Microwave Data Inversions Using the Source-Receiver Compression Scheme

• Published in: IEEE transactions on antennas and propagation Vol. 60; no. 6; pp. 2853 - 2864
• Main Authors: Abubakar, A., Habashy, T. M., Pan, G.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied classical electromagnetism; Compression; Computation; Data compression; Data models; Decomposition; Eigenvalues and eigenfunctions; electromagnetic; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Equations; Exact sciences and technology; Fundamental areas of phenomenology (including applications); inverse problem; Inversions; Jacobian matrices; Mathematical model; microwave; Microwaves; Noise measurement; Nonlinearity; Physics; Receivers; Studies; Three dimensional; Signal compression; inverse problem; Compression; Electromagnetism; Quasi Newton method; Redundancy; Data compression; Steepest descent method; Gauss Newton method; Conjugate gradient methods; Nonlinear estimation; Statistical method; Computation time; Three dimensional model; Inverse problems; three-dimensional; electromagnetic; Eigenvalues; Eigenvectors; Non linear processing; microwave; Principal component analysis; Singular value decomposition
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2012.2194675

We apply a source-receiver compression approach to reduce the computational time and memory usage of the nonlinear inversion approaches for interpreting three-dimensional microwave data. By detecting and quantifying the extent of redundancy in the data, we assemble a reduced set of simultaneous sources and receivers that are weighted sums of the physical sources and receivers employed in the measurement setup. Because the number of these simultaneous sources and receivers can be significantly less than those of the physical sources and receivers, the computational time and memory usage of any inversion method such as steepest-descent, nonlinear conjugate-gradient, contrast-source inversion, and quasi-Newton can be tremendously reduced. The scheme is based on decomposing the data into their principal components using a singular-value decomposition approach and the data compression is done through the elimination of eigenvectors corresponding to small eigenvalues. Consequently, this will also suppress the effect of noise in the data. As a concept demonstration we show that this approach has the potential of significantly reducing both computational time and memory usage of the Gauss-Newton inversion method by few orders of magnitude.