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Constrained total least squares
ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005The Total Least Squares (TLS) method is a generalized least square technique to solve an overdetermined system of equations Ax\simeqb . The TLS solution differs from the usual Least Square (LS) in that it tries to compensate for arbitrary noise present in both A and b .
Theagenis J. Abatzoglou, Jerry M. Mendel
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Incomplete total least squares
Numerische Mathematik, 1999Total least squares (TLS) are fitting data points with some model function such that the sum of squared orthogonal distances is minimized. The authors consider situations where the model is such that there might be no perpendiculars from certain data points onto the model function and where one has to replace certain orthogonal distances by shortest ...
K. Brüntjen, Helmuth Späth
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On the recursive total least-squares
1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2002In this paper, by exploiting the total least-square (TLS) closed-form solution and using state-space structure in Krein space, we show that the solution of the TLS problems can be computed via the recursive Kalman filtering algorithm. This makes it possible to use the TLS for real-time applications.
Cuong Pham 0005, Tokunbo Ogunfunmi
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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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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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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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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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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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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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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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