Compression of astronomical images by means of polyspline wavelets
by
Ognyan Kounchev
Institute of Mathematics and Informatics
Coauthors: Damyan Kalaglarsky, Space Research Institute

We present a new approach to compression of images which is based on a new multivariate spline paradigm, see O. Kounchev "Multivariate Polysplines. Applications to Numerical and Wavelet Analysis", Academic Press, 2001. An essential property of the polyspline wavelets is that their support is elongated - this is important for the sparseness of the representation of two-dimensional images. Not less important is that they enjoy many beautiful algebraic properties embedding them in the framework of the Multiresolution Analysis. One should compare our alternative approach to data compression with other paradigms, as the curvelets of E. Candes, D. Donoho, New tight frames of curvelets and optimal representation of objects with C^2 singularities, Comm. Pure Appl. Mathematics, 2004, and with another recent paradigm in a similar direction, see E. Le Pennec, S. Mallat, Sparse geometric image representations with bandelets, preprint, submitted, 2003. Let us note some recent applications of curvelets to astronomical data representation with which we will make a numerical comparison, see J.L. Starck, D.L. Donoho and E.J. Candès, Astronomical Image Representation by the Curvelet Transform, http://www-stat.stanford.edu/~beamlab/aa_cur02.pdf

Date received: January 17, 2005