Image Co-addition Research Articles

SNIa DETECTION ANALYSIS RESULTS FROM REAL AND SIMULATED IMAGES USING SPECIALIZED SOFTWARE

The detection of transient events, Type Ia supernovae in particular, has become an important research subject in today's astronomy. We use as a base tool the software suite for astronomical image processing called LSSTsp and adapt it to assemble a type Ia supernova detection pipe. We study some straightforward changes on the overall pipeline by selecting better quality inputs to perform a coaddition of reference images, we analyze the different residual sources detected on the difference images and, lastly, we build light curves by taking into account the features of detected difference image analysis sources. Finally, we build a catalog of supernova candidates by using a random forest classification, and check the relevance these additions. We reduced the overall source detection density with our changes while finding between 82% and 85% of the present Type Ia supernovae.

Simulating image coaddition with the Nancy Grace Roman Space Telescope – II. Analysis of the simulated images and implications for weak lensing

ABSTRACT One challenge for applying current weak lensing analysis tools to the Nancy Grace Roman Space Telescope is that individual images will be undersampled. Our companion paper presented an initial application of Imcom – an algorithm that builds an optimal mapping from input to output pixels to reconstruct a fully sampled combined image – on the Roman image simulations. In this paper, we measure the output noise power spectra, identify the sources of the major features in the power spectra, and show that simple analytic models that ignore sampling effects underestimate the power spectra of the coadded noise images. We compute the moments of both idealized injected stars and fully simulated stars in the coadded images, and their one- and two-point statistics. We show that the idealized injected stars have root-mean-square ellipticity errors (1–6) × 10−4 per component depending on the band; the correlation functions are ≥2 orders of magnitude below requirements, indicating that the image combination step itself is using a small fraction of the overall Roman second moment error budget, although the fourth moments are larger and warrant further investigation. The stars in the simulated sky images, which include blending and chromaticity effects, have correlation functions near the requirement level (and below the requirement level in a wide-band image constructed by stacking all four filters). We evaluate the noise-induced biases in the ellipticities of injected stars, and explain the resulting trends with an analytical model. We conclude by enumerating the next steps in developing an image coaddition pipeline for Roman.

Simulating image coaddition with the Nancy Grace Roman Space Telescope – I. Simulation methodology and general results

ABSTRACT The upcoming Nancy Grace Roman Space Telescope will carry out a wide-area survey in the near-infrared. A key science objective is the measurement of cosmic structure via weak gravitational lensing. Roman data will be undersampled, which introduces new challenges in the measurement of source galaxy shapes; a potential solution is to use linear algebra-based coaddition techniques such as imcom that combine multiple undersampled images to produce a single oversampled output mosaic with a desired ‘target’ point spread function (PSF). We present here an initial application of imcom to 0.64 square degrees of simulated Roman data, based on the Roman branch of the Legacy Survey of Space and Time (LSST) Dark Energy Science Collaboration (DESC) Data Challenge 2 (DC2) simulation. We show that imcom runs successfully on simulated data that includes features such as plate scale distortions, chip gaps, detector defects, and cosmic ray masks. We simultaneously propagate grids of injected sources and simulated noise fields as well as the full simulation. We quantify the residual deviations of the PSF from the target (the ‘leakage’), as well as noise properties of the output images; we discuss how the overall tiling pattern as well as Moiré patterns appear in the final leakage and noise maps. We include appendices on interpolation algorithms and the interaction of undersampling with image processing operations that may be of broader applicability. The companion paper (‘Paper II’) explores the implications for weak lensing analyses.

Applying weighted image coaddition to observations of GRB optical afterglows at the D50 telescope in Ondřejov

AbstractOne of the primary observational objectives of the 0.5 m robotic telescope of Ondřejov observatory is the ground‐based follow‐up of gamma‐ray burst triggers. This independent robotic observatory has been in operation since 2008 and has followed up more than a hundred events localized by the Swift or INTEGRAL satellites. We describe the use of the weighted coaddition of astronomical images while applying this method to observations of GRB optical afterglows. We present optical photometric observations of the detected optical afterglows. The collection contains several faint optical afterglows, in some cases a lightcurve is available, in some cases only a single point detection has been achieved. A brief collection of available information is presented for each of the events together with our fitting and analysis.

