36,919 research outputs found
Bivariate Gamma Distributions for Image Registration and Change Detection
This paper evaluates the potential interest of using bivariate gamma distributions for image registration and change detection. The first part of this paper studies estimators for the parameters of bivariate gamma distributions based on the maximum likelihood principle and the method of moments. The performance of both methods are compared in terms of estimated mean square errors and theoretical asymptotic variances. The mutual information is a classical similarity measure which can be used for image registration or change detection. The second part of the paper studies some properties of the mutual information for bivariate Gamma distributions. Image registration and change detection techniques based on bivariate gamma distributions are finally investigated. Simulation results conducted on synthetic and real data are very encouraging. Bivariate gamma distributions are good candidates allowing us to develop new image registration algorithms and new change detectors
Exact asymptotic distribution of change-point mle for change in the mean of Gaussian sequences
We derive exact computable expressions for the asymptotic distribution of the
change-point mle when a change in the mean occurred at an unknown point of a
sequence of time-ordered independent Gaussian random variables. The derivation,
which assumes that nuisance parameters such as the amount of change and
variance are known, is based on ladder heights of Gaussian random walks hitting
the half-line. We then show that the exact distribution easily extends to the
distribution of the change-point mle when a change occurs in the mean vector of
a multivariate Gaussian process. We perform simulations to examine the accuracy
of the derived distribution when nuisance parameters have to be estimated as
well as robustness of the derived distribution to deviations from Gaussianity.
Through simulations, we also compare it with the well-known conditional
distribution of the mle, which may be interpreted as a Bayesian solution to the
change-point problem. Finally, we apply the derived methodology to monthly
averages of water discharges of the Nacetinsky creek, Germany.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS294 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Robust Orthogonal Complement Principal Component Analysis
Recently, the robustification of principal component analysis has attracted
lots of attention from statisticians, engineers and computer scientists. In
this work we study the type of outliers that are not necessarily apparent in
the original observation space but can seriously affect the principal subspace
estimation. Based on a mathematical formulation of such transformed outliers, a
novel robust orthogonal complement principal component analysis (ROC-PCA) is
proposed. The framework combines the popular sparsity-enforcing and low rank
regularization techniques to deal with row-wise outliers as well as
element-wise outliers. A non-asymptotic oracle inequality guarantees the
accuracy and high breakdown performance of ROC-PCA in finite samples. To tackle
the computational challenges, an efficient algorithm is developed on the basis
of Stiefel manifold optimization and iterative thresholding. Furthermore, a
batch variant is proposed to significantly reduce the cost in ultra high
dimensions. The paper also points out a pitfall of a common practice of SVD
reduction in robust PCA. Experiments show the effectiveness and efficiency of
ROC-PCA in both synthetic and real data
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