41,803 research outputs found
A Spectral CT Method to Directly Estimate Basis Material Maps From Experimental Photon-Counting Data
The proposed spectral CT method solves the constrained one-step spectral CT reconstruction (cOSSCIR) optimization problem to estimate basis material maps while modeling the nonlinear X-ray detection process and enforcing convex constraints on the basis map images. In order to apply the optimization-based reconstruction approach to experimental data, the presented method empirically estimates the effective energy-window spectra using a calibration procedure. The amplitudes of the estimated spectra were further optimized as part of the reconstruction process to reduce ring artifacts. A validation approach was developed to select constraint parameters. The proposed spectral CT method was evaluated through simulations and experiments with a photon-counting detector. Basis material map images were successfully reconstructed using the presented empirical spectral modeling and cOSSCIR optimization approach. In simulations, the cOSSCIR approach accurately reconstructed the basis map images
General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
The estimation of parameters characterizing dynamical processes is central to
science and technology. The estimation error changes with the number N of
resources employed in the experiment (which could quantify, for instance, the
number of probes or the probing energy). Typically, it scales as 1/N^(1/2).
Quantum strategies may improve the precision, for noiseless processes, by an
extra factor 1/N^(1/2). For noisy processes, it is not known in general if and
when this improvement can be achieved. Here we propose a general framework for
obtaining attainable and useful lower bounds for the ultimate limit of
precision in noisy systems. We apply this bound to lossy optical interferometry
and atomic spectroscopy in the presence of dephasing, showing that it captures
the main features of the transition from the 1/N to the 1/N^(1/2) behaviour as
N increases, independently of the initial state of the probes, and even with
use of adaptive feedback.Comment: Published in Nature Physics. This is the revised submitted version.
The supplementary material can be found at
http://www.nature.com/nphys/journal/v7/n5/extref/nphys1958-s1.pd
Calculation of time resolution of the J-PET tomograph using the Kernel Density Estimation
In this paper we estimate the time resolution of the J-PET scanner built from
plastic scintillators. We incorporate the method of signal processing using the
Tikhonov regularization framework and the Kernel Density Estimation method. We
obtain simple, closed-form analytical formulas for time resolutions. The
proposed method is validated using signals registered by means of the single
detection unit of the J-PET tomograph built out from 30 cm long plastic
scintillator strip. It is shown that the experimental and theoretical results,
obtained for the J-PET scanner equipped with vacuum tube photomultipliers, are
consistent.Comment: 25 pages, 11 figure
Photon-Efficient Computational 3D and Reflectivity Imaging with Single-Photon Detectors
Capturing depth and reflectivity images at low light levels from active
illumination of a scene has wide-ranging applications. Conventionally, even
with single-photon detectors, hundreds of photon detections are needed at each
pixel to mitigate Poisson noise. We develop a robust method for estimating
depth and reflectivity using on the order of 1 detected photon per pixel
averaged over the scene. Our computational imager combines physically accurate
single-photon counting statistics with exploitation of the spatial correlations
present in real-world reflectivity and 3D structure. Experiments conducted in
the presence of strong background light demonstrate that our computational
imager is able to accurately recover scene depth and reflectivity, while
traditional maximum-likelihood based imaging methods lead to estimates that are
highly noisy. Our framework increases photon efficiency 100-fold over
traditional processing and also improves, somewhat, upon first-photon imaging
under a total acquisition time constraint in raster-scanned operation. Thus our
new imager will be useful for rapid, low-power, and noise-tolerant active
optical imaging, and its fixed dwell time will facilitate parallelization
through use of a detector array.Comment: 11 pages, 8 figure
Progressive Transient Photon Beams
In this work we introduce a novel algorithm for transient rendering in
participating media. Our method is consistent, robust, and is able to generate
animations of time-resolved light transport featuring complex caustic light
paths in media. We base our method on the observation that the spatial
continuity provides an increased coverage of the temporal domain, and
generalize photon beams to transient-state. We extend the beam steady-state
radiance estimates to include the temporal domain. Then, we develop a
progressive version of spatio-temporal density estimations, that converges to
the correct solution with finite memory requirements by iteratively averaging
several realizations of independent renders with a progressively reduced kernel
bandwidth. We derive the optimal convergence rates accounting for space and
time kernels, and demonstrate our method against previous consistent transient
rendering methods for participating media
Detector-Agnostic Phase-Space Distributions
The representation of quantum states via phase-space functions constitutes an
intuitive technique to characterize light. However, the reconstruction of such
distributions is challenging as it demands specific types of detectors and
detailed models thereof to account for their particular properties and
imperfections. To overcome these obstacles, we derive and implement a
measurement scheme that enables a reconstruction of phase-space distributions
for arbitrary states whose functionality does not depend on the knowledge of
the detectors, thus defining the notion of detector-agnostic phase-space
distributions. Our theory presents a generalization of well-known phase-space
quasiprobability distributions, such as the Wigner function. We implement our
measurement protocol, using state-of-the-art transition-edge sensors without
performing a detector characterization. Based on our approach, we reveal the
characteristic features of heralded single- and two-photon states in phase
space and certify their nonclassicality with high statistical significance
Fisher information matrix for single molecules with stochastic trajectories
Tracking of objects in cellular environments has become a vital tool in
molecular cell biology. A particularly important example is single molecule
tracking which enables the study of the motion of a molecule in cellular
environments and provides quantitative information on the behavior of
individual molecules in cellular environments, which were not available before
through bulk studies. Here, we consider a dynamical system where the motion of
an object is modeled by stochastic differential equations (SDEs), and
measurements are the detected photons emitted by the moving fluorescently
labeled object, which occur at discrete time points, corresponding to the
arrival times of a Poisson process, in contrast to uniform time points which
have been commonly used in similar dynamical systems. The measurements are
distributed according to optical diffraction theory, and therefore, they would
be modeled by different distributions, e.g., a Born and Wolf profile for an
out-of-focus molecule. For some special circumstances, Gaussian image models
have been proposed. In this paper, we introduce a stochastic framework in which
we calculate the maximum likelihood estimates of the biophysical parameters of
the molecular interactions, e.g., diffusion and drift coefficients. More
importantly, we develop a general framework to calculate the Cram\'er-Rao lower
bound (CRLB), given by the inverse of the Fisher information matrix, for the
estimation of unknown parameters and use it as a benchmark in the evaluation of
the standard deviation of the estimates. There exists no established method,
even for Gaussian measurements, to systematically calculate the CRLB for the
general motion model that we consider in this paper. We apply the developed
methodology to simulated data of a molecule with linear trajectories and show
that the standard deviation of the estimates matches well with the square root
of the CRLB
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