Telescopes based on the imaging atmospheric Cherenkov technique (IACTs) detect images of the atmospheric showers generated by gamma rays and cosmic rays as they are absorbed by the atmosphere. The much more frequent cosmic-ray events form the main background when looking for gamma-ray sources, and therefore IACT sensitivity is significantly driven by the capability to distinguish between these two types of events. Supervised learning algorithms, like random forests and boosted decision trees, have been shown to effectively classify IACT events. In this contribution we present results from exploratory work using deep learning as an event classification method for the Cherenkov Telescope Array (CTA). CTA, conceived as an array of tens of IACTs, is an international project for a next-generation ground-based gamma-ray observatory, aiming to improve on the sensitivity of current-generation experiments by an order of magnitude and provide energy coverage from 20 GeV to more than 300 TeV.
Schwarzschild-Couder Telescope, Optical System Figure 1: Left: Ray-tracing simulation of the Schwarzschild-Couder telescope optical system, which includes the primary and secondary mirrors as well as their respective baffles and the focal plane. Right: CAD model of the full size prototype Schwarzschild-Couder telescope (pSCT) under construction at the Fred Lawrence Whipple Observatory in Arizona.
A coarse-to-fine data fitting algorithm for irregularly spaced data based on boundary-adapted adaptive tensor-product semi-orthogonal spline-wavelets has been proposed in Castaño and Kunoth, 2003. This method has been extended in Castaño and Kunoth, 2005 to include regularization in terms of Sobolev and Besov norms. In this paper, we develop within this least-squares approach some statistical robust estimators to handle outliers in the data. Our wavelet scheme yields a numerically fast and reliable way to detect outliers.
In [6], an adaptive method to approximate unorganized clouds of points by smooth surfaces based on wavelets has been described. The general fitting algorithm operates on a coarse-tofine basis. It selects on each refinement level in a first step a reduced number of wavelets which are appropriate to represent the features of the data set. In a second step, the fitting surface is constructed as the linear combination of the wavelets which minimizes the distance to the data in a least squares sense. This is followed by a thresholding procedure on the wavelet coefficients to discard those which are too small to contribute much to the surface representation.In this paper, we firstly generalize this strategy to a classically regularized least squares functional by adding a Sobolev norm, taking advantage of the capability of wavelets to characterize Sobolev spaces of even fractional order. After recalling the usual cross-validation technique to determine the involved smoothing parameters, some examples of fitting severely irregularly distributed data, synthetically produced and of geophysical origin, are presented. In order to reduce computational costs, we then introduce a multilevel generalized crossvalidation technique which goes beyond the Sobolev formulation and exploits the hierarchical setting based on wavelets. We illustrate the performance of the new strategy on some geophysical data.
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