Two methods to deconvolve: L1-method using simplex algorithm and L2-method using least squares and parameter

If r(t) is the linear scattering response of an object to an excitation waveform e(t) , then r(t) = (e \ast h) (t) . One would like to deconvolve and solve for h(t) , the impulse response. It is well-known that this is often an ill-conditioned problem. Two methods are discussed. The first method rep...

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Vydáno v:	IEEE transactions on antennas and propagation Ročník 32; číslo 3; s. 219 - 225
Hlavní autor:	Drachman, B.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.03.1984 Institute of Electrical and Electronics Engineers
Témata:	Applied sciences Convolution Deconvolution Exact sciences and technology Filtering Frequency domain analysis Information, signal and communications theory Least squares methods Linear programming Mathematics Scattering parameters Signal processing Telecommunications and information theory Vectors Deconvolution Least squares method Simplex method Wave scattering Information processing
ISSN:	0018-926X, 1558-2221
On-line přístup:	Získat plný text
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Popis
Shrnutí:	If r(t) is the linear scattering response of an object to an excitation waveform e(t) , then r(t) = (e \ast h) (t) . One would like to deconvolve and solve for h(t) , the impulse response. It is well-known that this is often an ill-conditioned problem. Two methods are discussed. The first method replaces the discretized matrix form E \cdot H = R by the following problem. Minimize \\|h_{1}\\|+ \ldots + \\|h_{n}\\| subject to R - \lambda \leq E \cdot H \leq R + \lambda where \lambda is a column vector chosen sufficiently small to yield acceptable residuals, yet large enough to make the problem well-conditioned. This problem is converted to a linear programming problem so that the simplex algorithm can be used. The second method is to minimize \parallel E \cdot H - R \parallel^{2} +\lambda \parallel H \parallel^{2} where again \lambda is chosen small enough to yield acceptable residuals and large enough to make the problem well-conditioned. The method will be demonstrated with a Hilbert matrix inversion problem, and also by the deconvolution of the impulse response of a simple target from measured data.
ISSN:	0018-926X 1558-2221
DOI:	10.1109/TAP.1984.1143312