A Possible Advantage of Telescopes with a Noncircular Pupil

Most telescope designs have a circular-shape aperture. We demonstrate that telescopes with an elongated pupil have better contrast, at lower separations, between a bright central star and a faint companion. We simulate images for an elongated-pupil telescope and for a circular-pupil telescope of equal aperture area and integration time, investigating specifically what is the maximal contrast for finding faint companions around bright stars as a function of angular separation. We show that this design gives better contrast at lower separation from a bright star. This is shown for diffraction-limited (for perfect and imperfect optics) and seeing-limited speckle images, assuming equal aperture area and observing time. We also show the results are robust to errors in measurement of the point spread function. To compensate for the wider point spread function of the short axis, images should be taken at different rotation angles, either by rotating the telescope around the optical axis or by allowing a stationary mirror array to scan different parallactic angles with time. Images taken at different rotation angles are added using the proper image coaddition algorithms developed by Zackay & Ofek. The final image has the same contrast in all angles, rather than in specific areas of diffraction nulls. We obtained speckle observations with a small, ground based elongated-aperture telescope and show the results are consistent with simulations.

How to COAAD Images. II. A Coaddition Image that is Optimal for Any Purpose in the Background-dominated Noise Limit

Image coaddition is one of the most basic operations that astronomers perform. In Paper~I, we presented the optimal ways to coadd images in order to detect faint sources and to perfrom flux measurements under the assumption that the noise is approximately Gaussian. Here, we build on these results and derive from first principles a coaddition technique which is optimal for any hypothesis testing and measurement (e.g., source detection, flux or shape measurements and star/galaxy separation), in the background-noise-dominated case. This method has several important properties. The pixels of the resulting coadd image are uncorrelated. This image preserves all the information (from the original individual images) on all spatial frequencies. Any hypothesis testing or measurement that can be done on all the individual images simultaneously, can be done on the coadded image without any loss of information. The PSF of this image is typically as narrow, or narrower than the PSF of the best image in the ensemble. Moreover, this image is practically indistinguishable from a regular single image, meaning that any code that measures any property on a regular astronomical image can be applied to it unchanged. In particular, the optimal source detection statistic derived in paper~I is reproduced by matched filtering this image with its own PSF. This coaddition process, which we call proper coaddition, can be understood as a the maximum signal-to-noise ratio measurement of the Fourier transform of the image, weighted in such a way that the noise in the entire Fourier domain is of equal variance. This method has important implications for multi-epoch seeing-limited deep surveys, weak lensing galaxy shape measurements, and diffraction-limited imaging via speckle observations. The last topic will be covered in depth in future papers. We provide an implementation of this algorithm in MATLAB.

How to COAAD Images. I. Optimal Source Detection and Photometry of Point Sources Using Ensembles of Images

Abstract Stacks of digital astronomical images are combined in order to increase image depth. The variable seeing conditions, sky background, and transparency of ground-based observations make the coaddition process nontrivial. We present image coaddition methods that maximize the signal-to-noise ratio (S/N) and optimized for source detection and flux measurement. We show that for these purposes, the best way to combine images is to apply a matched filter to each image using its own point-spread function (PSF) and only then to sum the images with the appropriate weights. Methods that either match the filter after coaddition or perform PSF homogenization prior to coaddition will result in loss of sensitivity. We argue that our method provides an increase of between a few and 25% in the survey speed of deep ground-based imaging surveys compared with weighted coaddition techniques. We demonstrate this claim using simulated data as well as data from the Palomar Transient Factory data release 2. We present a variant of this coaddition method, which is optimal for PSF or aperture photometry. We also provide an analytic formula for calculating the S/N for PSF photometry on single or multiple observations. In the next paper in this series, we present a method for image coaddition in the limit of background-dominated noise, which is optimal for any statistical test or measurement on the constant-in-time image (e.g., source detection, shape or flux measurement, or star–galaxy separation), making the original data redundant. We provide an implementation of these algorithms in MATLAB.

