Journal ArticleDOI
Fast Structured Total Least Squares Algorithm for Solving the Basic Deconvolution Problem
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A fast algorithm for the basic deconvolution problem is developed due to the low displacement rank of the involved matrices and the sparsity of the generators and Monte-Carlo simulations indicate the superior statistical performance of the structured total least squares estimator compared to other estimators such as the ordinary total least square estimator.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 and the sparsity of the generators, 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 our algorithm as compared to other algorithms for solving this type of structured total least squares problem. In addition, Monte-Carlo simulations indicate the superior statistical performance of the structured total least squares estimator compared to other estimators such as the ordinary total least squares estimator.read more
Citations
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Overview of total least-squares methods
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Proceedings ArticleDOI
A practical method for wireless channel reciprocity exploitation through relative calibration
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Proceedings of the second international workshop on Recent advances in total least squares techniques and errors-in-variables modeling
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Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis
TL;DR: In this article, the weighted total least squares (TLS) method has been extended to a partial EIV model, in which not all the elements of the design matrix are random and the total number of unknowns in the normal equations has been significantly reduced.
References
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Book
The Total Least Squares Problem: Computational Aspects and Analysis
TL;DR: This paper presents a meta-analyses of the relationships between total least squares estimation and classical linear regression in Multicollinearity problems and some of the properties of these relationships are explained.
Journal ArticleDOI
Displacement ranks of matrices and linear equations
TL;DR: In this paper, the concept of displacement ranks is introduced to measure how close a given matrix is to Toeplitz matrices, and it is shown that these non-Toeplitzer matrices should be invertible with a complexity between O(N2 and O(3).
Journal ArticleDOI
Displacement structure: theory and applications
Thomas Kailath,Ali H. Sayed +1 more
TL;DR: This survey paper describes how strands of work that are important in two different fields, matrix theory and complex function theory, have come together in some work on fast computational algorithms for matrices with what the authors call displacement structure, and develops a fast triangularization procedure.