Application of the partitioning method to specific Toeplitz matrices

Banham, M.R. and Katsaggelos, A.K. (1997). Digital image restoration, IEEE Signal Processing Magazine 14(2): 24-41.10.1109/79.581363Search in Google Scholar

Ben-Israel, A. and Grevile, T.N.E. (2003). Generalized Inverses, Theory and Applications, Second Edition, Canadian Mathematical Society/Springer, New York, NY.Search in Google Scholar

Bhimasankaram, P. (1971). On generalized inverses of partitioned matrices, Sankhya: The Indian Journal of Statistics, Series A 33(3): 311-314.Search in Google Scholar

Bovik, A. (2005). Handbook of Image and Video Processing, Elsevier Academic Press, Burlington.Search in Google Scholar

Bovik, A. (2009). The Essential Guide to the Image Processing, Elsevier Academic Press, Burlington.Search in Google Scholar

Chantas, G.K., Galatsanos, N.P. and Woods, N.A. (2007). Super-resolution based on fast registration and maximum a posteriori reconstruction, IEEE Transactions on Image Processing 16(7): 1821-1830.10.1109/TIP.2007.896664Search in Google Scholar

Chountasis, S., Katsikis, V.N. and Pappas, D. (2009a). Applications of the Moore-Penrose inverse in digital image restoration, Mathematical Problems in Engineering 2009, Article ID: 170724, DOI: 10.1155/2010/750352.10.1155/2010/750352Search in Google Scholar

Chountasis, S., Katsikis, V.N. and Pappas, D. (2009b). Image restoration via fast computing of the Moore-Penrose inverse matrix, 16th International Conference on Systems, Signals and Image Processing, IWSSIP 2009,Chalkida, Greece, Article number: 5367731.10.1109/IWSSIP.2009.5367731Search in Google Scholar

Chountasis, S., Katsikis, V.N. and Pappas, D. (2010). Digital image reconstruction in the spectral domain utilizing the Moore-Penrose inverse, Mathematical Problems in Engineering 2010, Article ID: 750352, DOI: 10.1155/2010/750352.10.1155/2010/750352Search in Google Scholar

Cormen, T.H., Leiserson, C.E., Rivest, R.L. and Stein, C. (2001). Introduction to Algorithms, Second Edition, MIT Press, Cambridge, MA.Search in Google Scholar

Courrieu, P. (2005). Fast computation ofMoore-Penrose inverse matrices, Neural Information Processing-Letters and Reviews 8(2): 25-29.Search in Google Scholar

Craddock, R.C., James, G.A., Holtzheimer, P.E. III, Hu, X.P. and Mayberg, H.S. (2012). A whole brain FMRI atlas generated via spatially constrained spectral clustering, Human Brain Mapping 33(8): 1914-1928.10.1002/hbm.21333383892321769991Search in Google Scholar

Dice, L.R. (1945). Measures of the amount of ecologic association between species, Ecology 26(3): 297-302.10.2307/1932409Search in Google Scholar

Górecki, T. and Łuczak, M. (2013). Linear discriminant analysis with a generalization of the Moore-Penrose pseudoinverse, International Journal of Applied Mathematics and Computer Science 23(2): 463-471, DOI: 10.2478/amcs-2013-0035.10.2478/amcs-2013-0035Search in Google Scholar

Graybill, F. (1983). Matrices with Applications to Statistics, Second Edition, Wadsworth, Belmont, CA.Search in Google Scholar

Greville, T.N.E. (1960). Some applications of the pseudo-inverse of matrix, SIAM Review 3(1): 15-22.10.1137/1002004Search in Google Scholar

Hansen, P.C., Nagy, J.G. and O’Leary, D.P. (2006). Deblurring Images: Matrices, Spectra, and Filtering, SIAM, Philadelphia, PA.10.1137/1.9780898718874Search in Google Scholar

Hillebrand, M. and Muller, C.H. (2007). Outlier robust corner-preserving methods for reconstructing noisy images, The Annals of Statistics 35(1): 132-165.10.1214/009053606000001109Search in Google Scholar

Hufnagel, R.E. and Stanley, N.R. (1964). Modulation transfer function associated with image transmission through turbulence media, Journal of the Optical Society of America 54(1): 52-60.10.1364/JOSA.54.000052Search in Google Scholar