FULL-DEPTH COADDS OF THE WISE AND FIRST-YEAR NEOWISE-REACTIVATION IMAGES

ABSTRACT The Near Earth Object Wide-field Infrared Survey Explorer (NEOWISE) Reactivation mission released data from its first full year of observations in 2015. This data set includes ∼2.5 million exposures in each of W1 and W2, effectively doubling the amount of WISE imaging available at 3.4 μm and 4.6 μm relative to the AllWISE release. We have created the first ever full-sky set of coadds combining all publicly available W1 and W2 exposures from both the AllWISE and NEOWISE-Reactivation (NEOWISER) mission phases. We employ an adaptation of the unWISE image coaddition framework, which preserves the native WISE angular resolution and is optimized for forced photometry. By incorporating two additional scans of the entire sky, we not only improve the W1/W2 depths, but also largely eliminate time-dependent artifacts such as off-axis scattered moonlight. We anticipate that our new coadds will have a broad range of applications, including target selection for upcoming spectroscopic cosmology surveys, identification of distant/massive galaxy clusters, and discovery of high-redshift quasars. In particular, our full-depth AllWISE+NEOWISER coadds will be an important input for the Dark Energy Spectroscopic Instrument selection of luminous red galaxy and quasar targets. Our full-depth W1/W2 coadds are already in use within the DECam Legacy Survey (DECaLS) and Mayall z-band Legacy Survey (MzLS) reduction pipelines. Much more work still remains in order to fully leverage NEOWISER imaging for astrophysical applications beyond the solar system.

PROPER IMAGE SUBTRACTION—OPTIMAL TRANSIENT DETECTION, PHOTOMETRY, AND HYPOTHESIS TESTING

ABSTRACT Transient detection and flux measurement via image subtraction stand at the base of time domain astronomy. Due to the varying seeing conditions, the image subtraction process is non-trivial, and existing solutions suffer from a variety of problems. Starting from basic statistical principles, we develop the optimal statistic for transient detection, flux measurement, and any image-difference hypothesis testing. We derive a closed-form statistic that: (1) is mathematically proven to be the optimal transient detection statistic in the limit of background-dominated noise, (2) is numerically stable, (3) for accurately registered, adequately sampled images, does not leave subtraction or deconvolution artifacts, (4) allows automatic transient detection to the theoretical sensitivity limit by providing credible detection significance, (5) has uncorrelated white noise, (6) is a sufficient statistic for any further statistical test on the difference image, and, in particular, allows us to distinguish particle hits and other image artifacts from real transients, (7) is symmetric to the exchange of the new and reference images, (8) is at least an order of magnitude faster to compute than some popular methods, and (9) is straightforward to implement. Furthermore, we present extensions of this method that make it resilient to registration errors, color-refraction errors, and any noise source that can be modeled. In addition, we show that the optimal way to prepare a reference image is the proper image coaddition presented in Zackay & Ofek. We demonstrate this method on simulated data and real observations from the PTF data release 2. We provide an implementation of this algorithm in MATLAB and Python.

Regularization techniques for PSF-matching kernels - I. Choice of kernel basis

We review current methods for building point spread function (PSF)-matching kernels for the purposes of image subtraction or co-addition. Such methods use a linear decomposition of the kernel on a series of basis functions. The correct choice of these basis functions is fundamental to the efficiency and effectiveness of the matching – the chosen bases should represent the underlying signal using a reasonably small number of shapes, and/or have a minimum number of user-adjustable tuning parameters. We examine methods whose bases comprise multiple Gauss–Hermite polynomials, as well as a form-free basis composed of delta-functions. Kernels derived from delta-functions are unsurprisingly shown to be more expressive; they are able to take more general shapes and perform better in situations where sum-of-Gaussian methods are known to fail. However, due to its many degrees of freedom (the maximum number allowed by the kernel size) this basis tends to overfit the problem and yields noisy kernels having large variance. We introduce a new technique to regularize these delta-function kernel solutions, which bridges the gap between the generality of delta-function kernels and the compactness of sum-of-Gaussian kernels. Through this regularization we are able to create general kernel solutions that represent the intrinsic shape of the PSF-matching kernel with only one degree of freedom, the strength of the regularization λ. The role of λ is effectively to exchange variance in the resulting difference image with variance in the kernel itself. We examine considerations in choosing the value of λ, including statistical risk estimators and the ability of the solution to predict solutions for adjacent areas. Both of these suggest moderate strengths of λ between 0.1 and 1.0, although this optimization is likely data set dependent. This model allows for flexible representations of the convolution kernel that have significant predictive ability and will prove useful in implementing robust image subtraction pipelines that must address hundreds to thousands of images per night.

