11,072 research outputs found
Cramer-Rao Lower Bound for Point Based Image Registration with Heteroscedastic Error Model for Application in Single Molecule Microscopy
The Cramer-Rao lower bound for the estimation of the affine transformation
parameters in a multivariate heteroscedastic errors-in-variables model is
derived. The model is suitable for feature-based image registration in which
both sets of control points are localized with errors whose covariance matrices
vary from point to point. With focus given to the registration of fluorescence
microscopy images, the Cramer-Rao lower bound for the estimation of a feature's
position (e.g. of a single molecule) in a registered image is also derived. In
the particular case where all covariance matrices for the localization errors
are scalar multiples of a common positive definite matrix (e.g. the identity
matrix), as can be assumed in fluorescence microscopy, then simplified
expressions for the Cramer-Rao lower bound are given. Under certain simplifying
assumptions these expressions are shown to match asymptotic distributions for a
previously presented set of estimators. Theoretical results are verified with
simulations and experimental data
zCap: a zero configuration adaptive paging and mobility management mechanism
Today, cellular networks rely on fixed collections of cells (tracking areas) for user equipment localisation. Locating users within these areas involves broadcast search (paging), which consumes radio bandwidth but reduces the user equipment signalling required for mobility management. Tracking areas are today manually configured, hard to adapt to local mobility and influence the load on several key resources in the network. We propose a decentralised and self-adaptive approach to mobility management based on a probabilistic model of local mobility. By estimating the parameters of this model from observations of user mobility collected online, we obtain a dynamic model from which we construct local neighbourhoods of cells where we are most likely to locate user equipment. We propose to replace the static tracking areas of current systems with neighbourhoods local to each cell. The model is also used to derive a multi-phase paging scheme, where the division of neighbourhood cells into consecutive phases balances response times and paging cost. The complete mechanism requires no manual tracking area configuration and performs localisation efficiently in terms of signalling and response times. Detailed simulations show that significant potential gains in localisation effi- ciency are possible while eliminating manual configuration of mobility management parameters. Variants of the proposal can be implemented within current (LTE) standards
Change detection in multisensor SAR images using bivariate gamma distributions
This paper studies a family of distributions constructed from multivariate gamma distributions to model the statistical properties of multisensor synthetic aperture radar (SAR) images. These distributions referred to as multisensor multivariate gamma distributions (MuMGDs) are potentially interesting for detecting changes in SAR images acquired by different sensors having different numbers of looks. The first part of the paper compares different estimators for the parameters of MuMGDs. These estimators are based on the maximum likelihood principle, the method of inference function for margins and the method of moments. The second part of the paper studies change detection algorithms based on the estimated correlation coefficient of MuMGDs. Simulation results conducted on synthetic and real data illustrate the performance of these change detectors
Estimating Renyi Entropy of Discrete Distributions
It was recently shown that estimating the Shannon entropy of a
discrete -symbol distribution requires samples,
a number that grows near-linearly in the support size. In many applications
can be replaced by the more general R\'enyi entropy of order
, . We determine the number of samples needed to
estimate for all , showing that
requires a super-linear, roughly samples, noninteger
requires a near-linear samples, but, perhaps surprisingly, integer
requires only samples. Furthermore,
developing on a recently established connection between polynomial
approximation and estimation of additive functions of the form , we reduce the sample complexity for noninteger values of by a
factor of compared to the empirical estimator. The estimators
achieving these bounds are simple and run in time linear in the number of
samples. Our lower bounds provide explicit constructions of distributions with
different R\'enyi entropies that are hard to distinguish
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