19 results found
The resolution of an imaging system is a key property that, despite many advances in optical imaging methods, remains difficult to define and apply. Rayleigh’s and Abbe’s resolution criteria were developed for observations with the human eye. However, modern imaging data is typically acquired on highly sensitive cameras and often requires complex image processing algorithms to analyze. Currently, no approaches are available for evaluating the resolving capability of such image processing algorithms that are now central to the analysis of imaging data, particularly location-based imaging data. Using methods of spatial statistics, we develop a novel algorithmic resolution limit to evaluate the resolving capabilities of location-based image processing algorithms. We show how insufficient algorithmic resolution can impact the outcome of location-based image analysis and present an approach to account for algorithmic resolution in the analysis of spatial location patterns.
Cohen E, Patel L, Ober R, et al., A hidden Markov model approach to characterizing the photo-switching behavior of fluorophores, Annals of Applied Statistics, ISSN: 1932-6157
Fluorescing molecules (fluorophores) that stochastically switch between photon-emitting and dark states underpin some of the most celebrated advancements in super-resolution microscopy. While this stochastic behavior has been heavily exploited, full characterization of the underlying models can potentially drive forward further imaging methodologies. Under the assumption that fluorophores move between fluorescing and dark states as continuous time Markov processes, the goal is to use a sequence of images to select a model and estimate the transition rates. We use a hidden Markov model to relate the observed discrete time signal to the hidden continuous time process. With imaging involving several repeat exposures of the fluorophore, we show the observed signal depends on both the current and past states of the hidden process, producing emission probabilities that depend on the transition rate parameters to be estimated. To tackle this unusual coupling of the transition and emission probabilities, we conceive transmission (transition-emission) matrices that capture all dependencies of the model. We provide a scheme of computing these matrices and adapt the forward-backward algorithm to compute a likelihood which is readily optimized to provide rate estimates. When confronted with several model proposals, combining this procedure with the Bayesian Information Criterion provides accurate model selection.
Gibberd A, Nobel J, Cohen E, 2018, Characterising dependency in computer networks using spectral coherence, International Conference on Time Series and Forecasting, Publisher: ITISE
The quantification of normal and anomalous traffic flowsacross computer networks is a topic of pervasive interest in network se-curity, and requires the timely application of time-series methods. Thetransmission or reception of packets passing between computers can berepresented in terms of time-stamped events and the resulting activityunderstood in terms of point-processes. Interestingly, in the disparate do-main of neuroscience, models for describing dependent point-processesare well developed. In particular, spectral methods which decomposesecond-order dependency across different frequencies allow for a richcharacterisation of point-processes. In this paper, we investigate usingthe spectral coherence statistic to characterise computer network activ-ity, and determine if, and how, device messaging may be dependent. Wedemonstrate on real data, that for many devices there appears to be verylittle dependency between device messaging channels. However, when sig-nificant coherence is detected it appears highly structured, a result whichsuggests coherence may prove useful for discriminating between types ofactivity at the network level.
Hoagn J, Cohen E, Adams N, 2017, Devising a fairer method for adjusting target scores in interrupted one-day international cricket, ELECTRONIC JOURNAL OF APPLIED STATISTICAL ANALYSIS, Vol: 10, Pages: 745-758, ISSN: 2070-5948
Griffié J, Shlomovich L, Williamson DJ, et al., 2017, 3D Bayesian cluster analysis of super-resolution data reveals LAT recruitment to the T cell synapse., Sci Rep, Vol: 7
Single-molecule localisation microscopy (SMLM) allows the localisation of fluorophores with a precision of 10-30 nm, revealing the cell's nanoscale architecture at the molecular level. Recently, SMLM has been extended to 3D, providing a unique insight into cellular machinery. Although cluster analysis techniques have been developed for 2D SMLM data sets, few have been applied to 3D. This lack of quantification tools can be explained by the relative novelty of imaging techniques such as interferometric photo-activated localisation microscopy (iPALM). Also, existing methods that could be extended to 3D SMLM are usually subject to user defined analysis parameters, which remains a major drawback. Here, we present a new open source cluster analysis method for 3D SMLM data, free of user definable parameters, relying on a model-based Bayesian approach which takes full account of the individual localisation precisions in all three dimensions. The accuracy and reliability of the method is validated using simulated data sets. This tool is then deployed on novel experimental data as a proof of concept, illustrating the recruitment of LAT to the T-cell immunological synapse in data acquired by iPALM providing ~10 nm isotropic resolution.
