Electrical impedance tomography (EIT) is a non-invasive imaging technique in medicine and industry. It can be used for determining the distribution of electrical impedance inside a body based upon current and voltage measurements made at the body’s surface. EIT is a non-linear inverse problem and the reconstruction problem is more complex and difficult. Estimation of the location and distribution of multi-conductivity distribution sources within the body, based on voltage recording from the source localization, is one of the fundamental problems in EIT. Independent component analysis (ICA) is a way to resolve signals into independent components based on the statistical characteristics of the signals. It is a method for factoring probability densities of measured signals into a set of densities that are as statistically independent as possible under the assumptions of a linear model. Under the approximate condition the independent component analysis is used to pre-process the acquired voltage measurements for EIT reconstruction in this paper. By using ICA the measured EIT voltage data can be separated into several independent component activation maps, in which the reconstruction algorithm is performed in order to obtain individual conductivity distributions. In our experiment the modified iterative reconstruction algorithm with an exponentially weighted least square criteria can be used for improving the performance of the reconstruction algorithm. Computer simulations show that this method is valid for locating the multi-conductivity distribution in electrical impedance tomography.
Independent component analysis (ICA) is a way to resolve signals into independent components based on the statistical characteristics of the signals. It is a method for factoring probability densities of measured signals into a set of densities that are as statistically independent as possible under the assumptions of a linear model. Electrical impedance tomography (EIT) is used to detect variations of the electric conductivity of the human body. Because there are variations of the conductivity distributions inside the body, EIT presents multi-channel data. In order to get all information contained in different location of tissue it is necessary to image the individual conductivity distribution. In this paper we consider to apply ICA to EIT on the signal subspace (individual conductivity distribution). Using ICA the signal subspace will then be decomposed into statistically independent components. The individual conductivity distribution can be reconstructed by the sensitivity theorem in this paper. Compute simulations show that the full information contained in the multi-conductivity distribution will be obtained by this method.
The fractional Fourier transform is the powerful tool for time-variant signal analysis. For space-variant degradation and non-stationary processes the filtering in fractional Fourier domains permits reduction of the error compared with ordinary Fourier domain filtering. In this paper the concept of filtering in fractional Fourier domains is applied to the problem of estimating degraded images. Efficient digital implementation using discrete Hermite eigenvectors can provide similar results to match the continuous outputs. Expressions for the 2D optimal filter function in fractional domains will be given for transform domains characterized by the two rotation angle parameters of the 2D fractional Fourier transform. The proposed method is used to restore images that have several degradations in the experiments. The results show that the method presented in this paper is valid.
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