Application Of Compressed Sensing To Solving3D Electromagnetic Scattering Problems Over A Wide Angle

Fast algorithm for three dimensional (3D) electromagnetic scattering problem over a wide angle is always a difficult problem in computational electromagnetism (CEM). As a representative of integral equation methods, method of moments (MoM) is applied extensively since its advantage of high calculation accuracy to solve electromagnetic scattering problem, and many fast algorithms based on MoM have already been proposed and improved, however, there is no efficient technique for fast solving wide angle scattering problems as so far. Traditional MoM needs to calculate iteration each time as incident angle changes, so the operation time is long and the efficiency is low. Compressed sensing (CS) is a new technology proposed in the area of signal processing in recent years. By introducing it into traditional MoM,3D electromagnetic scattering problems over a wide angle can be solved rapidly, and based on this, some further improvement work of the new method and the topic of how to apply it into engineering practice are studied. The main work can be expanded as:Firstly, on the basis of investigation of traditional MoM and CS theory, modeling for scattering problem over a wide angle is constructed for3D electromagnetic scattering problems.Secondly, a new kind of excitation is constructed, which includes plentiful incident information over a wide angle. By these new excitations, and on the foundation of original matrix equation of traditional MoM, several measurements of unknown currents over the wide angle which is needed by CS computing are achieved. By these measured values which include plentiful information about incident angles and the other two element factors of CS-sparse transform matrix and recovery algorithm, currents over each angle of incidence can be reconstructed accurately. While using this method, currents over any incident angles can be calculated after only several measurements, thus fast calculation of scattering problem over a wide angle is finished.Thirdly, some improvement of this new fast algorithm are researched and discovered. Five new sparse transform matrices are set up by discretization of five types of classical orthogonal polynomials-Legendre, Chebyshev, the second kind of Chebyshev, Laguerre and Hermite polynomials. By applying these matrcis and some common basis such as Fourier basis, discrete cosine transform basis into the new method as the sparse transform matrix to calculate several3D objects which have different shapes and comparing their performances, numerical results show that the number of times of measurement is different as sparse transform matrix changes. So a conclusion that the fast algorithm can be improved by constructing better sparse transform matrices is obtained. On the other hand, by comparing numbers of times of measurement while using different kinds of random or certain measurement matrix, the method is further improved from the point of view of measurement matrix.Fourthly, apriori knowledges for the new method are established. A priori technique based on physical optics (PO) is proposed. By this technique, sparsity of the projection of current coefficients over the wide angle and the number of times of measurement can be pre-estimated, thus total number of measurements and choice of sparse transform can be acquired before operating the algorithm. This priori technique makes the fast algorithm possess abilities of practical application, and with the help of apriori knowledges, the method can be applied into engineering practice in a real sense.