Filter design for the detection of compact sources based on the Neyman-Pearson detector

This paper considers the problem of compact source detection on a Gaussian background in 1D. Two aspects of this problem are considered: the design of the detector and the filtering of the data. Our detection scheme is based on local maxima and it takes into account not only the amplitude but also the curvature of the maxima. A Neyman-Pearson test is used to define the region of acceptance, that is given by a sufficient linear detector that is independent on the amplitude distribution of the sources. We study how detection can be enhanced by means of linear filters with a scaling parameter and compare some of them (the Mexican Hat wavelet, the matched and the scale-adaptive filters). We introduce a new filter, that depends on two free parameters (biparametric scale-adaptive filter). The value of these two parameters can be determined, given the a priori pdf of the amplitudes of the sources, such that the filter optimizes the performance of the detector in the sense that it gives the maximum number of real detections once fixed the number density of spurious sources. The combination of a detection scheme that includes information on the curvature and a flexible filter that incorporates two free parameters (one of them a scaling) improves significantly the number of detections in some interesting cases. In particular, for the case of weak sources embedded in white noise the improvement with respect to the standard matched filter is of the order of 40%. Finally, an estimation of the amplitude of the source is introduced and it is proven that such an estimator is unbiased and it has maximum efficiency. We perform numerical simulations to test these theoretical ideas and conclude that the results of the simulations agree with the analytical ones.Comment: 15 pages, 13 figures, version accepted for publication in MNRAS. Corrected typos in Tab.

MIMO Radar Target Localization and Performance Evaluation under SIRP Clutter

Multiple-input multiple-output (MIMO) radar has become a thriving subject of research during the past decades. In the MIMO radar context, it is sometimes more accurate to model the radar clutter as a non-Gaussian process, more specifically, by using the spherically invariant random process (SIRP) model. In this paper, we focus on the estimation and performance analysis of the angular spacing between two targets for the MIMO radar under the SIRP clutter. First, we propose an iterative maximum likelihood as well as an iterative maximum a posteriori estimator, for the target's spacing parameter estimation in the SIRP clutter context. Then we derive and compare various Cram\'er-Rao-like bounds (CRLBs) for performance assessment. Finally, we address the problem of target resolvability by using the concept of angular resolution limit (ARL), and derive an analytical, closed-form expression of the ARL based on Smith's criterion, between two closely spaced targets in a MIMO radar context under SIRP clutter. For this aim we also obtain the non-matrix, closed-form expressions for each of the CRLBs. Finally, we provide numerical simulations to assess the performance of the proposed algorithms, the validity of the derived ARL expression, and to reveal the ARL's insightful properties.Comment: 34 pages, 12 figure

Direct exoplanet detection and characterization using the ANDROMEDA method: Performance on VLT/NaCo data

Context. The direct detection of exoplanets with high-contrast imaging requires advanced data processing methods to disentangle potential planetary signals from bright quasi-static speckles. Among them, angular differential imaging (ADI) permits potential planetary signals with a known rotation rate to be separated from instrumental speckles that are either statics or slowly variable. The method presented in this paper, called ANDROMEDA for ANgular Differential OptiMal Exoplanet Detection Algorithm is based on a maximum likelihood approach to ADI and is used to estimate the position and the flux of any point source present in the field of view. Aims. In order to optimize and experimentally validate this previously proposed method, we applied ANDROMEDA to real VLT/NaCo data. In addition to its pure detection capability, we investigated the possibility of defining simple and efficient criteria for automatic point source extraction able to support the processing of large surveys. Methods. To assess the performance of the method, we applied ANDROMEDA on VLT/NaCo data of TYC-8979-1683-1 which is surrounded by numerous bright stars and on which we added synthetic planets of known position and flux in the field. In order to accommodate the real data properties, it was necessary to develop additional pre-processing and post-processing steps to the initially proposed algorithm. We then investigated its skill in the challenging case of a well-known target, $\beta$ Pictoris, whose companion is close to the detection limit and we compared our results to those obtained by another method based on principal component analysis (PCA). Results. Application on VLT/NaCo data demonstrates the ability of ANDROMEDA to automatically detect and characterize point sources present in the image field. We end up with a robust method bringing consistent results with a sensitivity similar to the recently published algorithms, with only two parameters to be fine tuned. Moreover, the companion flux estimates are not biased by the algorithm parameters and do not require a posteriori corrections. Conclusions. ANDROMEDA is an attractive alternative to current standard image processing methods that can be readily applied to on-sky data

