Related papers: Maximum-likelihood detection of sources among Pois…
Linear inverse problems $A \mu = \delta$ with Poisson noise and non-negative unknown $\mu \geq 0$ are ubiquitous in applications, for instance in Positron Emission Tomography (PET) in medical imaging. The associated maximum likelihood…
We present the X-ray pipeline developed for the purpose of the cluster search in the XMM-LSS survey. It is based on a two-stage procedure via a dedicated handling of the Poisson nature of the signal: (1) source detection on multi-resolution…
The problem of maximum likelihood (ML) detection in training-assisted single-input multiple-output (SIMO) systems with phase noise impairments is studied for two different scenarios, i.e. the case when the channel is deterministic and known…
We describe the method used to detect sources for the Herschel-ATLAS survey. The method is to filter the individual bands using a matched filter, based on the point-spread function (PSF) and confusion noise, and then form the inverse…
This article considers the detection of point sources in two dimensional astronomical images. The detection scheme we propose is based on peak statistics. We discuss the example of the detection of far galaxies in Cosmic Microwave…
Point-source contamination in high-precision Cosmic Microwave Background (CMB) maps severely affects the precision of cosmological parameter estimates. Among the methods that have been proposed for source detection, wavelet techniques based…
We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
Stochastic Maximum Likelihood (SML) is a popular direction of arrival (DOA) estimation technique in array signal processing. It is a parametric method that jointly estimates signal and instrument noise by maximum likelihood, achieving…
In Positron Emission Tomography, movement leads to blurry reconstructions when not accounted for. Whether known a priori or estimated jointly to reconstruction, motion models are increasingly defined in continuum rather that in discrete,…
The article addresses the problem of detecting presence and location of a small low emission source inside of an object, when the background noise dominates. This problem arises, for instance, in some homeland security applications. The…
The detection and quantification of narrow emission lines in X-ray spectra is a challenging statistical task. The Poisson nature of the photon counts leads to local random fluctuations in the observed spectrum that often results in excess…
We develop two algorithms, based on maximum likelihood (ML) inference, for estimating the parameters of polarized radio sources which emit at a single rotation measure (RM), e.g., pulsars. These algorithms incorporate the flux density…
In the context of Independent Component Analysis (ICA), noisy mixtures pose a dilemma regarding the desired objective. On one hand, a "maximally separating" solution, providing the minimal attainable Interference-to-Source-Ratio (ISR),…
The reliability of detecting source variability in sparsely and irregularly sampled X-ray light curves is investigated. This is motivated by the unprecedented survey capabilities of eROSITA onboard SRG, providing light curves for many…
We present a new source separation method which maximizes the likelihood of a model of noisy mixtures of stationary, possibly Gaussian, independent components. The method has been devised to address the problem of imaging CMB anisotropies.…
Likelihood functions evaluated using particle filters are typically noisy, computationally expensive, and non-differentiable due to Monte Carlo variability. These characteristics make conventional optimization methods difficult to apply…
Astronomical images in the Poisson regime are typically characterized by a spatially varying cosmic background, large variety of source morphologies and intensities, data incompleteness, steep gradients in the data, and few photon counts…
The method of maximum likelihood estimation (MLE) is a widely used statistical approach for estimating the values of one or more unknown parameters of a probabilistic model based on observed data. In this tutorial, I briefly review the…
The maximum likelihood estimator for CMB map-making is optimal and unbiased as long as the data model is correct, but in practice it rarely is, with model errors including sub-pixel structure and instrumental problems like time-variable…
The matched filter (MF) represents one of the main tools to detect signals from known sources embedded in the noise. In the Gaussian case the noise is assumed to be the realization of a Gaussian random field (GRF). The most important…