Kalaba, R.E. and Udwadia, F.E. (1993). Associative memory approach to the identification of structural and mechanical systems, Journal of Optimization Theory and Applications 76(2): 207-223.10.1007/BF00939605Search in Google Scholar

Kalaba, R.E. and Udwadia, F.E. (1996). Analytical Dynamics: A New Approach, Cambridge University Press, Cambridge.Search in Google Scholar

Karanasios, S. and Pappas, D. (2006). Generalized inverses and special type operator algebras, Facta Universitatis, Mathematics and Informatics Series 21(1): 41-48.Search in Google Scholar

Katsikis, V.N., Pappas, D. and Petralias, A. (2011). An improved method for the computation of the Moore-Penrose inverse matrix, Applied Mathematics and Computation 217(23): 9828-9834.10.1016/j.amc.2011.04.080Search in Google Scholar

Katsikis, V. and Pappas, D. (2008). Fast computing of the Moore-Penrose inverse matrix, Electronic Journal of Linear Algebra 17(1): 637-650.10.13001/1081-3810.1287Search in Google Scholar

MathWorks (2009). Image Processing Toolbox User’s Guide, The Math Works, Inc., Natick, MA.Search in Google Scholar

MathWorks (2010). MATLAB 7 Mathematics, TheMathWorks, Inc., Natick, MA.Search in Google Scholar

Noda, M.T., Makino, I. and Saito, T. (1997). Algebraic methods for computing a generalized inverse, ACM SIGSAM Bulletin 31(3): 51-52.10.1145/271130.271204Search in Google Scholar

Penrose, R. (1956). On a best approximate solution to linear matrix equations, Proceedings of the Cambridge Philosophical Society 52(1): 17-19.10.1017/S0305004100030929Search in Google Scholar

Prasath, V.B.S. (2011). A well-posed multiscale regularization scheme for digital image denoising, International Journal of Applied Mathematics and Computer Science 21(4): 769-777, DOI: 10.2478/v10006-011-0061-7.10.2478/v10006-011-0061-7Search in Google Scholar

Rao, C. (1962). A note on a generalized inverse of a matrix with applications to problems in mathematical statistics, Journal of the Royal Statistical Society, Series B 24(1): 152-158.10.1111/j.2517-6161.1962.tb00447.xSearch in Google Scholar

Röbenack, K. and Reinschke, K. (2011). On generalized inverses of singular matrix pencils, International Journal of Applied Mathematics and Computer Science 21(1): 161-172, DOI: 10.2478/v10006-011-0012-3.10.2478/v10006-011-0012-3Search in Google Scholar

Schafer, R.W., Mersereau, R.M. and Richards, M.A. (1981). Constrained iterative restoration algorithms, Proceedings of the IEEE 69(4): 432-450.10.1109/PROC.1981.11987Search in Google Scholar

Shinozaki, N., Sibuya, M. and Tanabe, K. (1972). Numerical algorithms for the Moore-Penrose inverse of a matrix: Direct methods, Annals of the Institute of Statistical Mathematics 24(1): 193-203.10.1007/BF02479751Search in Google Scholar

Smoktunowicz, A. and Wr´obel, I. (2012). Numerical aspects of computing the Moore-Penrose inverse of full column rank matrices, BIT Numerical Mathematics 52(2): 503-524.10.1007/s10543-011-0362-0Search in Google Scholar

Stojanović, I., Stanimirovi´c, P. and Miladinovi´c, M. (2012). Applying the algorithm of Lagrange multipliers in digital image restoration, Facta Universitatis, Mathematics and Informatics Series 27(1): 41-50.Search in Google Scholar

Udwadia, F.E. and Kalaba, R.E. (1997). An alternative proof for Greville’s formula, Journal of Optimization Theory and Applications 94(1): 23-28.10.1023/A:1022699317381Search in Google Scholar

Udwadia, F.E. and Kalaba, R.E. (1999). General forms for the recursive determination of generalized inverses: Unified approach, Journal of Optimization Theory and Applications 101(3): 509-521. 10.1023/A:1021781918962Search in Google Scholar