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Abstract: In this paper we develop a fast algorithm for the basic deconvolution problem. First we show that the kernel problem to be solved in the basic deconvolution problem is a so-called structured Total Least Squares problem. Due to the low displacement rank of the involved matrices, we are able to develop a fast algorithm. We apply the new algorithm on a deconvolution problem arising in a medical application in renography. By means of this example, we show the increased computational performance of... (Update)
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...errors in variables method, image deblurring, Tikhonov regularization. Running Title: Fast Structured Total Least Squares 1. Introduction. In [4], Mastronardi, Lemmerling, and Van Hu el present an algorithm for solving fast structured total least squares problems of the...
...displacement theory for symmetric strongly regular matrices are introduced. In STLS problems the involved matrices are of this kind [14, 10], indeed. An extensive treatment of the displacement theory can be found in [7] including the non symmetric and the complex case. In x 3...
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4: The John Hopkins University Press (context) - Golub, Van Loan - 1989
4: Displacement Ranks of Matrices and Linear Equations (context) - Kailath, Kung et al. - 1979
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BibTeX entry: (Update)
Mastronardi, N., Lemmerling, P., Van Hu el,S.: Fast structured total least squares algorithm for solving the basic deconvolution problem. SIAM J. Matrix Anal. Appl.(to appear). http://citeseer.ist.psu.edu/mastronardi98fast.html More
@article{ mastronardi01fast,
author = "Nicola Mastronardi and Philippe Lemmerling and Sabine Van Huffel",
title = "Fast Structured Total Least Squares Algorithm for Solving the Basic Deconvolution Problem",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "22",
number = "2",
pages = "533--553",
year = "2001",
url = "citeseer.ist.psu.edu/mastronardi98fast.html" }
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72 Displacement ranks of matrices and linear equations (context) - Kailath, Kung et al. - 1979
71 The total least squares problem : computational aspects and .. (context) - Van Huffel, Vandewalle - 1991
46 Fast parallel algorithms for QR and triangular factorization (context) - Chun, Kailath et al. - 1987
46 The Constrained Total Least Squares Technique and its Applic.. (context) - Abatzoglou, Mendel et al. - 1991
33 Generalized displacement structure for block--Toeplitz (context) - Kailath, Chun - 1994
32 A note on downdating the Cholesky factorization (context) - Bojanczyk, Brent et al. - 1980
32 State-space and singular-value decomposition-based approxima.. (context) - Kung, Arun et al. - 1983
28 Total least norm formulation and solution for structured pro.. (context) - Rosen, Park et al. - 1996
19 Stability issues in the factorization of structured matrices - Stewart, Van Dooren - 1997
18 Maximum Likelihood Estimation of the Parameters of Multiple .. (context) - Stoica, Moses et al. - 1989
12 Constrained Total Least Squares (context) - Abatzoglou, Mendel - 1987
6 Fast inverse QR factorization for Toeplitz matrices (context) - Nagy - 1993
5 Formulation and Solution of Structured Total Least Norm Prob.. - Van Huffel, Park et al. - 1996
5 Total least squares for affinely structured matrices and the.. (context) - De Moor - 1994
4 Structured total least squares problems : formulations, algo.. - Lemmerling, Van Huffel et al. - 1997
4 Speech compression based on exact modeling and structured to.. - Lemmerling, Dologlou et al. - 1998
3 Algorithm for Time-Domain NMR Data Fitting Based on Total Le.. (context) - Van Huffel, Decanniere et al. - 1994
2 Variable rate speech compression based on exact modeling and.. - Lemmerling, Dologlou et al. - 1998
1 MAG3 renogram deconvolution in kidney transplantation: utili.. (context) - Bajen, Puchal et al. - 1997
1 Measurement of Hippuran plasma clearance using a gamma camer.. (context) - Fleming - 1977
1 A technique for the deconvolution of the renogram (context) - Fleming, Goddard - 1974
1 Hepatobiliary scintigraphy in a pediatric population: determ.. (context) - Giles, Moase et al. - 1993
1 Non-invasive assessment of technetium-99m albumin transit ti.. (context) - Capderou, Douguet et al. - 1997
1 Total least norm problem formulation and solution of structu.. (context) - Van Huffel, Park et al. - 1995
1 Stability analysis and fast triangularization of Toeplitz ma.. (context) - Park, Eld'en - 1997
1 Reliable and efficient deconvolution technique based on tota.. (context) - Van Huffel, Vandewalle et al. - 1987
1 Nuclear medicine and mathematics (context) - de Lima - 1996
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On the Stability of the Generalized Schur Algorithm - Mastronardi, van Dooren.. (2000) (Correct)
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