Two approaches for the simultaneous separation and deblurring; application to astrophysical data. (Deux méthodes de déconvolution et séparation simultanées; application à la reconstruction des amas de galaxies.) (French. English summary) Zbl 1245.94013

Anthoine, S.; Pierpaoli, E.; Daubechies, I.

Trait. Signal 23, No. 5-6, 439-447 (2006).

Summary: Two approaches are presented to solve the problem of simultaneously deconvolving and separating mixtures of components. The first one uses a statistical description of the wavelet coefficients of the signals. The second one consists in minimizing a variational functional. Both methods are applied to the reconstruction of Sunyaev-Zel’dovich galaxy clusters from cosmic microwave background experiments such as ACT. We find that both methods, when tuned, yield similar results and that the reconstruction of intense clusters is substantially improved when their non-Gaussianity is taken into account.

MSC:

94A08	Image processing (compression, reconstruction, etc.) in information and communication theory
65T60	Numerical methods for wavelets
68T10	Pattern recognition, speech recognition
85-04	Software, source code, etc. for problems pertaining to astronomy and astrophysics

Keywords:

signal estimation; separation; deconvolution; statistical approach; variational approach; wavelets; astrophysics