References
- Banham, M.R. and Katsaggelos, A.K. (1997). Digital image restoration, IEEE Signal Processing Magazine 14(2): 24-41.
- Ben-Israel, A. and Grevile, T.N.E. (2003). Generalized Inverses, Theory and Applications, Second Edition, Canadian Mathematical Society/Springer, New York, NY.
- Bhimasankaram, P. (1971). On generalized inverses of partitioned matrices, Sankhya: The Indian Journal of Statistics, Series A 33(3): 311-314.
- Bovik, A. (2005). Handbook of Image and Video Processing, Elsevier Academic Press, Burlington.
- Bovik, A. (2009). The Essential Guide to the Image Processing, Elsevier Academic Press, Burlington.
- 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.
- 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.
- 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.
- 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.
- Cormen, T.H., Leiserson, C.E., Rivest, R.L. and Stein, C. (2001). Introduction to Algorithms, Second Edition, MIT Press, Cambridge, MA.
- Courrieu, P. (2005). Fast computation ofMoore-Penrose inverse matrices, Neural Information Processing-Letters and Reviews 8(2): 25-29.
- 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.
- Dice, L.R. (1945). Measures of the amount of ecologic association between species, Ecology 26(3): 297-302.
- 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.
- Graybill, F. (1983). Matrices with Applications to Statistics, Second Edition, Wadsworth, Belmont, CA.
- Greville, T.N.E. (1960). Some applications of the pseudo-inverse of matrix, SIAM Review 3(1): 15-22.
- Hansen, P.C., Nagy, J.G. and O’Leary, D.P. (2006). Deblurring Images: Matrices, Spectra, and Filtering, SIAM, Philadelphia, PA.
- Hillebrand, M. and Muller, C.H. (2007). Outlier robust corner-preserving methods for reconstructing noisy images, The Annals of Statistics 35(1): 132-165.
- 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.
- 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.
- Kalaba, R.E. and Udwadia, F.E. (1996). Analytical Dynamics: A New Approach, Cambridge University Press, Cambridge.
- Karanasios, S. and Pappas, D. (2006). Generalized inverses and special type operator algebras, Facta Universitatis, Mathematics and Informatics Series 21(1): 41-48.
- 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.
- Katsikis, V. and Pappas, D. (2008). Fast computing of the Moore-Penrose inverse matrix, Electronic Journal of Linear Algebra 17(1): 637-650.
- MathWorks (2009). Image Processing Toolbox User’s Guide, The Math Works, Inc., Natick, MA.
- MathWorks (2010). MATLAB 7 Mathematics, TheMathWorks, Inc., Natick, MA.
- Noda, M.T., Makino, I. and Saito, T. (1997). Algebraic methods for computing a generalized inverse, ACM SIGSAM Bulletin 31(3): 51-52.
- Penrose, R. (1956). On a best approximate solution to linear matrix equations, Proceedings of the Cambridge Philosophical Society 52(1): 17-19.
- 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.
- 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.
- 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.
- Schafer, R.W., Mersereau, R.M. and Richards, M.A. (1981). Constrained iterative restoration algorithms, Proceedings of the IEEE 69(4): 432-450.
- 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.
- 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.
- 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.
- 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.
- 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.