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On the computational model of a kind of deconvolution problem
Zou Mou-yan; Unbehauen, R.;
Image Processing, IEEE Transactions on
Volume 4,
Issue 10,
Oct. 1995
Page(s):1464
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1467
Abstract:
It is known that discretization of a continuous deconvolution problem can alleviate the ill-posedness of the problem. The currently used circulant matrix model, however, does not play such a role. Moreover, the approximation of deconvolution problems by circulant matrix model is rational only if the size of the kernel function is very small. We propose an aperiodic model of deconvolution. For discrete and finite deconvolution problems the new model is an exact one. In the general case, the new model can lead to a nonsingular system of equations that has a lower condition number than the circulant one, and the related computations in the deconvolution can be done efficiently by means of the DFT technique, as in the ease for circulant matrices. The rationality of the new model holds without regard to the size of the kernel and the image. The use of the aperiodic model is illustrated by gradient-based algorithms
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