Estimation of the number of single-photon emitters for multiple fluorophores with the same spectral signature.

Fluorescence microscopy is of vital importance for understanding biological function. However most fluorescence experiments are only qualitative inasmuch as the absolute number of fluorescent particles can often not be determined. Additionally, conventional approaches to measuring fluorescence intensity cannot distinguish between two or more fluorophores that are excited and emit in the same spectral window, as only the total intensity in a spectral window can be obtained. Here we show that, by using photon number resolving experiments, we are able to determine the number of emitters and their probability of emission for a number of different species, all with the same measured spectral signature. We illustrate our ideas by showing the determination of the number of emitters per species and the probability of photon collection from that species, for one, two, and three otherwise unresolvable fluorophores. The convolution Binomial model is presented to model the counted photons emitted by multiple species. And then the Expectation-Maximization (EM) algorithm is used to match the measured photon counts to the expected convolution Binomial distribution function. In applying the EM algorithm, to leverage the problem of being trapped in a sub-optimal solution, the moment method is introduced in finding the initial guess of the EM algorithm. Additionally, the associated Cram\'er-Rao lower bound is derived and compared with the simulation results.

Estimation of the number of single-photon emitters for multiple fluorophores with the same spectral signature.

Fluorescence microscopy is of vital importance for understanding biological function. However, most fluorescence experiments are only qualitative inasmuch as the absolute number of fluorescent particles can often not be determined. Additionally, conventional approaches to measuring fluorescence intensity cannot distinguish between two or more fluorophores that are excited and emit in the same spectral window, as only the total intensity in a spectral window can be obtained. Here we show that, by using photon number resolving experiments, we are able to determine the number of emitters and their probability of emission for a number of different species, all with the same measured spectral signature. We illustrate our ideas by showing the determination of the number of emitters per species and the probability of photon collection from that species, for one, two and three otherwise unresolvable fluorophores. The convolution binomial model is presented to represent the counted photons emitted by multiple species. Then, the expectation-maximization (EM) algorithm is used to match the measured photon counts to the expected convolution binomial distribution function. In applying the EM algorithm, to leverage the problem of being trapped in a sub-optimal solution, the moment method is introduced to yield an initial guess for the EM algorithm. Additionally, the associated Cramér-Rao lower bound is derived and compared with the simulation results.

Public access is not equal access.

On 25 August, the White House Office of Science and Technology Policy provided guidance for scientific publishing aimed at making publications and their supporting data-the products of federally funded research-publicly available without an embargo by the end of 2025. The American Association for the Advancement of Science (AAAS, the publisher of Science and the Science family of journals) strongly supports this guidance. As written, several paths to public access remain possible. It will matter greatly to the scientific enterprise which become predominant.

The Information Geometry of Sensor Configuration.

In problems of parameter estimation from sensor data, the Fisher information provides a measure of the performance of the sensor; effectively, in an infinitesimal sense, how much information about the parameters can be obtained from the measurements. From the geometric viewpoint, it is a Riemannian metric on the manifold of parameters of the observed system. In this paper, we consider the case of parameterized sensors and answer the question, "How best to reconfigure a sensor (vary the parameters of the sensor) to optimize the information collected?" A change in the sensor parameters results in a corresponding change to the metric. We show that the change in information due to reconfiguration exactly corresponds to the natural metric on the infinite-dimensional space of Riemannian metrics on the parameter manifold, restricted to finite-dimensional sub-manifold determined by the sensor parameters. The distance measure on this configuration manifold is shown to provide optimal, dynamic sensor reconfiguration based on an information criterion. Geodesics on the configuration manifold are shown to optimize the information gain but only if the change is made at a certain rate. An example of configuring two bearings-only sensors to optimally locate a target is developed in detail to illustrate the mathematical machinery, with Fast Marching methods employed to efficiently calculate the geodesics and illustrate the practicality of using this approach.

Cooperative Localization Using Distance Measurements for Mobile Nodes.

This paper considers the two-dimensional (2D) anchorless localization problem for sensor networks in global positioning system (GPS)-denied environments. We present an efficient method, based on the multidimensional scaling (MDS) algorithm, in order to estimate the positions of the nodes in the network using measurements of the inter-node distances. The proposed method takes advantage of the mobility of the nodes to address the location ambiguity problem, i.e., rotation and flip ambiguity, which arises in the anchorless MDS algorithm. Knowledge of the displacement of the moving node is used to produce an analytical solution for the noise-free case. Subsequently, a least squares estimator is presented for the noisy scenario and the associated closed-form solution derived. The simulations show that the proposed algorithm accurately and efficiently estimates the locations of nodes, outperforming alternative methods.

Terrain constrained path planning for long-haul cables.

