On a Direct Approach for the Solution of Linear Space-Invariant 2-D Differential Convolution Models
2-D differential convolution operators in a rectangular discrete domain are modelled as linear differential matrix equations of the form Х(t) = Σ AjX(t)Bi + F(t), where the coefficient matrices Ai ∈ IR(MxM),Bi ∈ IR(NxN) and F(t) ∈ IR(MxN) is a piecewise continuous function matrix of t. Under some periodicity assumptions an analytical solution method is presented making use of the 2-D discrete Fourier transform (DFT). For most general problems an iterative computational method founded in the Peano-Baker series is proposed.
KeywordsConvolution Hunt Deconvolution
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- Andrews, H.C. and B.R. Hunt (1977) Digital Image Restoration, Prentice Hall, Englewood Cliffs, New Jersey.Google Scholar
- Cooley J.W. and J.W. Tuckey (1972) An algorithm for the machine computation of complex Fourier series, IEEE Press, Compiled in Digital Signal Processing, 223–228.Google Scholar
- Fromm, J.E. (1969) Lectures on large scale finite difference computation of incomprensible fluid flows, Rpt. RJ 617, IBM Research, San Jose, Calif.Google Scholar
- Gonzalez, R.G. and P. Wints (1977) Digital Image Processing, Addison Wesley, Advanced Book Program, New York.Google Scholar
- Goodman, Y.W. (1968) Introduction to Furier Optics, Mac GrawHill, New York.Google Scholar
- Incertis, F.C. (1981) On a novel matrix approach for linear space invariant 2-D deconvolutions, (in press) IEEE Trans. Automat. Contr. vol. AC-27, 4.Google Scholar
- Lancaster, P. (1970) Explicit solutions of linear matrix equations, SIAM J. Appl. Math., 12, 4: 554–556.Google Scholar
- Neudecker, H. (1969) A note on Kronecker matrix product and matrix equation systems, SIAM J. Appl. Math. 17: 603–606.Google Scholar
- Rabiner, L.R. and C.M. Rader (1972) Digital Signal Processing, IEEE Press, New York.Google Scholar