1,550 research outputs found

    A Hybrid Segmentation and D-bar Method for Electrical Impedance Tomography

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    The Regularized D-bar method for Electrical Impedance Tomography provides a rigorous mathematical approach for solving the full nonlinear inverse problem directly, i.e. without iterations. It is based on a low-pass filtering in the (nonlinear) frequency domain. However, the resulting D-bar reconstructions are inherently smoothed leading to a loss of edge distinction. In this paper, a novel approach that combines the rigor of the D-bar approach with the edge-preserving nature of Total Variation regularization is presented. The method also includes a data-driven contrast adjustment technique guided by the key functions (CGO solutions) of the D-bar method. The new TV-Enhanced D-bar Method produces reconstructions with sharper edges and improved contrast while still solving the full nonlinear problem. This is achieved by using the TV-induced edges to increase the truncation radius of the scattering data in the nonlinear frequency domain thereby increasing the radius of the low pass filter. The algorithm is tested on numerically simulated noisy EIT data and demonstrates significant improvements in edge preservation and contrast which can be highly valuable for absolute EIT imaging

    Incorporating a Spatial Prior into Nonlinear D-Bar EIT imaging for Complex Admittivities

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    Electrical Impedance Tomography (EIT) aims to recover the internal conductivity and permittivity distributions of a body from electrical measurements taken on electrodes on the surface of the body. The reconstruction task is a severely ill-posed nonlinear inverse problem that is highly sensitive to measurement noise and modeling errors. Regularized D-bar methods have shown great promise in producing noise-robust algorithms by employing a low-pass filtering of nonlinear (nonphysical) Fourier transform data specific to the EIT problem. Including prior data with the approximate locations of major organ boundaries in the scattering transform provides a means of extending the radius of the low-pass filter to include higher frequency components in the reconstruction, in particular, features that are known with high confidence. This information is additionally included in the system of D-bar equations with an independent regularization parameter from that of the extended scattering transform. In this paper, this approach is used in the 2-D D-bar method for admittivity (conductivity as well as permittivity) EIT imaging. Noise-robust reconstructions are presented for simulated EIT data on chest-shaped phantoms with a simulated pneumothorax and pleural effusion. No assumption of the pathology is used in the construction of the prior, yet the method still produces significant enhancements of the underlying pathology (pneumothorax or pleural effusion) even in the presence of strong noise.Comment: 18 pages, 10 figure

    NOWY ALGORYTM HYBRYDOWY WYKORZYSTUJĄCY AUTOENKODER KONWOLUCYJNY Z SVM DLA ELEKTRYCZNEJ TOMOGRTAFII IMPEDANCYJNEJ I TOMOGRAFII ULTRADŹWIĘKOWEJ

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    This paper presents a new hybrid algorithm using multiple Support Vector Machines models with convolutional autoencoder to Electrical Impedance Tomography, and Ultrasound Computed Tomography image reconstruction. The ultimate hybrid solution uses multiple SVM models to convert input measurements to individual autoencoder codes representing a given scene then the decoder part of the autoencoder can reconstruct the sceneArtykuł przedstawia nowy hybrydowy algorytm który używa modeli maszyn wektorów nośnych wraz z autoenkoderem konwolucyjnym do rekonstrukcji obrazu z Elektrycznej Tomografii Impedancyjnej oraz Ultrasonograficznej Tomografii Transmisyjnej. Ostateczne rozwiązanie hybrydowe używa wielu modeli SVM do konwersji pomiarów wejściowych do pojedynczych kodów autoenkodera reprezentujących daną scenę a wtedy dekoder wycięty z autoenkodera może zrekonstruować daną scen

    Hybrid Learning based Cell Aggregate Imaging with Miniature Electrical Impedance Tomography

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    Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT

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    In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal partition from boundary measurements. The key tool is to use a distributed shape derivative of a suitable cost functional with respect to movements of the partition. Numerical simulations showing the robustness and accuracy of the method are presented for simulated test cases in two dimensions

    Transformer Meets Boundary Value Inverse Problems

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    A Transformer-based deep direct sampling method is proposed for a class of boundary value inverse problems. A real-time reconstruction is achieved by evaluating the learned inverse operator between carefully designed data and the reconstructed images. An effort is made to give a specific example to a fundamental question: whether and how one can benefit from the theoretical structure of a mathematical problem to develop task-oriented and structure-conforming deep neural networks? Specifically, inspired by direct sampling methods for inverse problems, the 1D boundary data in different frequencies are preprocessed by a partial differential equation-based feature map to yield 2D harmonic extensions as different input channels. Then, by introducing learnable non-local kernels, the direct sampling is recast to a modified attention mechanism. The proposed method is then applied to electrical impedance tomography, a well-known severely ill-posed nonlinear inverse problem. The new method achieves superior accuracy over its predecessors and contemporary operator learners, as well as shows robustness with respect to noise. This research shall strengthen the insights that the attention mechanism, despite being invented for natural language processing tasks, offers great flexibility to be modified in conformity with the a priori mathematical knowledge, which ultimately leads to the design of more physics-compatible neural architectures

