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On the weighting method for mixed least squares–total least squares problems
Numerical Linear Algebra with Applications, 2017SummaryIt is well known that the standard algorithm for the mixed least squares–total least squares (MTLS) problem uses the QR factorization to reduce the original problem into a standard total least squares problem with smaller size, which can be solved based on the singular value decomposition (SVD).
Qiaohua Liu, Minghui Wang
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Least squares and total least squares methods in image restoration
1997Image restoration is the process of removing or minimizing degradations (blur) in an image. Mathematically, it can be modeled as a discrete ill-posed problem Hf=g, where H is a matrix of large dimension representing the blurring phenomena, and g is a vector representing the observed image.
Julie Kamm, James G. Nagy
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2002 14th International Conference on Digital Signal Processing Proceedings. DSP 2002 (Cat. No.02TH8628), 2003
In the robot navigation problem, noisy sensor data. must be filtered to obtain the best estimate of the robot position. The discrete Kalman filter, which usually is used for prediction and detection of signals in communication and control problems has become a commonly used method to reduce the effect of uncertainty from the sensor data.
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In the robot navigation problem, noisy sensor data. must be filtered to obtain the best estimate of the robot position. The discrete Kalman filter, which usually is used for prediction and detection of signals in communication and control problems has become a commonly used method to reduce the effect of uncertainty from the sensor data.
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Bounds for the least squares distance using scaled total least squares
Numerische Mathematik, 2002The authors analyze fundamentals of the scaled total least squares problem. They present a theoretical analysis of the relationship between the sizes of least squares and scaled least squares corrections in terms of the real positive corrections restricted parameter.
Christopher C. Paige, Zdenek Strakos
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Perturbation analysis for mixed least squares–total least squares problems
Numerical Linear Algebra with Applications, 2019SummaryIn many linear parameter estimation problems, one can use the mixed least squares–total least squares (MTLS) approach to solve them. This paper is devoted to the perturbation analysis of the MTLS problem. Firstly, we present the normwise, mixed, and componentwise condition numbers of the MTLS problem, and find that the normwise, mixed, and ...
Bing Zheng, Zhanshan Yang
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Total least square kernel regression
Journal of Visual Communication and Image Representation, 2012In this paper, we study the problem of robust image fusion in the context of multi-frame super-resolution. Given multiple aligned noisy low-resolution images, image fusion produces a new image on a high-resolution grid. Recently, kernel regression is presented as a powerful image fusion technique.
Hiêp Quang Luong +3 more
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Total least squares with linear constraints
[Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing, 1992Numerically stable closed form expressions for the solution of the total least squares (TLS) problem with linear equality constraints (LCTLS) are derived. A constrained subspace linear predictive frequency estimation technique called LCTLS-linear predictive (LCTLS-LP) is proposed.
Eric M. Dowling +2 more
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2010
In atmospheric remote sensing, near real-time software processors frequently use approximations of the Jacobian matrix in order to speed up the calculation. If the forward model F(x) depends on the state vector x through some model parameters bk, F(x) = F(b1 (x),..., bN (x)),
Adrian Doicu +2 more
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In atmospheric remote sensing, near real-time software processors frequently use approximations of the Jacobian matrix in order to speed up the calculation. If the forward model F(x) depends on the state vector x through some model parameters bk, F(x) = F(b1 (x),..., bN (x)),
Adrian Doicu +2 more
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Fast total least squares vectorization
Journal of Real-Time Image Processing, 2016This paper proposes a novel algorithm for the vectorization of ordered sets of points, named Fast Total Least Squares (FTLS) vectorization. The emphasis was put on low computational complexity, which allows it to be run online on a mobile device at a speed comparable to the fastest algorithms, such as the Douglas–Peucker (DP) algorithm, while ...
Ales Jelinek, Ludek Zalud, Tomás Jílek
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An Analysis of the Total Least Squares Problem
SIAM Journal on Numerical Analysis, 1980Totla least squares (TLS) is a method of fitting that is appropriate when there are errors in both the observation vector $b (mxl)$ and in the data matrix $A (mxn)$. The technique has been discussed by several authors and amounts to fitting a "best" subspace to the points $(a^{T}_{i},b_{i}), i=1,\ldots,m,$ where $a^{T}_{i}$ is the $i$-th row of $A$. In
Golub, Gene H., Van Loan, Charles F.
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