Sparse Transform Matrices and Their Application in the Calculation of Electromagnetic Scattering Problems

Abstract

When compressed sensing is introduced into the moment method, a 3D electromagnetic scattering problem over a wide angle can be solved rapidly, and the selection of sparse basis has a direct influence on the performance of this algorithm, especially the number of measurements. We set up five sparse transform matrices by discretization of five types of classical orthogonal polynomials, i.e., Legendre, Chebyshev, the second kind of Chebyshev, Laguerre, and Hermite polynomials. Performances of the algorithm using these matrices are compared via numerical experiments, and the results show that some of them obviously work excellently and can accelerate wide angle scattering analysis greatly.

Application of Compressive Sensing to Asymptotic Waveform Evaluation for Fast Frequency-Sweep Analysis of Electromagnetic Scattering Problems

“…Based on CS, the choice of sparse transform plays an important role in accuracy of the reconstructed solution [16,17]. For different signals, some empirical knowledge has been obtained in selecting suitable sparse transform matrices; for example, DCT and 2nd-Chebyshev Transform are suitable for slowly changing signal, and DFT is suitable for signals containing rich frequency components, and DWT shows advantage in abrupt changes signal [18], etc.…”

“…Equation (17) can be explained under the CS framework as follows: [Z ( 0 )] × is a measurement matrix that satisfies the RIP since the Toeplitz property of impedance matrix [14], and [V( 0 )] ×1 is the known measurement of the sparse signal [ ] ×1 . To reconstruct the unknown [ ] ×1 , (13) can be solved by the orthogonal matching pursuit (OMP) technique [15], and finally [m 0 ] ×1 can be obtained by (16).…”

Compressed Sensing for Fast Electromagnetic Scattering Analysis of Complex Linear Structures

“…To avoid this situation, sparse transform techniques mentioned in [7][8][9][10] are used to obtain an alternative equation for MOM. Then the compressed sensing theory [11][12][13][14] is introduced, and several rows of the impedance matrix in transform domain are extracted to form an undermined low dimension matrix equation, with the help of reconstruct algorithms instead of iterative approach. The current coefficients can be computed, and the amount of memory consumption and computational efficiency can be improved greatly.…”

Measurement with random sampling for solving EM scattering problems over a wide angle by compressed sensing

“…to sparsify the rows of the measurement matrix. In [3,4], we used to construct some different sparsifying transforms to optimise the CS-based EM scattering computing from the first part. Aiming at the second part of optimisation, random sampling is introduced in this Letter, the main frame is as follows:…”