A regularized structured total least squares algorithm for high-resolution image reconstruction

Linear Algebra and Its Applications

Volumn 391, Issue 1-3 SPEC. ISS., 2004, Pages 75-98

  Fu, Haoying ^a   Barlow, Jesse ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

High resolution image reconstruction; Ill conditioned matrices; Image deblurring; Regularization; Regularized structured total least squares; Structured matrices; Total least squares

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; FUNCTIONS; LEAST SQUARES APPROXIMATIONS; LINEAR SYSTEMS; MATRIX ALGEBRA; OPTICAL RESOLVING POWER; PROBLEM SOLVING;

ILL CONDITIONED MATRICES; REGULARIZATION; STRUCTURED MATRICES; TOTAL LEAST SQUARES;

IMAGE RECONSTRUCTION;

EID: 4644354196     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(03)00660-8     Document Type: Article

References (19)

1. Björck Å., Elfving T. Accelerated projection methods for computing pseudoinverse solutions of linear equations. BIT. 19:1979;145-163.
2. Bose N.K., Boo K.J. High-resolution image reconstruction with multisensors. Int. J. Imaging Systems Technol. 9:1998;294-304.
3. Etter D.M., Kuncicky D.C., Hull D.W. Introduction to Matlab 6. 2002;Prentice Hall, Upper Saddle River, NJ.
4. Golub G.H., Hansen P.C., O'Leary D.P. Tikhonov regularization and total least squares. SIAM J. Matrix Anal. Appl. 21(1):1999;185-194.
5. Hansen P.C., O'Leary D.P. The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comput. 14:1993;1487-1503.
6. A. Kalsi, D.P. O'Leary, Algorithms for structured total least squares problems with applications to blind image deblurring, Technical Report, Department of Computer Science, University of Maryland, 2002.
7. Kamm J., Nagy J.G. A total least squares method for toeplitz systems of equations. BIT. 38:1998;560-582.
8. Van Loan C. Computational Frameworks for the Fast Fourier Transform. 1992;SIAM Publications, Philadelphia, PA.
9. Mastronardi N., Lemmerling P., Van Huffel S. Fast structured total least squares algorithm for solving the basic deconvolution problem. SIAM J. Matrix Anal. Appl. 22(2):2000;533-553.
10. N. Mastronardi, P. Lemmerling, S. Van Huffel, Fast algorithms for solving regularized structured total least squares problems, in: Tenth International Congress on Computational and Applied Mathematics, Katholieke Universiteit Leuven, Belgium, 2002.
11. Mesarović V.Z., Galatsanos N.P., Katsaggelos A.K. Regularized constrained total least squares image restoration. IEEE Trans. Image Process. 4(8):1995;1096-1108.
12. Ng M.K., Chan R.H., Chan T.F., Yip A.M. Cosine transform preconditioners for high resolution image reconstruction. Linear Algebra Appl. 316:2000;89-104.
13. Ng M.K., Chan R.H., Tang W.C. A fast algorithm for deblurring models with Neumann boundary conditions. SIAM J. Sci. Comput. 21(3):1999;851-866.
14. Ng M.K., Koo J., Bose N.K. Constrained total least squares computations for high resolution image reconstruction with multisensors. Int. J. Imaging Systems Technol. 12:2002;35-42.
15. Ng M.K., Plemmons R.J., Pimentel F. A new approach to constrained total least squares image restoration. Linear Algebra Appl. 316:2000;237-258.
16. Paige C.C., Saunders M.A. LSQR: an algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Software. 8(1):1982;43-71.
17. Pruessner A., O'Leary D.P. Blind deconvolution using a regularized structured total least norm algorithm. SIAM J. Matrix Anal. Appl. 24(4):2003;1018-1037.
18. Rao K., Yip P. Discrete Cosine Transform: Algorithms, Advantages, Applications. 1990;Academic Press, Boston, MA.
19. Rosen J.B., Park H., Click J. Total least norm formulation and solution for structured problems. SIAM J. Matrix Anal. Appl. 17(1):1996;110-126.