Open AccessFrequency domain optimal inverse convolution filtering of noisy data
Author(s) -
Chittineni C. B.
Publication year - 1984
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1984.tb01953.x
Subject(s) - deconvolution , noise (video) , convolution (computer science) , algorithm , dirac delta function , frequency domain , energy (signal processing) , mathematics , wiener deconvolution , signal (programming language) , computer science , blind deconvolution , mathematical optimization , mathematical analysis , statistics , artificial intelligence , image (mathematics) , programming language , artificial neural network
Summary. In many physical experiments, the observations can be represented as the convolution of a model with a source function subject to additive noise. Deconvolution or inverse filtering is a signal‐processing procedure for removing the effects of distortions from the desired signal using all the available information. Assuming the source function and either the signal to noise ratio or the noise energy are known, frequency domain filtering algorithms are developed for estimating the model by formulating the problem (1) as a constrained Wiener restoration problem, (2) as a minimization of a measure of smoothness subject to a constraint either on the signal to noise ratio or on the noise energy, or (3) as a mapping of a source function to a desired signal (e.g. a Dirac delta function) subject to a constraint either on the signal to noise ratio or on the noise energy. The algorithms involve the adjustment of a Lagrangian multiplier to satisfy the constraints, and it is shown that it can be adjusted very efficiently in the frequency domain. Using the above algorithms, a method is suggested for recovering both the source function and the model. Furthermore, experimental results are presented to illustrate the efficiency of the developed methods for different signal to noise ratios.