@mastersthesis{elediasc12651,
          school = {University of Trento},
           title = {Reconstructing buried object within Born I approximation by means of GPR Data and an Interval Analysis based optimization algorithm},
          author = {A. Malacarne},
           month = {August},
            year = {2014},
        abstract = {Interval Analysis (IA) consists of a set of rules and tools for the analysis and optimization of functions where the variables at hand are intervals of numbers and not single values as in classical arithmetical/ optimization problems. For example, an interval of real values (a real interval) can be defined as a one-dimensional compact set (a segment) between two extreme points, namely the Infimum and Supremum of the interval values. Firstly proposed to determine the error bounds on the rounding operations in numerical computation, IA has then been applied to solve linear and non-linear equations as well as optimization problems . Referring to the last point, IA offers ad-hoc global optimization techniques able to identify the global optimum with the desired level of accuracy.
Consequently, IA-based optimization seems to be an useful tool to solve the so called ?inverse scattering problems?. In such problems the geometrical and the electrical properties of an unknown object (namely scatterer) are usually computed by minimizing a suitable cost function that measures the distance between the electrical field collected in probes surrounding the investigation domain and the  electrical field generated numerically by a trial solution. In dealing with inverse scattering problem classical optimization algorithms (deterministic and stochastic) could be trapped in local minima and then the inversion process failed.
On the contrary, an algorithm based on IA iteratively divide the space of the solution in intervals and it discharges intervals in which it is sure the optimal solution does not lie. As a consequence, the algorithm is able to minimize the cost function related with the inverse scattering problem and then obtaining the unknown scatterer parameters with a desired level of accuracy. 
This project is aimed to implement an inversion algorithm for microwave imaging based on the Interval  Analysis for the reconstruction of buried objects from the GPR acquired data, when the characteristics of the object respect the 1st Born Approximation.
},
             url = {http://www.eledia.org/students-reports/651/},
        keywords = {Interval Analysis, Inverse Scattering, Compressive Sensing, Direction-of-Arrival, Compressive Sensing}
}