Electron density distribution is the major determining parameter of the ionosphere. Computerized Ionospheric Tomography (CIT) is a method to reconstruct ionospheric electron density image by computing Total Electron Content (TEC) values from the recorded Global Positioning Satellite System (GPS) signals. Due to the multi-scale variability of the ionosphere and inherent biases and errors in the computation of TEC, CIT constitutes an underdetermined ill-posed inverse problem. In this study, a novel Singular Value Decomposition (SVD) based CIT reconstruction technique is proposed for the imaging of electron density in both space (latitude, longitude, altitude) and time. The underlying model is obtained from International Reference Ionosphere (IRI) and the necessary measurements are obtained from earth based and satellite based GPS recordings. Based on the IRI-2007 model, a basis is formed by SVD for the required location and the time of interest. Selecting the first few basis vectors corresponding to the most significant singular values, the 3-D CIT is formulated as a weighted least squares estimation problem of the basis coefficients. By providing significant regularization to the tomographic inversion problem with limited projections, the proposed technique provides robust and reliable 3-D reconstructions of ionospheric electron density.
We propose a cost-effective algorithm for the dynamic image reconstruction problem in magnetic resonance imaging (MRI). The proposed imaging method, the ensemble Kalman filter, is a Monte Carlo approximation to the Kalman filter with reduced computational cost. The technique reconstructs images of snapshots taken during a cardiac cycle from a low number of measurements that can be obtained during the time interval. The algorithm makes use of a dynamic imaging model of the object derived from prior information. The results are produced by applying the method on the extended cardiac-torso (XCAT) human body phantom with real life parameter selections. The reconstructions are sharp, accurate and fast without any ringing artifacts caused by the conventional methods.
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