Doctoral Schools WUT

Electrical capacitance tomography (ECT) allows to visualize a spatial distribution of electrical permittivity of objects. Images are reconstructed using capacitance values measured between electrodes surrounding the visualized volume. Due to a small number of electrodes (8 to 32), the number of measurements is much smaller than number of image elements which makes image reconstruction ill-posed and ill-conditioned. State-of-the-art algorithms like Levenberg-Marquardt are mostly iterative and nonlinear, i.e. they require many recalculations of the Jacobian matrix which constitutes relation between permittivity values and capacitances (sensitivity matrix). This is a very time-consuming task which makes real-time imaging very hard. It is necessary to acquire new knowledge that will overcome the existing limitations. The project will consider an alternative solution based on deep neural networks (DNNs).

The research planned in the project aims to investigate deep network architectures that will achieve not only comparable but significantly better results than classical methods. Various DNNs will be analyzed and tested. The behavior of the DNNs in tomography with the increased number of electrodes will be investigated (32-electrode sensor). We are curious if the use of neural networks will push the limits of image quality in ECT, especially image spatial resolution. Numerical modeling of electrical capacitance tomography sensors and test objects will be carried out using the ECTsim toolbox for MATLAB. The finite volume method (FVM) using non-uniform mesh will be applied to compute electrical field distributions and sensitivity matrices of sensors. The numerical modeling will allow to optimize the electrode configuration in the sensing probe. The arrangement of electrodes in one ring (32 electrodes) and in two rings of 16 electrodes each will be considered. Generation of datasets for learning, testing and validation will be performed. The training data will be generated numerically and using real measurements. The permittivity distribution in the probe will be randomized according to the assumed probability distributions describing the number of objects, their shape, location and the value of permittivity. 

• Keywords: Deep neural networks for image reconstruction in electrical capacitance tomography” |

Capacitance measurements will be estimated. The selection of training datasets that may be application-dependent will be performed. Real data generation will consist in dynamic image acquisition when test objects are moved and rotated in the tomographic probe. It will be required to equip the measuring station with appropriate mechanics. For obvious reasons, the number of test objects will be very limited compared to the numerical simulation. It will be necessary to use data augmentation methods. The measurements will be carried out using an EVT4 electrical capacitance tomography scanner which was entirely designed and built by our group. The architecture of the hardware is based on fast programmable devices and allows fast measurements with high signal-to-noise ratio using 32 channels. A comparative study on deep learning architectures in the context of image reconstruction will be performed. Networks that have already been used in electrical capacitance tomography or electrical impedance tomography will be considered as well as several popular deep learning architectures, such as convolutional neural networks, recurrent neural networks, long short-term memory/gated recurrent unit, self-organizing map, autoencoders and restricted Boltzman machine. Learning and testing of selected DNNs with different dataset configurations will be done. The different loss functions and different solvers will be used to optimize the networks. The images will be reconstructed using DNNs and a state-of-the-art algorithm (Levenberg-Marquardt) will be used as a base reference in comparative analysis. The results will be assessed using selected image quality norms.

The conducted research should influence the shift of paradigms prevailing in the ECT environment. The use of deep networks may allow for increasing the spatial resolution of ECT scanners. The knowledge gained in the selection of a deep network, analysis of its architecture, and training techniques can be used in inverse problems occurring in other fields. The results of the research will be the subject of publications in renowned journals. All datasets, DNN architectures as well as software tools like ECTsim will be made available to the scientific community in public repositories.

• Keywords: ' | Deep neural networks for image reconstruction in electrical capacitance tomography |

Electrical tomography allows to visualize a spatial distribution of electrical parameters of tested objects. Until now, electrical impedance tomography (EIT) with sinusoidal excitation was considered to have the greatest potential for application in diagnostic medical imaging among electrical imaging techniques, however impedance of electrode-skin contact, which is a major challenge in this imaging technique, limits the development of this technique and its practical use. It is necessary to acquire new knowledge that will overcome the existing limitations. In this project, an alternative approach with non-contact electrodes and pulse excitation will be investigated.

The aim is to verify the properties of capacitively coupled electrical tomography in the context of diagnostic medical imaging. Studies will be performed using numerical and physical lung phantom, taking into account regional ventilation distribution. Measurement sensitivity, contrast and spatial-temporal resolution of images will be assessed. 3D numerical modeling of a tomographic sensor with capacitance electrodes will be performed. The simulation will be performed for the developed numerical model of a thorax. ECTsim package for MATLAB, developed at the Nuclear and Medical Electronics Division (ZEJiM), will be used to solve forward and inverse problems. Based on calculated distributions of the electric field in a thorax, sensitivity matrices and measurements for the numerical phantom of lungs in exhalation and inspiration will be determined. Non-linear iterative algorithms and deep learning will be used for image reconstruction.

• Keywords: Capacitively coupled impedance tomography for anatomical and functional imaging |

The simulations will allow to determine the optimal parameters of a tomographic sensor, which will be in the form of an elastic belt or a vest worn by the patient. Real measurements on a simple thorax phantom which will simulate the respiratory cycle will be performed. A prototype of a flexible sensor with surface electrodes and a mechanical-electrical lung phantom will be built. Measurements will be performed using the 32-channel electrical capacitance tomograph EVT4, designed and built at ZEJiM. In order to perform the measurements, the signal channels of the tomographic system will be rebuilt in accordance with the results of theoretical considerations and numerical simulation, so as to adapt them to the new concept of measuring electric permittivity and electrical conductivity. Results of the research, evaluation of the sensitivity of measurements, spatial and temporal resolution as well as image quality will be the subject of publications in renowned journals. Modification of the measuring system including electrodes will be the subject of a patent application. The developed scripts for the simulation of the thorax phantom as well as the measurement data and reconstructed images will be made available to the scientific community in public repositories.

• Keywords: Capacitively coupled impedance tomography for anatomical and functional imaging |