A method for path planning for a long-haul submarine optical fiber cable connecting two locations on the surface of the Earth is presented. Previous work on path planning takes account of the laying cost of the cable including material, labor, and its survivability, with consideration of risk of future cable break arising from laying of the cable in sensitive and risky areas, such as, in particular, earthquake prone areas. Previous work has also taken account of variation in the cost per unit length to optimize shielding (and associated increased costs) in higher risk areas. The key novelty here is to take account of the important requirement to reduce the likelihood of capsize of a remotely operated cable laying vehicle as it buries the cable in an uneven terrain. This instability risk depends on the direction of the path and slope of the terrain and is included here in the laying cost. Minimization of the cable laying cost and the expected number of potential cable repairs are the two objectives used to formulate the multi-objective optimal control problem. Using a Pareto approach, we solve the problem via dynamic programming and a computationally efficient algorithm based on the Ordered Upwind Method. Numerical results are consistent with an intuitive assessment of path quality, e.g., we can observe that the algorithm avoids high slope areas when better solutions are clearly available. Pareto optimal solutions and an approximate Pareto front are obtained to provide insight and guidance for cable path design that considers trade-offs between cost effectiveness (that includes consideration for stability of the remotely operated cable laying vehicle) and seismic resilience.

An Iterative Nonlinear Filter Using Variational Bayesian Optimization.

We propose an iterative nonlinear estimator based on the technique of variational Bayesian optimization. The posterior distribution of the underlying system state is approximated by a solvable variational distribution approached iteratively using evidence lower bound optimization subject to a minimal weighted Kullback-Leibler divergence, where a penalty factor is considered to adjust the step size of the iteration. Based on linearization, the iterative nonlinear filter is derived in a closed-form. The performance of the proposed algorithm is compared with several nonlinear filters in the literature using simulated target tracking examples.

High-Dimensional Probabilistic Fingerprinting in Wireless Sensor Networks Based on a Multivariate Gaussian Mixture Model.

The extensive deployment of wireless infrastructure provides a low-cost way to track mobile users in indoor environment. This paper demonstrates a prototype model of an accurate and reliable room location awareness system in a real public environment in which three typical problems arise. Firstly, a massive number of access points (APs) can be sensed leading to a high-dimensional classification problem. Secondly, heterogeneous devices record different received signal strength (RSS) levels because of the variations in chip-set and antenna attenuation. Thirdly, APs are not necessarily visible in every scanning cycle leading to missing data issue. This paper presents a probabilistic Wi-Fi fingerprinting method in a hidden Markov model (HMM) framework for mobile user tracking. To account for spatial correlation of the signal strengths from multiple APs, a Multivariate Gaussian Mixture Model (MVGMM) was fitted to model the probability distribution of RSS measurements in each cell. Furthermore, the unseen property of invisible AP was investigated in this research, and demonstrated the efficiency as a beneficial information to differentiate between cells. The proposed system is able to achieve comparable localisation performance. Filed test results achieve a reliable 97% localisation room level accuracy of multiple mobile users in a real university campus Wi-Fi network.

Golay Complementary Waveforms in Reed-Müller Sequences for Radar Detection of Nonzero Doppler Targets.

Golay complementary waveforms can, in theory, yield radar returns of high range resolution with essentially zero sidelobes. In practice, when deployed conventionally, while high signal-to-noise ratios can be achieved for static target detection, significant range sidelobes are generated by target returns of nonzero Doppler causing unreliable detection. We consider signal processing techniques using Golay complementary waveforms to improve radar detection performance in scenarios involving multiple nonzero Doppler targets. A signal processing procedure based on an existing, so called, Binomial Design algorithm that alters the transmission order of Golay complementary waveforms and weights the returns is proposed in an attempt to achieve an enhanced illumination performance. The procedure applies one of three proposed waveform transmission ordering algorithms, followed by a pointwise nonlinear processor combining the outputs of the Binomial Design algorithm and one of the ordering algorithms. The computational complexity of the Binomial Design algorithm and the three ordering algorithms are compared, and a statistical analysis of the performance of the pointwise nonlinear processing is given. Estimation of the areas in the Delay-Doppler map occupied by significant range sidelobes for given targets are also discussed. Numerical simulations for the comparison of the performances of the Binomial Design algorithm and the three ordering algorithms are presented for both fixed and randomized target locations. The simulation results demonstrate that the proposed signal processing procedure has a better detection performance in terms of lower sidelobes and higher Doppler resolution in the presence of multiple nonzero Doppler targets compared to existing methods.

Autonomous Multi-Robot Search for a Hazardous Source in a Turbulent Environment.

Finding the source of an accidental or deliberate release of a toxic substance into the atmosphere is of great importance for national security. The paper presents a search algorithm for turbulent environments which falls into the class of cognitive (infotaxi) algorithms. Bayesian estimation of the source parameter vector is carried out using the Rao-Blackwell dimension-reduction method, while the robots are controlled autonomously to move in a scalable formation. Estimation and control are carried out in a centralised replicated fusion architecture assuming all-to-all communication. The paper presents a comprehensive numerical analysis of the proposed algorithm, including the search-time and displacement statistics.

Range Sidelobe Suppression Using Complementary Sets in Distributed Multistatic Radar Networks.

