Overview of total least-squares methods

By Ivan Markovsky, S. Van Huffel. Signal Processing, 2007

879 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/75bdc9c371dfda230e0cc8ecc6d3b88c3e855577

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Control and Systems Engineering

Citations in the corpus

De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets (2015, background): “…DMD as a “best-ﬁt” least-squares/minimum-norm operator determined from measured snapshot data, we establish that the same sources of noise-induced bias arising in standard least-squares problems—extensively studied in statistics and numerical analysis [26, 27, 28, 29, 30, 31]—will also plague DMD.”
Sparsity-Cognizant Total Least-Squares for Perturbed Compressive Sampling (2010, background): “Sincex⋆g is not the exact global minimum of (12), positivity ofg(x⋆g, a) does not necessarily implyg ⋆(a) > 0.”
Spatially Sparse Precoding in Millimeter Wave MIMO Systems (2013, background): “as a sparsity constrained matrix reconstruction problem [38]– [43].”
The Supernova Legacy Survey 3-year sample: Type Ia supernovae photometric distances and cosmological constraints , (2010, methodology): “…from the Hubble diagram were used. i) The fitted value ofβ depends on the assumed uncertainties of (B − V) (known as a total least-squares problem, see Markovsky & Huffel 2007 for a review). ii) Because of a limited detection/selection efficiency, we miss red SNe at highz, and hence the range of…”
Variance components in errors-in-variables models: estimability, stability and bias analysis (2014, methodology): “The former may be referred to Golub and Loan (1980) and the generalized TLS method by Huffel and Vandewalle (1989) and Markovsky and Huffel (2007), because the so-called positive definite matrix of weighting there is not the inverse of a variance–covariance matrix in the statistical sense, as…”