DocumentCode :
1089924
Title :
Deconvolution when the convolution kernel has no inverse
Author :
Prost, Rémy ; Goutte, Robert
Author_Institution :
Institut National des Sciences Appliqueés de Lyon, Villeurbanne, Cedex, France
Volume :
25
Issue :
6
fYear :
1977
fDate :
12/1/1977 12:00:00 AM
Firstpage :
542
Lastpage :
549
Abstract :
A short study on the general deconvolution problem when the kernel has no inverse proves that a priori information on the signal to be restored is a necessary condition for deconvolution. The proposed deconvolution method uses the following information: the signal to be restored has a bounded support; this support is known or is inside a known interval. This method concerns the convolution kernels whose Fourier transform has a cutoff frequency. This type of kernel has a wide practical field. The image restoration and the processing of "the principal value solution" of the deconvolution problem are the most characteristic elements. The method is derived from the general Liouville-Neuman theory of solving integral equations. This new method incorporates and extends Ville\´s analytic continuation and Van Cittert\´s successive convolution method. The iterative deconvolution algorithm is very simple. The advantages of this method are shown by numerical results and, in particular, by an experimental spectroscopic application.
Keywords :
Convolution; Cutoff frequency; Deconvolution; Fourier transforms; Image restoration; Integral equations; Iterative algorithms; Kernel; Signal restoration; Spectroscopy;
fLanguage :
English
Journal_Title :
Acoustics, Speech and Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
0096-3518
Type :
jour
DOI :
10.1109/TASSP.1977.1163003
Filename :
1163003
Link To Document :
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