Image Co-Addition with Temporally Varying Kernels

ABSTRACTLarge, multifrequency imaging surveys, such as the Large Synaptic Survey Telescope (LSST), need to do near-real-time analysis of very large data sets. This raises a host of statistical and computational problems for which standard methods do not work. In this article, we study a proposed method for combining stacks of images into a single summary image, sometimes referred to as a template. We evaluate this method by comparing it with using pixelwise medians or means by various criteria. Note that the goal is not to propose these comparison methods for use in their own right, but to ensure that additional complexity also provides substantially improved performance.

Astronomy in the Cloud: Using MapReduce for Image Co-Addition

ABSTRACTIn the coming decade, astronomical surveys of the sky will generate tens of terabytes of images and detect hundreds of millions of sources every night. The study of these sources will involve computation challenges such as anomaly detection and classification and moving-object tracking. Since such studies benefit from the highest-quality data, methods such as image co-addition, i.e., astrometric registration followed by per-pixel summation, will be a critical preprocessing step prior to scientific investigation. With a requirement that these images be analyzed on a nightly basis to identify moving sources such as potentially hazardous asteroids or transient objects such as supernovae, these data streams present many computational challenges. Given the quantity of data involved, the computational load of these problems can only be addressed by distributing the workload over a large number of nodes. However, the high data throughput demanded by these applications may present scalability challenges for certain storage architectures. One scalable data-processing method that has emerged in recent years is MapReduce, and in this article we focus on its popular open-source implementation called Hadoop. In the Hadoop framework, the data are partitioned among storage attached directly to worker nodes, and the processing workload is scheduled in parallel on the nodes that contain the required input data. A further motivation for using Hadoop is that it allows us to exploit cloud computing resources: i.e., platforms where Hadoop is offered as a service. We report on our experience of implementing a scalable image-processing pipeline for the SDSS imaging database using Hadoop. This multiterabyte imaging data set provides a good testbed for algorithm development, since its scope and structure approximate future surveys. First, we describe MapReduce and how we adapted image co-addition to the MapReduce framework. Then we describe a number of optimizations to our basic approach and report experimental results comparing their performance.

Pencil-Beam Surveys for Trans-Neptunian Objects: Novel Methods for Optimization and Characterization

ABSTRACTDigital co-addition of astronomical images is a common technique for increasing signal-to-noise ratio (S/N) and image depth. A modification of this simple technique has been applied to the detection of minor bodies in the solar system: first stationary objects are removed through the subtraction of a high-S/N template image, then the sky motion of the solar system bodies of interest is predicted and compensated for by shifting pixels in software prior to the co-addition step. This “shift-and-stack” approach has been applied with great success in directed surveys for minor solar system bodies. In these surveys, the shifts have been parameterized in a variety of ways. However, these parameterizations have not been optimized and in most cases cannot be effectively applied to data sets with long observation arcs due to objects’ real trajectories diverging from linear tracks on the sky. This paper presents two novel probabilistic approaches for determining a near-optimum set of shift vectors to apply to any image set given a desired region of orbital space to search. The first method is designed for short observational arcs, and the second for observational arcs long enough to require nonlinear shift vectors. Using these techniques and other optimizations, we derive optimized grids for previous surveys that have used “shift-and-stack” approaches to illustrate the improvements that can be made with our method, and at the same time derive new limits on the range of orbital parameters these surveys searched. We conclude with a simulation of a future application for this approach with LSST, and show that combining multiple nights of data from such next-generation facilities is within the realm of computational feasibility.

Optimal Co‐Addition of Imaging Data for Rapidly Fading Gamma‐Ray Burst Afterglows

We present a technique for optimal co-addition of image data for rapidly varying sources, with specific application to gamma-ray burst (GRB) afterglows. Unweighted co-addition of rapidly fading afterglow light curve data becomes counterproductive relatively quickly. It is better to stop co-addition of the data once noise dominates late exposures. A better alternative is to optimally weight each exposure to maximize the signal-to-noise ratio (S/N) of the final co-added image data. By using information about GRB light curves and image noise characteristics, optimal image co-addition increases the probability of afterglow detection and places the most stringent upper limits on nondetections. For a temporal power-law flux decay typical of GRB afterglows, optimal co-addition has the greatest potential to improve the S/N of afterglow imaging data (relative to unweighted co-addition) when the decay rate is high, the source count rate is low, and the background rate is high. The optimal co-addition technique is demonstrated with applications to Swift Ultraviolet/Optical Telescope (UVOT) data of several GRBs, with and without detected afterglows.

