Polar shapelets

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Polar shapelets

The shapelets method for astronomical image analysis is based around the decomposition of localised objects into a series of orthogonal components with particularly convenient mathematical properties. We extend the “Cartesian shapelet” formalism from earlier work, and construct “polar shapelet” basis functions that separate an image into components with explicit rotational symmetries. This prov...

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Weak gravitational shear and flexion with polar shapelets

We derive expressions, in terms of ‘polar shapelets’, for the image distortion operations associated with weak gravitational lensing. Shear causes galaxy shapes to become elongated, and is sensitive to the second derivative of the projected gravitational potential along their line of sight; flexion bends galaxy shapes into arcs, and is sensitive to the third derivative. Polar shapelets provide ...

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Fast Shapelets: A Scalable Algorithm for Discovering Time Series Shapelets

Time series shapelets are a recent promising concept in time series data mining. Shapelets are time series snippets that can be used to classify unlabeled time series. Shapelets not only provide interpretable results, which are useful for domain experts and developers alike, but shapelet-based classifiers have been shown by several independent research groups to have superior accuracy on many d...

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Shears from shapelets

Aims. Accurate measurement of gravitational shear from images of distant galaxies is one of the most direct ways of studying the distribution of mass in the universe. We describe an implementation of a technique that is based on the shapelets formalism. Methods. The shapelets technique describes PSF and observed images in terms of Gauss-Hermite expansions (Gaussians times polynomials). It allow...

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Image Simulation with Shapelets

We present a method to simulate deep sky images, including realistic galaxy morphologies and telescope characteristics. To achieve a wide diversity of simulated galaxy morphologies, we first use the shapelets formalism to parametrize the shapes of all objects in the Hubble Deep Fields. We measure this distribution of real galaxy morphologies in shapelet parameter space, then resample it to gene...

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ژورنال

عنوان ژورنال: Monthly Notices of the Royal Astronomical Society

سال: 2005

ISSN: 0035-8711,1365-2966

DOI: 10.1111/j.1365-2966.2005.09453.x