Fast regularized structured total least squares algorithm for solving the basic deconvolution problem

Numerical Linear Algebra with Applications

Volumn 12, Issue 2-3, 2005, Pages 201-209

  Mastronardi, N ^a   Lemmerling, P ^b   Van Huffel, S ^b  

^a CNR   (Italy)

^b Katholieke Universiteit Leuven   (Belgium)

Author keywords

Deconvolution; Displacement rank; Generalized Schur algorithm; Structured total least norm; Structured total least squares; Tikhonov regularization; Toeplitz matrices

Indexed keywords

EID: 20744459276     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.413     Document Type: Article

References (15)

1. Golub GH, Van Loan CF. Matrix Computations (3rd edn). The John Hopkins University Press: Baltimore, MD, 1996.
2. Golub GH, Van Loan CF. An analysis of the total least squares problem. SIAM Journal on Numerical Analysis 1980; 17:883-893.
3. Van Huffel S, Vandewalle J. The Total Least Squares Problem: Computational Aspects and Analysis. SIAM: Philadelphia, 1991.
4. Mastronardi N, Lemmerling P, Van Huffel S. Fast structured total least squares algorithm for solving the basic deconvolution problem. SIAM Journal on Matrix Analysis and Applications 1980; 17:883-893.
5. Rosen JB, Park H, Glick J. Total least norm formulation and solution for structured problems. SIAM Journal on Matrix Analysis and Applications 2003; 17(1):110-126.
6. Van Huffel S, Park H, Rosen JB. Formulation and solution of structured total least norm problems for parameter estimation. IEEE Transactions on Signal Processing 1996; 44(10):2464-2474.
7. Lemmerling P, Van Huffel S, De Moor B. Structured total least squares problems: formulations, algorithms and applications. In Recent Advances in Total Least Squares Techniques and Errors-in-Variables modeling. Van Huffel S (ed.). SIAM: Philadelphia, 1997; 215-223.
8. Kailath T. Displacement structure and array algorithms. In Fast Reliable Algorithms for Matrices with Structure, Kailath T, Sayed AH (eds). SIAM: Philadelphia, 1999; 1-56.
9. Hansen PC. Deconvolution and regularization with Toeplitz matrices. Numerical Algorithms 2002; 29:323-378.
10. Pruessner A, O'Leary DP. Blind deconvolution using a regularized structured total least norm approach. SIAM Journal on Matrix Analysis and Applications 2003; 24(4): 1018-1037.
11. Hansen PC. Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion. SIAM: Philadelphia, 1998.
12. Van Huffel S, Vandewalle J, De Roo MC, Willems JL. Reliable and efficient deconvolution technique based on total linear least squares for calculating the renal retention function. Medical and Biological Engineering and Computing 1987; 25:26-33.
13. Fleming JS. Measurement of Hippuran plasma clearance using a gamma camera. Physics in Medicine and Biology 1977; 22:526-530.
14. Kalsi A, O'Leary DP. Algorithms for structured total least squares problems with applications to blind image deblurring, CS-TR-4390, University of Maryland, August 2002.
15. Ng MK, Plemmons RJ, Pimentel F. A new approach to constrained total least squares image restoration. Linear Algebra and Its Applications 2000; 316(2000):237-258.