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We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of unknown shapes in the case of nonparametric noise. The noise density is unknown and can be heavy-tailed. The objects of interest have unknown varying intensities. No boundary shape constraints are imposed on the objects, only a set of weak bulk conditions is required. We view the object detection problem as a multiple hypothesis testing for discrete statistical inverse problems. We present an algorithm that allows to detect greyscale objects of various shapes in noisy images. We prove results on consistency and algorithmic complexity of our procedures. Applications to cryo-electron microscopy are presented.
We present a machine learning model for the analysis of randomly generated discrete signals, which we model as the points of a homogeneous or inhomogeneous, compound Poisson point process. Like the wavelet scattering transform introduced by S. Mallat
Spatial statistics is an area of study devoted to the statistical analysis of data that have a spatial label associated with them. Geographers often refer to the location information associated with the attribute information, whose study defines a re
Data competitions rely on real-time leaderboards to rank competitor entries and stimulate algorithm improvement. While such competitions have become quite popular and prevalent, particularly in supervised learning formats, their implementations by th
In this study, we begin a comprehensive characterisation of temperature extremes in Ireland for the period 1981-2010. We produce return levels of anomalies of daily maximum temperature extremes for an area over Ireland, for the 30-year period 1981-20
Road traffic casualties represent a hidden global epidemic, demanding evidence-based interventions. This paper demonstrates a network lattice approach for identifying road segments of particular concern, based on a case study of a major city (Leeds,