Astronomical image representation by the curvelet transform

¹ DAPNIA/SEDI-SAP, Service d'Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
² Department of Statistics, Stanford University, Sequoia Hall, Stanford, CA 94305, USA
³ Department of Applied Mathematics, Mail Code 217-50, California Institute of Technology, Pasadena, CA 91125, USA

Corresponding author: J. L. Starck, jstarck@cea.fr

Received: 12 April 2002
Accepted: 29 October 2002

Abstract

We outline digital implementations of two newly developed multiscale representation systems, namely, the ridgelet and curvelet transforms. We apply these digital transforms to the problem of restoring an image from noisy data and compare our results with those obtained via well established methods based on the thresholding of wavelet coefficients. We show that the curvelet transform allows us also to well enhance elongated features contained in the data. Finally, we describe the Morphological Component Analysis, which consists in separating features in an image which do not present the same morphological characteristics. A range of examples illustrates the results.