Iterative methods for tomography problems: implementation to a cross-well tomography problem

The velocity distribution between two boreholes is reconstructed by cross-well tomography, which is commonly used in geology. In this paper, iterative methods, Kaczmarz's algorithm, algebraic reconstruction technique (ART), and simultaneous iterative reconstruction technique (SIRT), are implemented to a specific cross-well tomography problem. Convergence to the solution of these methods and their CPU time for the cross-well tomography problem are compared. Furthermore, these three methods for this problem are compared for different tolerance values

Solar Reector Design

The design of solar panels is investigated. Different aspects of this problem are presented. A formula averaging the solar energy received on a given location is derived rst. The energy received by the collecting solar panel is then calculated using a specially designed algorithm. The geometry of the device collecting the energy may then be optimised using different algorithms. The results show that for a given depth, devices of smaller width are more energy efficient than those of wider dimensions. This leads to a more economically efficient design

Tunable high-resolution synthetic aperture radar imaging

We have recently introduced a modification of the multiple signal classification (MUSIC) method for synthetic aperture radar. This method depends on a tunable, user-defined parameter, $\epsilon$, that allows for quantitative high-resolution imaging. It requires however, relative large single-to-noise ratios (SNR) to work effectively. Here, we first identify the fundamental mechanism in that method that produces high-resolution images. Then we introduce a modification to Kirchhoff Migration (KM) that uses the same mechanism to produces tunable, high-resolution images. This modified KM method can be applied to low SNR measurements. We show simulation results that demonstrate the features of this method

Inversion of limited-aperture Fresnel experimental data using orthogonality sampling method with single and multiple sources

In this study, we consider the application of orthogonality sampling method (OSM) with single and multiple sources for a fast identification of small objects in limited-aperture inverse scattering problem. We first apply the OSM with single source and show that the indicator function with single source can be expressed by the Bessel function of order zero of the first kind, infinite series of Bessel function of nonzero integer order of the first kind, range of signal receiver, and the location of emitter. Based on this result, we explain that the objects can be identified through the OSM with single source but the identification is significantly influenced by the location of source and applied frequency. For a successful improvement, we then consider the OSM with multiple sources. Based on the identified structure of the OSM with single source, we design an indicator function of the OSM with multiple sources and show that it can be expressed by the square of the Bessel function of order zero of the first kind an infinite series of the square of Bessel function of nonzero integer order of the first kind. Based on the theoretical results, we explain that the objects can be identified uniquely through the designed OSM. Several numerical experiments with experimental data provided by the Institute Fresnel demonstrate the pros and cons of the OSM with single source and how the designed OSM with multiple sources behave.Comment: 17 pages, 11 figure