Algorithms for box constrained M-estimation: Fitting large data sets with application to geodynamics

Bougeard, M. L.; Gambis, D.; Ray, R. N.

doi:10.1016/s1464-1895(00)00105-8

Physics and Chemistry of the Earth, Part A: Solid Earth and Geo

2000

DOI: 10.1016/s1464-1895(00)00105-8

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Algorithms for box constrained M-estimation: Fitting large data sets with application to geodynamics

M. L. Bougeard

D. Gambis

R. N. Ray

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Cited by 2 publications

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“…Although this estimation has been extensively used for data analysis, it has some drawbacks linked to problems of ill-conditioning and in the non-robust detection of outliers. Alternative methods based on robust estimators like M-Huber can be used (Bougeard M.L et a/., 1999). These estimators are a generalization of both the LI and L2 class.…”

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Long-term Earth Orientation Monitoring Using Various Techniques

Gambis

2000

International Astronomical Union Colloquium

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A continuous composite series of polar motion components extending from 1846 until now called EOP (IERS) C01 is available at the Earth Orientation Section of the Central Bureau of the IERS. This series is the basis of the IERS system. It relies on different series derived from optical astrometry until 1972 and geodetic techniques since. It is given at 0.1 year intervals (1846–1889) and 0.05 year intervals (1890-now). Its accuracy has dramatically improved from 100 mas in 1846 to about 0.2 mas at present.Now the IERS combined solutions involve mainly the contributions of VLBI, GPS and SLR techniques. It is regularly recomputed to take advantage of the improvement of the various recent individual contributions and of the refinement of the analyses procedures.The objective of this paper is to describe this long-term polar motion series and to present the evolution and the state of the art of the multi-technique EOP combined solutions and the predictions regularly computed at the IERS/CB.

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confidence: 99%

Long-term Earth Orientation Monitoring Using Various Techniques

Gambis

2000

International Astronomical Union Colloquium

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A Primal-Dual Algorithm for Robust Fractal Image Coding

et al. 2019

Fractals

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The essence of Huber fractal image coding (HFIC) is to predict the fractal code of a noiseless image as accurately as possible from its corrupted observation with outliers by adopting Huber M-estimation technique. However, the traditional HFIC is not quite satisfactory mainly due to the absence of contractivity restriction for the estimate of the fractal parameters (actually, it is a fundamental requirement in the theory of fractal image coding). In this paper, we introduce a primal-dual algorithm for robust fractal image coding (PD-RFIC), which formulates the problem of robust prediction of the fractal parameters with contractivity condition as a constrained optimization model and then adopts a primal-dual algorithm to solve it. Furthermore, in order to relieve using the corrupted domain block as the independent variable in the proposed method, instead of using the mean operation on a [Formula: see text] subblock in the traditional HFIC, we apply a median operation on a larger subblock to obtain the contracted domain blocks for achieving the robustness against outliers. The effectiveness of the proposed method is experimentally illustrated on problems of image denoising with impulse noise (specifically, salt & pepper noise and random-valued noise). Remarkable improvements of the proposed method over conventional HFIC are demonstrated in terms of both numerical evaluations and visual quality. In addition, a median-based version of Fisher classification method is also developed to accelerate the encoding speed of the proposed method.

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Algorithms for box constrained M-estimation: Fitting large data sets with application to geodynamics

Cited by 2 publications

References 10 publications

Long-term Earth Orientation Monitoring Using Various Techniques

Long-term Earth Orientation Monitoring Using Various Techniques

A Primal-Dual Algorithm for Robust Fractal Image Coding

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