Bayesian methods of astronomical source extraction

We present two new source extraction methods, based on Bayesian model selection and using the Bayesian Information Criterion (BIC). The first is a source detection filter, able to simultaneously detect point sources and estimate the image background. The second is an advanced photometry technique, which measures the flux, position (to sub-pixel accuracy), local background and point spread function. We apply the source detection filter to simulated Herschel-SPIRE data and show the filter's ability to both detect point sources and also simultaneously estimate the image background. We use the photometry method to analyse a simple simulated image containing a source of unknown flux, position and point spread function; we not only accurately measure these parameters, but also determine their uncertainties (using Markov-Chain Monte Carlo sampling). The method also characterises the nature of the source (distinguishing between a point source and extended source). We demonstrate the effect of including additional prior knowledge. Prior knowledge of the point spread function increase the precision of the flux measurement, while prior knowledge of the background has onlya small impact. In the presence of higher noise levels, we show that prior positional knowledge (such as might arise from a strong detection in another waveband) allows us to accurately measure the source flux even when the source is too faint to be detected directly. These methods are incorporated in SUSSEXtractor, the source extraction pipeline for the forthcoming Akari FIS far-infrared all-sky survey. They are also implemented in a stand-alone, beta-version public tool that can be obtained at http://astronomy.sussex.ac.uk/$\sim$rss23/sourceMiner\_v0.1.2.0.tar.gzComment: Accepted for publication by ApJ (this version compiled used emulateapj.cls

Online Localization and Tracking of Multiple Moving Speakers in Reverberant Environments

We address the problem of online localization and tracking of multiple moving speakers in reverberant environments. The paper has the following contributions. We use the direct-path relative transfer function (DP-RTF), an inter-channel feature that encodes acoustic information robust against reverberation, and we propose an online algorithm well suited for estimating DP-RTFs associated with moving audio sources. Another crucial ingredient of the proposed method is its ability to properly assign DP-RTFs to audio-source directions. Towards this goal, we adopt a maximum-likelihood formulation and we propose to use an exponentiated gradient (EG) to efficiently update source-direction estimates starting from their currently available values. The problem of multiple speaker tracking is computationally intractable because the number of possible associations between observed source directions and physical speakers grows exponentially with time. We adopt a Bayesian framework and we propose a variational approximation of the posterior filtering distribution associated with multiple speaker tracking, as well as an efficient variational expectation-maximization (VEM) solver. The proposed online localization and tracking method is thoroughly evaluated using two datasets that contain recordings performed in real environments.Comment: IEEE Journal of Selected Topics in Signal Processing, 201

Improving and Assessing Planet Sensitivity of the GPI Exoplanet Survey with a Forward Model Matched Filter

We present a new matched filter algorithm for direct detection of point sources in the immediate vicinity of bright stars. The stellar Point Spread Function (PSF) is first subtracted using a Karhunen-Lo\'eve Image Processing (KLIP) algorithm with Angular and Spectral Differential Imaging (ADI and SDI). The KLIP-induced distortion of the astrophysical signal is included in the matched filter template by computing a forward model of the PSF at every position in the image. To optimize the performance of the algorithm, we conduct extensive planet injection and recovery tests and tune the exoplanet spectra template and KLIP reduction aggressiveness to maximize the Signal-to-Noise Ratio (SNR) of the recovered planets. We show that only two spectral templates are necessary to recover any young Jovian exoplanets with minimal SNR loss. We also developed a complete pipeline for the automated detection of point source candidates, the calculation of Receiver Operating Characteristics (ROC), false positives based contrast curves, and completeness contours. We process in a uniform manner more than 330 datasets from the Gemini Planet Imager Exoplanet Survey (GPIES) and assess GPI typical sensitivity as a function of the star and the hypothetical companion spectral type. This work allows for the first time a comparison of different detection algorithms at a survey scale accounting for both planet completeness and false positive rate. We show that the new forward model matched filter allows the detection of $50\%$ fainter objects than a conventional cross-correlation technique with a Gaussian PSF template for the same false positive rate.Comment: ApJ accepte

Methods for detection and characterization of signals in noisy data with the Hilbert-Huang Transform

The Hilbert-Huang Transform is a novel, adaptive approach to time series analysis that does not make assumptions about the data form. Its adaptive, local character allows the decomposition of non-stationary signals with hightime-frequency resolution but also renders it susceptible to degradation from noise. We show that complementing the HHT with techniques such as zero-phase filtering, kernel density estimation and Fourier analysis allows it to be used effectively to detect and characterize signals with low signal to noise ratio.Comment: submitted to PRD, 10 pages, 9 figures in colo