566 research outputs found
Structural Variability from Noisy Tomographic Projections
In cryo-electron microscopy, the 3D electric potentials of an ensemble of
molecules are projected along arbitrary viewing directions to yield noisy 2D
images. The volume maps representing these potentials typically exhibit a great
deal of structural variability, which is described by their 3D covariance
matrix. Typically, this covariance matrix is approximately low-rank and can be
used to cluster the volumes or estimate the intrinsic geometry of the
conformation space. We formulate the estimation of this covariance matrix as a
linear inverse problem, yielding a consistent least-squares estimator. For
images of size -by- pixels, we propose an algorithm for calculating this
covariance estimator with computational complexity
, where the condition number
is empirically in the range --. Its efficiency relies on the
observation that the normal equations are equivalent to a deconvolution problem
in 6D. This is then solved by the conjugate gradient method with an appropriate
circulant preconditioner. The result is the first computationally efficient
algorithm for consistent estimation of 3D covariance from noisy projections. It
also compares favorably in runtime with respect to previously proposed
non-consistent estimators. Motivated by the recent success of eigenvalue
shrinkage procedures for high-dimensional covariance matrices, we introduce a
shrinkage procedure that improves accuracy at lower signal-to-noise ratios. We
evaluate our methods on simulated datasets and achieve classification results
comparable to state-of-the-art methods in shorter running time. We also present
results on clustering volumes in an experimental dataset, illustrating the
power of the proposed algorithm for practical determination of structural
variability.Comment: 52 pages, 11 figure
Wavelets, ridgelets and curvelets on the sphere
We present in this paper new multiscale transforms on the sphere, namely the
isotropic undecimated wavelet transform, the pyramidal wavelet transform, the
ridgelet transform and the curvelet transform. All of these transforms can be
inverted i.e. we can exactly reconstruct the original data from its
coefficients in either representation. Several applications are described. We
show how these transforms can be used in denoising and especially in a Combined
Filtering Method, which uses both the wavelet and the curvelet transforms, thus
benefiting from the advantages of both transforms. An application to component
separation from multichannel data mapped to the sphere is also described in
which we take advantage of moving to a wavelet representation.Comment: Accepted for publication in A&A. Manuscript with all figures can be
downloaded at http://jstarck.free.fr/aa_sphere05.pd
Quantum State Tomography of a Single Qubit: Comparison of Methods
The tomographic reconstruction of the state of a quantum-mechanical system is
an essential component in the development of quantum technologies. We present
an overview of different tomographic methods for determining the
quantum-mechanical density matrix of a single qubit: (scaled) direct inversion,
maximum likelihood estimation (MLE), minimum Fisher information distance, and
Bayesian mean estimation (BME). We discuss the different prior densities in the
space of density matrices, on which both MLE and BME depend, as well as ways of
including experimental errors and of estimating tomography errors. As a measure
of the accuracy of these methods we average the trace distance between a given
density matrix and the tomographic density matrices it can give rise to through
experimental measurements. We find that the BME provides the most accurate
estimate of the density matrix, and suggest using either the pure-state prior,
if the system is known to be in a rather pure state, or the Bures prior if any
state is possible. The MLE is found to be slightly less accurate. We comment on
the extrapolation of these results to larger systems.Comment: 15 pages, 4 figures, 2 tables; replaced previous figure 5 by new
table I. in Journal of Modern Optics, 201
Probabilistic RGB-D Odometry based on Points, Lines and Planes Under Depth Uncertainty
This work proposes a robust visual odometry method for structured
environments that combines point features with line and plane segments,
extracted through an RGB-D camera. Noisy depth maps are processed by a
probabilistic depth fusion framework based on Mixtures of Gaussians to denoise
and derive the depth uncertainty, which is then propagated throughout the
visual odometry pipeline. Probabilistic 3D plane and line fitting solutions are
used to model the uncertainties of the feature parameters and pose is estimated
by combining the three types of primitives based on their uncertainties.
Performance evaluation on RGB-D sequences collected in this work and two public
RGB-D datasets: TUM and ICL-NUIM show the benefit of using the proposed depth
fusion framework and combining the three feature-types, particularly in scenes
with low-textured surfaces, dynamic objects and missing depth measurements.Comment: Major update: more results, depth filter released as opensource, 34
page
Efficient Calculation of Resolution and Covariance for Penalized-Likelihood Reconstruction in Fully 3-D SPECT
Resolution and covariance predictors have been derived previously for penalized-likelihood estimators. These predictors can provide accurate approximations to the local resolution properties and covariance functions for tomographic systems given a good estimate of the mean measurements. Although these predictors may be evaluated iteratively, circulant approximations are often made for practical computation times. However, when numerous evaluations are made repeatedly (as in penalty design or calculation of variance images), these predictors still require large amounts of computing time. In Stayman and Fessler (2000), we discussed methods for precomputing a large portion of the predictor for shift-invariant system geometries. In this paper, we generalize the efficient procedure discussed in Stayman and Fessler (2000) to shift-variant single photon emission computed tomography (SPECT) systems. This generalization relies on a new attenuation approximation and several observations on the symmetries in SPECT systems. These new general procedures apply to both two-dimensional and fully three-dimensional (3-D) SPECT models, that may be either precomputed and stored, or written in procedural form. We demonstrate the high accuracy of the predictions based on these methods using a simulated anthropomorphic phantom and fully 3-D SPECT system. The evaluation of these predictors requires significantly less computation time than traditional prediction techniques, once the system geometry specific precomputations have been made.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85992/1/Fessler54.pd
Feasibility and performances of compressed-sensing and sparse map-making with Herschel/PACS data
The Herschel Space Observatory of ESA was launched in May 2009 and is in
operation since. From its distant orbit around L2 it needs to transmit a huge
quantity of information through a very limited bandwidth. This is especially
true for the PACS imaging camera which needs to compress its data far more than
what can be achieved with lossless compression. This is currently solved by
including lossy averaging and rounding steps on board. Recently, a new theory
called compressed-sensing emerged from the statistics community. This theory
makes use of the sparsity of natural (or astrophysical) images to optimize the
acquisition scheme of the data needed to estimate those images. Thus, it can
lead to high compression factors.
