Deconvolving Measured Electromagnetic Responses

This chapter presents two deconvolution techniques to illustrate how the ill‐posed deconvolution problem has been regularized. The two techniques presented have the built in self‐regularizing schemes. The first method is based on solving the ill‐posed deconvolution problem by the iterative conjugate gradient method. The second method uses the method of total least squares implemented through the singular value decomposition (SVD) technique. The conjugate gradient method essentially performs singular value decomposition without actually computing the eigenvalues and the criteria that one utilizes to stop the iterative process is that the magnitude of the largest element in the residual must be a certain value. Two methods ‐ the conjugate gradient method with the Fast Fourier Transform Technique and the Total Least Squares based on the SVD has been presented to obtain the impulse responses of some electromagnetic systems with measured input and output data.