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