Object detection in multi-epoch data

In astronomy multiple images are frequently obtained at the same position of the sky for follow-up coaddition as it helps one go deeper and look for fainter objects. With large scale panchromatic synoptic surveys becoming more common, image co-addition has become even more necessary as new observations start to get compared with coadded fiducial sky in real time. The standard coaddition techniques have included straight averages, variance weighted averages, medians etc. A more sophisticated nonlinear response chi-square method is also used when it is known that the data are background noise limited and the point spread function is homogenized in all channels. A more robust object detection technique capable of detecting faint sources, even those not seen at all epochs which will normally be smoothed out in traditional methods, is described. The analysis at each pixel level is based on a formula similar to Mahalanobis distance.

In Pursuit of LSST Science Requirements: A Comparison of Photometry Algorithms

ABSTRACTWe have developed an end-to-end photometric data-processing pipeline to compare current photometric algorithms commonly used on ground-based imaging data. This test bed is exceedingly adaptable and enables us to perform many research and development tasks, including image subtraction and co-addition, object detection and measurements, the production of photometric catalogs, and the creation and stocking of database tables with time-series information. This testing has been undertaken to evaluate existing photometry algorithms for consideration by a next-generation image-processing pipeline for the Large Synoptic Survey Telescope (LSST). We outline the results of our tests for four packages: the Sloan Digital Sky Survey’s Photo package, DAOPHOT and ALLFRAME, DOPHOT, and two versions of Source Extractor (SExtractor). The ability of these algorithms to perform point-source photometry, astrometry, shape measurements, and star-galaxy separation and to measure objects at low signal-to-noise ratio is quantified. We also perform a detailed crowded-field comparison of DAOPHOT and ALLFRAME, and profile the speed and memory requirements in detail for SExtractor. We find that both DAOPHOT and Photo are able to perform aperture photometry to high enough precision to meet LSST’s science requirements, and less adequately at PSF-fitting photometry. Photo performs the best at simultaneous point- and extended-source shape and brightness measurements. SExtractor is the fastest algorithm, and recent upgrades in the software yield high-quality centroid and shape measurements with little bias toward faint magnitudes. ALLFRAME yields the best photometric results in crowded fields.

Science applications of the Montage image mosaic engine

Montage is a portable, scaleable toolkit that runs on end-users desktops, clusters, and computing grids. It generates astronomical image mosaics that preserve the calibration and photometry in the input FITS files. The code is available for download at the project website at <http://montage.ipac.caltech.edu>, and includes independent modules for image discovery (including support for VO image access protocols), image reprojection, rectification of the sky background to a common level and image co-addition.

Shape Reconstruction and Weak Lensing Measurement with Interferometers: A Shapelet Approach

We present a new approach for image reconstruction and weak lensing measurements with interferometers. Based on the shapelet formalism presented in Refregier (2001), object images are decomposed into orthonormal Hermite basis functions. The shapelet coefficients of a collection of sources are simultaneously fit on the uv plane, the Fourier transform of the sky brightness distribution observed by interferometers. The resulting chi-square fit is linear in its parameters and can thus be performed efficiently by simple matrix multiplications. We show how the complex effects of bandwidth smearing, time averaging and non-coplanarity of the array can be easily and fully corrected for in our method. Optimal image reconstruction, co-addition, astrometry, and photometry can all be achieved using weighted sums of the derived coefficients. As an example we consider the observing conditions of the FIRST radio survey (Becker et al. 1995; White et al. 1997). We find that our method accurately recovers the shapes of simulated images even for the sparse uv sampling of this snapshot survey. Using one of the FIRST pointings, we find our method compares well with CLEAN, the commonly used method for interferometric imaging. Our method has the advantage of being linear in the fit parameters, of fitting all sources simultaneously, and of providing the full covariance matrix of the coefficients, which allows us to quantify the errors and cross-talk in image shapes. It is therefore well-suited for quantitative shape measurements which require high-precision. In particular, we show how our method can be combined with the results of Refregier & Bacon (2001) to provide an accurate measurement of weak lensing from interferometric data.