquence et en s’aidant de la théorie de l’homogénéisation. / Different modalities in wave imaging each present limitations in terms of resolution or contrast. In this work, we present a mathematical model of the ultrafast ultrasound imaging modality and reconstruction methods which can improve contrast and resolution in ultrasonic imaging. We introduce two methods which allow to improve contrast and to locate blood vessels belowthe diffraction limit while simultaneously estimating the blood velocity. We also present a reconstruction method in electrical impedance tomography which allows reconstruction of microscopic parameters from multi-frequency measurements using the theory of homogenization.