We propose an alternative waveform scheme built on mutually-orthogonal complementary sets for a distributed multistatic radar. Our analysis and simulation show a reduced frequency band requirement for signal separation between antennas with centralized signal processing using the same carrier frequency. While the scheme can tolerate fluctuations of carrier frequencies and phases, range sidelobes arise when carrier frequencies between antennas are significantly different.

Modelling and estimation of multicomponent T(2) distributions.

Estimation of multiple T2 components within single imaging voxels typically proceeds in one of two ways; a nonparametric grid approximation to a continuous distribution is made and a regularized nonnegative least squares algorithm is employed to perform the parameter estimation, or a parametric multicomponent model is assumed with a maximum likelihood estimator for the component estimation. In this work, we present a Bayesian algorithm based on the principle of progressive correction for the latter choice of a discrete multicomponent model. We demonstrate in application to simulated data and two experimental datasets that our Bayesian approach provides robust and accurate estimates of both the T2 model parameters and nonideal flip angles. The second contribution of the paper is to present a Cramér-Rao analysis of T2 component width estimators. To this end, we introduce a parsimonious parametric and continuous model based on a mixture of inverse-gamma distributions. This analysis supports the notion that T2 spread is difficult, if not infeasible, to estimate from relaxometry data acquired with a typical clinical paradigm. These results justify the use of the discrete distribution model.

Robust observation detection for single object tracking: deterministic and probabilistic patch-based approaches.

In video analytics, robust observation detection is very important as the content of the videos varies a lot, especially for tracking implementation. Contrary to the image processing field, the problems of blurring, moderate deformation, low illumination surroundings, illumination change and homogenous texture are normally encountered in video analytics. Patch-Based Observation Detection (PBOD) is developed to improve detection robustness to complex scenes by fusing both feature- and template-based recognition methods. While we believe that feature-based detectors are more distinctive,however, for finding the matching between the frames are best achieved by a collection of points as in template-based detectors. Two methods of PBOD-the deterministic and probabilistic approaches-have been tested to find the best mode of detection. Both algorithms start by building comparison vectors at each detected points of interest. The vectors are matched to build candidate patches based on their respective coordination. For the deterministic method, patch matching is done in 2-level test where threshold-based position and size smoothing are applied to the patch with the highest correlation value. Forthe second approach, patch matching is done probabilistically by modelling the histograms of the patches by Poisson distributions for both RGB and HSV colour models. Then,maximum likelihood is applied for position smoothing while a Bayesian approach is appliedfor size smoothing. The result showed that probabilistic PBOD outperforms the deterministic approach with average distance error of 10.03% compared with 21.03%. This algorithm is best implemented as a complement to other simpler detection methods due to heavy processing requirement.

Robust foreground detection: a fusion of masked grey world, probabilistic gradient information and extended conditional random field approach.

Foreground detection has been used extensively in many applications such as people counting, traffic monitoring and face recognition. However, most of the existing detectors can only work under limited conditions. This happens because of the inability of the detector to distinguish foreground and background pixels, especially in complex situations. Our aim is to improve the robustness of foreground detection under sudden and gradual illumination change, colour similarity issue, moving background and shadow noise. Since it is hard to achieve robustness using a single model, we have combined several methods into an integrated system. The masked grey world algorithm is introduced to handle sudden illumination change. Colour co-occurrence modelling is then fused with the probabilistic edge-based background modelling. Colour co-occurrence modelling is good in filtering moving background and robust to gradual illumination change, while an edge-based modelling is used for solving a colour similarity problem. Finally, an extended conditional random field approach is used to filter out shadow and afterimage noise. Simulation results show that our algorithm performs better compared to the existing methods, which makes it suitable for higher-level applications.

Performance analysis for magnetic resonance imaging with nonlinear encoding fields.

Nonlinear spatial encoding fields for magnetic resonance imaging (MRI) hold great promise to improve on the linear gradient approaches by, for example, enabling reduced imaging times. Imaging schemes that employ general nonlinear encoding fields are difficult to analyze using traditional measures. In particular, the resolution is spatially varying, characterized by a position-dependent point spread function (PSF). Likewise, the use of nonlinear encoding fields creates an additional spatial dependence on the signal-to-noise ratio (SNR). Although the two properties of resolution and SNR are linked, in this work we focus on the latter. To this end, we examine the pixel variance, which requires a computation that is often not feasible for nonlinear encoding schemes. This paper presents a general formulation for the performance analysis of imaging schemes using arbitrary encoding fields. The analysis leads to the derivation of a practical and computationally efficient performance metric, which is demonstrated through simulation examples.

Adapting magnetic resonance imaging performance using nonlinear encoding fields.

Nonlinear spatial encoding fields for magnetic resonance imaging (MRI) hold great promise to improve on the linear gradient approaches. Unlike the linear techniques, the nonlinear encoding leads to a spatially varying signal-to-noise ratio (SNR). This paper demonstrates the possibility to tailor the encoding fields to focus the high SNR areas to a region of interest. To achieve this, a metric is derived to quantify the spatially dependent performance for arbitrary encoding schemes.