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SELF‐MATCHING DECONVOLUTION IN THE FREQUENCY DOMAIN *
Author(s) -
DEREGOWSKI S. M.
Publication year - 1978
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1978.tb01591.x
Subject(s) - deconvolution , inverse filter , wavelet , filter (signal processing) , wiener filter , wiener deconvolution , noise (video) , algorithm , computer science , frequency domain , sensitivity (control systems) , blind deconvolution , mathematics , inverse , electronic engineering , artificial intelligence , engineering , computer vision , image (mathematics) , geometry
A bstract In a previous paper the author showed how, by computing an inverse filter in the frequency domain, an automatic compromise could be made between the conflicting requirements to spike a wavelet and to keep the attendant noise amplification within bounds. This paper extends the technique to take account of errors in the estimated shape of the wavelet defined to the deconvolution process. The drastic effects which such errors can have if they are ignored are demonstrated. A novel form of filter–called the “self‐matching filter”–is defined which allows the user to limit not only the noise amplification but also the sensitivity of the filter to random uncertainties in the estimated wavelet. This is achieved by whitening the spectrum only within automatically selected pass bands whilst suppressing other noise‐dominated or uncertainly defined frequency components. Conventional Wiener filtering is shown to be a special case of this more general filter, namely one in which the wavelet uncertainty is completely ignored. The type of phase spectrum which the output pulse should be designed to possess (e.g. zero phase or minimum phase) is briefly discussed.