Reference-less detection, astrometry, and photometry of faint companions with adaptive optics

We propose a complete framework for the detection, astrometry, and photometry of faint companions from a sequence of adaptive optics corrected short exposures. The algorithms exploit the difference in statistics between the on-axis and off-axis intensity. Using moderate-Strehl ratio data obtained with the natural guide star adaptive optics system on the Lick Observatory's 3-m Shane Telescope, we compare these methods to the standard approach of PSF fitting. We give detection limits for the Lick system, as well as a first guide to expected accuracy of differential photometry and astrometry with the new techniques. The proposed approach to detection offers a new way of determining dynamic range, while the new algorithms for differential photometry and astrometry yield accurate results for very faint and close-in companions where PSF fitting fails. All three proposed algorithms are self-calibrating, i.e. they do not require observation of a calibration star thus improving the observing efficiency.Comment: Astrophysical Journal 698 (2009) 28-4

The Strehl Ratio in Adaptive Optics Images: Statistics and Estimation

Statistical properties of the intensity in adaptive optics images are usually modeled with a Rician distribution. We study the central point of the image, where this model is inappropriate for high to very high correction levels. The central point is an important problem because it gives the Strehl ratio distribution. We show that the central point distribution can be modeled using a non-central Gamma distribution.Comment: 8 pages, 5 figure

Balmer filaments in Tycho's supernova remnant: an interplay between cosmic-ray and broad-neutral precursors

We present H$\alpha$ spectroscopic observations and detailed modelling of the Balmer filaments in the supernova remnant Tycho. We used Galaxy H$\alpha$ Fabry-P\'erot Spectrometer on the William Herschel Telescope with a 3.4'$\times$3.4' field-of-view, 0.2" pixel scale and \sigma_\rm{instr}=8.1 km/s resolution at 1" seeing for $\sim10$ hours, resulting in 82 spatial-spectral bins that resolve the narrow H$\alpha$ line in the entire Tycho's northeastern rim. For the first time, we can mitigate artificial line broadening from unresolved differential motion, and probe H$\alpha$ emission parameters in varying shock and ambient medium conditions. Broad H$\alpha$ line remains unresolved within spectral coverage of 392 km/s. We employed Bayesian inference to obtain reliable parameter confidence intervals, and quantify the evidence for models with multiple line components. The median H$\alpha$ narrow-line full-width at half-maximum of all bins and models is W_\rm{NL}=(54.8\pm1.8) km/s at the $95\%$ confidence level, varying within [35, 72] km/s between bins and clearly broadened compared to the intrinsic (thermal) $\approx20$ km/s. Possible line splits are accounted for, significant in $\approx18\%$ of the filament, and presumably due to remaining projection effects. We also find wide-spread evidence for intermediate-line emission of a broad-neutral precursor, with median W_\rm{IL}=(180\pm14) km/s ($95\%$ confidence). Finally, we present a measurement of the remnant's systemic velocity, V_\rm{LSR}=-34 km/s, and map differential line-of-sight motions. Our results confirm the existence and interplay of shock precursors in Tycho's remnant. In particular, we show that suprathermal narrow-line emission is near-universal in Tycho and that, in absence of an alternative explanation, collisionless supernova remnant shocks constitute a viable acceleration source for Galactic TeV Cosmic-Ray protons.Comment: 36 pages, 17 figures, 5 tables, Paper accepted for publication in the Astrophysical Journal; References correcte

False discovery rate analysis of brain diffusion direction maps

Diffusion tensor imaging (DTI) is a novel modality of magnetic resonance imaging that allows noninvasive mapping of the brain's white matter. A particular map derived from DTI measurements is a map of water principal diffusion directions, which are proxies for neural fiber directions. We consider a study in which diffusion direction maps were acquired for two groups of subjects. The objective of the analysis is to find regions of the brain in which the corresponding diffusion directions differ between the groups. This is attained by first computing a test statistic for the difference in direction at every brain location using a Watson model for directional data. Interesting locations are subsequently selected with control of the false discovery rate. More accurate modeling of the null distribution is obtained using an empirical null density based on the empirical distribution of the test statistics across the brain. Further, substantial improvements in power are achieved by local spatial averaging of the test statistic map. Although the focus is on one particular study and imaging technology, the proposed inference methods can be applied to other large scale simultaneous hypothesis testing problems with a continuous underlying spatial structure.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS133 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations

This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time suppressing the inevitable corrupting observational errors. We present a simple nonparametric modeling technique and an algorithm implementing it - an improved and generalized version of Bayesian Blocks (Scargle 1998) - that finds the optimal segmentation of the data in the observation interval. The structure of the algorithm allows it to be used in either a real-time trigger mode, or a retrospective mode. Maximum likelihood or marginal posterior functions to measure model fitness are presented for events, binned counts, and measurements at arbitrary times with known error distributions. Problems addressed include those connected with data gaps, variable exposure, extension to piecewise linear and piecewise exponential representations, multi-variate time series data, analysis of variance, data on the circle, other data modes, and dispersed data. Simulations provide evidence that the detection efficiency for weak signals is close to a theoretical asymptotic limit derived by (Arias-Castro, Donoho and Huo 2003). In the spirit of Reproducible Research (Donoho et al. 2008) all of the code and data necessary to reproduce all of the figures in this paper are included as auxiliary material.Comment: Added some missing script files and updated other ancillary data (code and data files). To be submitted to the Astophysical Journa

A Detailed Investigation into Low-Level Feature Detection in Spectrogram Images

Being the first stage of analysis within an image, low-level feature detection is a crucial step in the image analysis process and, as such, deserves suitable attention. This paper presents a systematic investigation into low-level feature detection in spectrogram images. The result of which is the identification of frequency tracks. Analysis of the literature identifies different strategies for accomplishing low-level feature detection. Nevertheless, the advantages and disadvantages of each are not explicitly investigated. Three model-based detection strategies are outlined, each extracting an increasing amount of information from the spectrogram, and, through ROC analysis, it is shown that at increasing levels of extraction the detection rates increase. Nevertheless, further investigation suggests that model-based detection has a limitation—it is not computationally feasible to fully evaluate the model of even a simple sinusoidal track. Therefore, alternative approaches, such as dimensionality reduction, are investigated to reduce the complex search space. It is shown that, if carefully selected, these techniques can approach the detection rates of model-based strategies that perform the same level of information extraction. The implementations used to derive the results presented within this paper are available online from http://stdetect.googlecode.com

A Framework for Temperature Imaging using the Change in Backscattered Ultrasonic Signals

Hyperthermia is a cancer treatment that elevates tissue temperature to 40 to 43oC. It would benefit from a non-invasive, safe, inexpensive and convenient thermometry to monitor heating patterns. Ultrasound is a modality that meets these requirements. In our initial work, using both prediction and experimental data, we showed that the change in the backscattered energy: CBE) is a potential parameter for TI. CBE, however, was computed in a straightforward yet ad hoc manner. In this work, we developed and exploited a mathematical representation for our approach to TI to optimize temperature accuracy. Non-thermal effects of noise and motion confound the use of CBE. Assuming additive white Gaussian noise, we applied signal averaging and thresholding to reduce noise effects. Our motion compensation algorithms were also applied to images with known motion to evaluate factors affecting the compensation performance. In the framework development, temperature imaging was modeled as a problem of estimating temperature from the random processes resulting from thermal changes in signals. CBE computation was formalized as a ratio between two random variables. Mutual information: MI) was studied as an example of possible parameters for temperature imaging based on the joint distributions. Furthermore, a maximum likelihood estimator: MLE) was developed. Both simulations and experimental results showed that noise effects were reduced by signal averaging. The motion compensation algorithms proved to be able to compensate for motion in images and were improved by choosing appropriate interpolation methods and sample rates. For images of uniformly distributed scatterers, CBE and MI can be computed independent of SNR to improve the temperature accuracy. The application of the MLE also showed improvements in temperature accuracy compared to the energy ratio from the signal mean in simulations. The application of the framework to experimental data requires more work to implement noise reduction approaches in 3D heating experiments. The framework identified ways in which we were able to reduce the effects of both noise and motion. The framework formalized our approaches to temperature imaging, improved temperature accuracy in simulations, and can be applied to experimental data if the noise reduction approaches can be implemented for 3D experiments

Automatic Counting of Canola Flowers from In-Field Time-Lapse Images

The combination of plant phenotyping and computer techniques has gained popularity amongst breeders and computer scientists. The recent evolution of the latter has allowed High-Throughput Phenotyping (HTP) to play a significant role in filling the genotype-to-phenotype gap. While most of the related work in HTP is performed in controlled environments, such as greenhouses, that allow automatic devices to capture the data reliably, research in in-field phenotyping is not as robust due to environmental confounds (i.e., fog or sun-reflections). The usage of high temporal density data has not been exploited to the same degree as high spatial resolution information. However, many phenotypes (e.g., canola flowering) have a temporal component. In this document, we present an image-processing-based method that attempts to detect and count flowers of canola during the early flowering stage on in-field time-lapse images. This approach can be used to analyze the evolution of the flower density of canola plants over short periods of time during the first days of flowering thanks to the availability of high temporal resolution images. We used images extracted during Summer 2016 to generate ground truth, tune the flower detection method and count the flowers during the first days of the flowering period. We provide an overview and a discussion about additional steps that might be needed to overcome the impact of sunlight reflection on canola leaves in the detection of flowers