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A short note on compressed sensing with partially known signal support

Abstract: This short note studies a variation of the compressed sensing paradigm introduced recently by Vaswani et al., i.e., the recovery of sparse signals from a certain number of linear measurements when the signal support is partially known.
2010 Signal Processing
DOI DIAL arXiv

Compressed sensing imaging techniques for radio interferometry

Abstract: Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or compressible signals.
2009 Royal Astronomical Society. Monthly Notices
DOI DIAL arXiv

A geometrical study of matching pursuit parametrization

Abstract: This paper studies the effect of discretizing the parametrization of a dictionary used for matching pursuit (MP) decompositions of signals. Our approach relies con viewing the continuously parametrized dictionary as an embedded manifold in the signal space on which the tools of differential, (Riemannian) geometry can be applied.
2008 IEEE Transactions on Signal Processing
Code DOI DIAL arXiv

Fast spin ±2 spherical harmonics transforms and application in cosmology

Abstract: A fast and exact algorithm is developed for the spin \(\pm2\) spherical harmonics transforms on equi-angular pixelizations on the sphere. It is based on the Driscoll and Healy fast scalar spherical harmonics transform.
2007 Journal of Computational Physics
Cite DOI DIAL arXiv

Multiselective pyramidal decomposition of images: Wavelets with adaptive angular selectivity

Abstract: Many techniques have been devised these last ten years to add an appropriate directionality concept in decompositions of images from the specific transformations of a small set of atomic functions.
2007 International Journal of Wavelets, Multiresolution and Information Processing
PDF DOI DIAL

Fast directional correlation on the sphere with steerable filters

Abstract: A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order \(O(L^5)\), where \(2L\) stands for the square-root of the number of sampling points on the sphere, also setting a band limit L for the signals and filters considered.
2006 Astrophys. J. 652, 820
Cite DOI arXiv DIAL

Correspondence principle between spherical and Euclidean wavelets

Abstract: Wavelets on the sphere are reintroduced and further developed independently of the original group theoretic formalism, in an equivalent, but more straightforward approach. These developments are motivated by the interest of the scale-space analysis of the cosmic microwave background (CMB) anisotropies on the sky.
2005 The Astrophysical Journal : an international review of astronomy and astronomical physics
DIAL arXiv

Stereographic wavelet frames on the sphere

Abstract: In this paper we exploit the continuous wavelet transform (CWT) on the two-dimensional sphere S-2, introduced previously by two of us, to build associated discrete wavelet frames. We first explore half-continuous frames, i.
2005 Applied and Computational Harmonic Analysis
PDF DOI DIAL

Wavelet spectrum analysis of EIT/SOHO images

Abstract: The extreme ultraviolet imaging telescope (EIT) of SOHO offers a unique record of the solar atmosphere for its sampling in temperature, field of view, resolution, duration, and cadence. To investigate globally and locally its topology and evolution during the solar cycle, we consider a multi-scale approach, and more precisely we use the wavelet spectrum.
2005 Solar Physics : a journal for solar and solar-stellar research and the study of solar terrestrial physics
DOI DIAL

Application of the 2-D wavelet transform to astrophysical images

Abstract: The 2-D continuous wavelet transform has been applied to a number of problems in astrophysics. We survey quickly some of these, then focus on two new applications. The first one is the automatic detection and analysis of special objects from the solar corona in the data taken by the EIT instrument aboard the SoHO satellite.
2002 Physicalia Magazine
PDF DIAL