9,237 research outputs found
Random action of compact Lie groups and minimax estimation of a mean pattern
This paper considers the problem of estimating a mean pattern in the setting
of Grenander's pattern theory. Shape variability in a data set of curves or
images is modeled by the random action of elements in a compact Lie group on an
infinite dimensional space. In the case of observations contaminated by an
additive Gaussian white noise, it is shown that estimating a reference template
in the setting of Grenander's pattern theory falls into the category of
deconvolution problems over Lie groups. To obtain this result, we build an
estimator of a mean pattern by using Fourier deconvolution and harmonic
analysis on compact Lie groups. In an asymptotic setting where the number of
observed curves or images tends to infinity, we derive upper and lower bounds
for the minimax quadratic risk over Sobolev balls. This rate depends on the
smoothness of the density of the random Lie group elements representing shape
variability in the data, which makes a connection between estimating a mean
pattern and standard deconvolution problems in nonparametric statistics
Improving Fiber Alignment in HARDI by Combining Contextual PDE Flow with Constrained Spherical Deconvolution
We propose two strategies to improve the quality of tractography results
computed from diffusion weighted magnetic resonance imaging (DW-MRI) data. Both
methods are based on the same PDE framework, defined in the coupled space of
positions and orientations, associated with a stochastic process describing the
enhancement of elongated structures while preserving crossing structures. In
the first method we use the enhancement PDE for contextual regularization of a
fiber orientation distribution (FOD) that is obtained on individual voxels from
high angular resolution diffusion imaging (HARDI) data via constrained
spherical deconvolution (CSD). Thereby we improve the FOD as input for
subsequent tractography. Secondly, we introduce the fiber to bundle coherence
(FBC), a measure for quantification of fiber alignment. The FBC is computed
from a tractography result using the same PDE framework and provides a
criterion for removing the spurious fibers. We validate the proposed
combination of CSD and enhancement on phantom data and on human data, acquired
with different scanning protocols. On the phantom data we find that PDE
enhancements improve both local metrics and global metrics of tractography
results, compared to CSD without enhancements. On the human data we show that
the enhancements allow for a better reconstruction of crossing fiber bundles
and they reduce the variability of the tractography output with respect to the
acquisition parameters. Finally, we show that both the enhancement of the FODs
and the use of the FBC measure on the tractography improve the stability with
respect to different stochastic realizations of probabilistic tractography.
This is shown in a clinical application: the reconstruction of the optic
radiation for epilepsy surgery planning
Reference-less detection, astrometry, and photometry of faint companions with adaptive optics
We propose a complete framework for the detection, astrometry, and photometry
of faint companions from a sequence of adaptive optics corrected short
exposures. The algorithms exploit the difference in statistics between the
on-axis and off-axis intensity. Using moderate-Strehl ratio data obtained with
the natural guide star adaptive optics system on the Lick Observatory's 3-m
Shane Telescope, we compare these methods to the standard approach of PSF
fitting. We give detection limits for the Lick system, as well as a first guide
to expected accuracy of differential photometry and astrometry with the new
techniques. The proposed approach to detection offers a new way of determining
dynamic range, while the new algorithms for differential photometry and
astrometry yield accurate results for very faint and close-in companions where
PSF fitting fails. All three proposed algorithms are self-calibrating, i.e.
they do not require observation of a calibration star thus improving the
observing efficiency.Comment: Astrophysical Journal 698 (2009) 28-4
On random tomography with unobservable projection angles
We formulate and investigate a statistical inverse problem of a random
tomographic nature, where a probability density function on is
to be recovered from observation of finitely many of its two-dimensional
projections in random and unobservable directions. Such a problem is distinct
from the classic problem of tomography where both the projections and the unit
vectors normal to the projection plane are observable. The problem arises in
single particle electron microscopy, a powerful method that biophysicists
employ to learn the structure of biological macromolecules. Strictly speaking,
the problem is unidentifiable and an appropriate reformulation is suggested
hinging on ideas from Kendall's theory of shape. Within this setup, we
demonstrate that a consistent solution to the problem may be derived, without
attempting to estimate the unknown angles, if the density is assumed to admit a
mixture representation.Comment: Published in at http://dx.doi.org/10.1214/08-AOS673 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A stochastic model dissects cell states in biological transition processes
Many biological processes, including differentiation, reprogramming, and disease transformations, involve transitions of cells through distinct states. Direct, unbiased investigation of cell states and their transitions is challenging due to several factors, including limitations of single-cell assays. Here we present a stochastic model of cellular transitions that allows underlying single-cell information, including cell-state-specific parameters and rates governing transitions between states, to be estimated from genome-wide, population-averaged time-course data. The key novelty of our approach lies in specifying latent stochastic models at the single-cell level, and then aggregating these models to give a likelihood that links parameters at the single-cell level to observables at the population level. We apply our approach in the context of reprogramming to pluripotency. This yields new insights, including profiles of two intermediate cell states, that are supported by independent single-cell studies. Our model provides a general conceptual framework for the study of cell transitions, including epigenetic transformations
Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)
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