A previous article by Bobin et al. (2008) showed how the new theory could be
applied to simulated Herschel/PACS data to solve the compression requirement of
the instrument. In this article, we show that compressed-sensing theory can
indeed be successfully applied to actual Herschel/PACS data and give
significant improvements over the standard pipeline. In order to fully use the
redundancy present in the data, we perform full sky map estimation and
decompression at the same time, which cannot be done in most other compression
methods. We also demonstrate that the various artifacts affecting the data
(pink noise, glitches, whose behavior is a priori not well compatible with
compressed-sensing) can be handled as well in this new framework. Finally, we
make a comparison between the methods from the compressed-sensing scheme and
data acquired with the standard compression scheme. We discuss improvements
that can be made on ground for the creation of sky maps from the data.Comment: 11 pages, 6 figures, 5 tables, peer-reviewed articl
PLVS: A SLAM System with Points, Lines, Volumetric Mapping, and 3D Incremental Segmentation
This document presents PLVS: a real-time system that leverages sparse SLAM,
volumetric mapping, and 3D unsupervised incremental segmentation. PLVS stands
for Points, Lines, Volumetric mapping, and Segmentation. It supports RGB-D and
Stereo cameras, which may be optionally equipped with IMUs. The SLAM module is
keyframe-based, and extracts and tracks sparse points and line segments as
features. Volumetric mapping runs in parallel with respect to the SLAM
front-end and generates a 3D reconstruction of the explored environment by
fusing point clouds backprojected from keyframes. Different volumetric mapping
methods are supported and integrated in PLVS. We use a novel reprojection error
to bundle-adjust line segments. This error exploits available depth information
to stabilize the position estimates of line segment endpoints. An incremental
and geometric-based segmentation method is implemented and integrated for RGB-D
cameras in the PLVS framework. We present qualitative and quantitative
evaluations of the PLVS framework on some publicly available datasets. The
appendix details the adopted stereo line triangulation method and provides a
derivation of the Jacobians we used for line error terms. The software is
available as open-source
Reduced and coded sensing methods for x-ray based security
Current x-ray technologies provide security personnel with non-invasive sub-surface imaging and contraband detection in various portal screening applications such as checked and carry-on baggage as well as cargo. Computed tomography (CT) scanners generate detailed 3D imagery in checked bags; however, these scanners often require significant power, cost, and space. These tomography machines are impractical for many applications where space and power are often limited such as checkpoint areas. Reducing the amount of data acquired would help reduce the physical demands of these systems. Unfortunately this leads to the formation of artifacts in various applications, thus presenting significant challenges in reconstruction and classification. As a result, the goal is to maintain a certain level of image quality but reduce the amount of data gathered. For the security domain this would allow for faster and cheaper screening in existing systems or allow for previously infeasible screening options due to other operational constraints. While our focus is predominantly on security applications, many of the techniques can be extended to other fields such as the medical domain where a reduction of dose can allow for safer and more frequent examinations.
This dissertation aims to advance data reduction algorithms for security motivated x-ray imaging in three main areas: (i) development of a sensing aware dimensionality reduction framework, (ii) creation of linear motion tomographic method of object scanning and associated reconstruction algorithms for carry-on baggage screening, and (iii) the application of coded aperture techniques to improve and extend imaging performance of nuclear resonance fluorescence in cargo screening. The sensing aware dimensionality reduction framework extends existing dimensionality reduction methods to include knowledge of an underlying sensing mechanism of a latent variable. This method provides an improved classification rate over classical methods on both a synthetic case and a popular face classification dataset. The linear tomographic method is based on non-rotational scanning of baggage moved by a conveyor belt, and can thus be simpler, smaller, and more reliable than existing rotational tomography systems at the expense of more challenging image formation problems that require special model-based methods. The reconstructions for this approach are comparable to existing tomographic systems. Finally our coded aperture extension of existing nuclear resonance fluorescence cargo scanning provides improved observation signal-to-noise ratios. We analyze, discuss, and demonstrate the strengths and challenges of using coded aperture techniques in this application and provide guidance on regimes where these methods can yield gains over conventional methods
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