    Structure-aware Dual-branch Network for Electrical Impedance Tomography in Cell Culture Imaging

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    Advances in D-bar methods for partial boundary data electrical impedance tomography : From continuum to electrode models and back

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    Electrical impedance tomography (EIT) is a rather new approach to medical imaging that is motivated by using electricity to determine the inside of a body. The clear advantage lies in the usage of harmless electric currents, in contrast to the ionizing radiation of X-rays, whereas the mathematical problem is inherently more challenging. In EIT we seek to reconstruct an image of the inner organs by determining their conductivity, i.e. how well electricity is conducted. As a medical imaging modality it is most promising in pulmonary and cardiac imaging, due to considerably different conductivity values in the air filled lungs (low conductive) and the blood filled heart (high conductive). EIT is in principle capable of monitoring the respiratory process, detecting pathologies in the lungs, and monitoring the heart activity. The main focus of this work is on the partial-boundary problem in EIT, that means one has only access to a certain part of the boundary and data can only be collected there. In a hospital setting these situations can arise when monitoring a critical or unconscious patient and hence one can only access the front of the torso (ventral position). Furthermore, practical complications can arise due to faulty, dislocated, or dispatched electrodes and hence leading to incomplete data. The methods presented in this thesis are capable of dealing with such incomplete data. Following the tradition of mathematical research we are also interested in quantifying the error incomplete data introduces to the reconstruction. In a short summary, this thesis investigates how to improve EIT reconstructions from partial-boundary data by utilizing concepts from an ideal mathematical setting as well as how to apply these methods to real electrode models and measurement data.Sähköinen impedanssitomografia (engl. electrical impedance tomography, lyh. EIT) on kohtalaisen uusi lääketieteellisen kuvantamisen muoto, jossa potilaan sisälle pyritään näkemään heikon sähkövirran avulla. Verrattuna ionisoivaan säteilyyn, kuten röntgensäteilyyn, EIT-kuvantaminen on potilaalle vähemmän haitallista. Kääntöpuolena on tähän kuvantamismuotoon liittyvän matematiikan haastavuus. EIT-kuvantamisessa tavoitteena on tutkia potilaan sisäelimiä selvittämällä niiden sähkönjohtavuus, eli se kuinka hyvin sisäelimet johtavat sähköä. Lääketieteellisen kuvantamisen muodoista se soveltuu erityisen hyvin sydämen ja keuhkojen kuvantamiseen. Tämä johtuu siitä, että sisään hengittäessä keuhkoissa on paljon ilmaa ja toisaalta sydämessä paljon verta. Siksi keuhkojen sähkönjohtavuus on huomattavasti sydäntä pienempi. EIT:llä voidaan tarkkailla potilaan hengitystä, keuhkojen fyysisiä vikoja sekä sydämen aktiivisuutta. Tämän työn pääteemana on EIT-kuvantamisen osittaiset reuna-arvo-ongelmat. Tämä tarkoittaa sitä, että mittauksia tehdään vain osassa mitattavan kappaleen ulkopintaa. Sairaalaolosuhteissa eräs esimerkki tällaisesta mittaustilanteesta on kriittisessä tai tajuttomassa tilassa olevan potilaan tutkiminen, jolloin mittaavia elektroneita voidaan asentaa potilaalle ainoastaan rinnan alueelle. Tämän lisäksi EIT-mittauksessa puutteellista mittausdataa saattavat aiheuttaa käytännön mittausvirheet, jotka voivat johtua viallisista, väärin asennetutuista tai väärässä paikassa olevista elektroneista. Tässä työssä esitetyt menetelmät tarjoavat matemaattisia sekä käytännön mittaustilanteissa tarvittavia keinoja edellä kuvattujen ongelmien ratkaisemiseksi. Matemaattista traditiota noudattaen olemme myös kiinnostuneita kvantifioimaan puutteellisen datan avulla tehtyjen rekonstruktioiden virheellisyyttä. Tiivistäen, tässä työssä tutkitaan kuinka parantaa EIT-kuvantamisen avulla tehtyjä rekonstruktioita, kun vaillinaiset mittaukset on tehty vain osassa kappaleen ulkopintaa. Ratkaisemme matemaattisen ongelman ja sovellamme tämän ongelman ratkaisua todellisen maailman mittausongelmiin

    A direct reconstruction algorithm for the anisotropic inverse conductivity problem based on Calderon's method in the plane

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    A direct reconstruction algorithm based on Calderon's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic inverse conductivity problem, the entries of the unperturbed anisotropic tensors are assumed known a priori, and it remains to reconstruct the multiplicative scalar field. The quasi-conformal map in the plane facilitates the Calderon-based approach for anisotropic conductivities. The method is demonstrated on discontinuous radially symmetric conductivities of high and low contrast.Peer reviewe
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