Taleb Y, Cohen E, 2016, A wavelet based likelihood ratio test for the homogeneity of poisson processes, 2016 IEEE Statistical Signal Processing Workshop (SSP), Publisher: IEEE
Estimating the rate (first-order intensity) of a point process is a task of great interest in the understanding of its nature. In this work we first address the estimation of the rate of an orderly point process on the real line using a multiresolution wavelet expansion approach. Implementing Haar wavelets, we find that in the case of a Poisson process the piecewise constant wavelet estimator of the rate has a scaled Poisson distribution. We apply this result in the design of a likelihood ratio test for a multiresolution formulation of the homogeneity of a Poisson process. We demonstrate this method with simulations and provide Type 1 error and empirical power plots under specific models.
Cohen E, Kim D, Ober RJ, 2015, The Cramer Rao lower bound for point based image registration with heteroscedastic error model for application in single molecule microscopy, IEEE Transactions on Medical Imaging, Vol: 34, Pages: 2632-2644, ISSN: 1558-254X
Rossy J, Cohen E, Gaus K, et al., 2014, Method for co-cluster analysis in multichannel single-molecule localisation data., Histochem Cell Biol, Vol: 141, Pages: 605-612
We demonstrate a combined univariate and bivariate Getis and Franklin's local point pattern analysis method to investigate the co-clustering of membrane proteins in two-dimensional single-molecule localisation data. This method assesses the degree of clustering of each molecule relative to its own species and relative to a second species. Using simulated data, we show that this approach can quantify the degree of cluster overlap in multichannel point patterns. The method is validated using photo-activated localisation microscopy and direct stochastic optical reconstruction microscopy data of the proteins Lck and CD45 at the T cell immunological synapse. Analysing co-clustering in this manner is generalizable to higher numbers of fluorescent species and to three-dimensional or live cell data sets.
Cohen EAK, 2014, Multi-wavelet coherence for point processes on the real-line, IEEE International Conference on Acoustics, Speech and Signal Processing, Pages: 2649-2653
Cohen EAK, Ober RJ, 2013, Analysis of Point Based Image Registration Errors With Applications in Single Molecule Microscopy, IEEE TRANSACTIONS ON SIGNAL PROCESSING, Vol: 61, Pages: 6291-6306, ISSN: 1053-587X
Cohen EAK, Ober RJ, 2013, Measurement errors in fluorescence microscopy image registration., Asilomar Conference on Signals, Systems and Computers, Pages: 1602-1606, ISSN: 1058-6393
Walden AT, Cohen EAK, 2012, Statistical Properties for Coherence Estimators From Evolutionary Spectra, IEEE TRANSACTIONS ON SIGNAL PROCESSING, Vol: 60, Pages: 4586-4597, ISSN: 1053-587X
Cohen EAK, Ober RJ, 2012, Image Registration Error Analysis with applications in single molecule microscopy., IEEE Biomedical Imaging Symposium - From Nano to Macro, Pages: 996-999, ISSN: 1945-7928
Cohen EAK, Ober RJ, 2012, Measurement Errors in Fluorescence Microscopy Experiments, Conf Rec Asilomar C, Pages: 1602 --- 1606-1602 --- 1606
Cohen EAK, Ober RJ, 2012, IMAGE REGISTRATION ERROR ANALYSIS WITH APPLICATIONS IN SINGLE MOLECULE MICROSCOPY, Proc I S Biomed Imaging, Pages: 996 --- 999-996 --- 999
Cohen E, 2011, A statistical study of wavelet coherence for stationary and non-stationary processes
Cohen EAK, Walden AT, 2011, Wavelet Coherence for Certain Nonstationary Bivariate Processes, IEEE TRANSACTIONS ON SIGNAL PROCESSING, Vol: 59, Pages: 2522-2531, ISSN: 1053-587X
Cohen EAK, Walden AT, 2010, A Statistical Study of Temporally Smoothed Wavelet Coherence, IEEE TRANSACTIONS ON SIGNAL PROCESSING, Vol: 58, Pages: 2964-2973, ISSN: 1053-587X
Cohen EAK, Walden AT, 2010, A Statistical Analysis of Morse Wavelet Coherence, IEEE TRANSACTIONS ON SIGNAL PROCESSING, Vol: 58, Pages: 980-989, ISSN: 1053-587X
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