In this paper we consider the deconvolution of high contrast images consisting of very bright stars (point component) and smooth structures underlying the stars (diffuse component). A typical case is a weak diffuse jet line emission superimposed to a strong stellar continuum. In order to reconstruct the diffuse component, the original object can be regarded as the sum of these two components. When the position of the point sources is known, a regularization term can be introduced for the second component. An approximation of the original object can be obtained by solving a reduced variational problem whose unknowns are the intensities of the stars and the diffuse component. We analyze this problem when the detected image is corrupted by Poisson noise and Tikhonov-like regularization is used, giving conditions for the existence and the uniqueness of the solution. Furthermore, since only an overestimation of the regularization parameter is available, we propose to solve the variational problem by inexact Bregman iteration combined with a Scaled Gradient Projection method (SGP). Numerical simulations show that the images obtained with this approach enable us to reconstruct the original intensity distribution around the point source with satisfactory accuracy.

Reprint of Inexact Bregman iteration for deconvolution of superimposed extended and point sources / A. Benfenati, V. Ruggiero. - In: COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION. - ISSN 1007-5704. - 21:1-3(2015 Apr), pp. 210-224. ((Intervento presentato al convegno International conference: Numerical computations: Theory and Algorithms (NUMTA) tenutosi a Falerna (CZ, Italy) nel 2013 [10.1016/j.cnsns.2014.10.020].

Reprint of Inexact Bregman iteration for deconvolution of superimposed extended and point sources

A. Benfenati;
2015

Abstract

In this paper we consider the deconvolution of high contrast images consisting of very bright stars (point component) and smooth structures underlying the stars (diffuse component). A typical case is a weak diffuse jet line emission superimposed to a strong stellar continuum. In order to reconstruct the diffuse component, the original object can be regarded as the sum of these two components. When the position of the point sources is known, a regularization term can be introduced for the second component. An approximation of the original object can be obtained by solving a reduced variational problem whose unknowns are the intensities of the stars and the diffuse component. We analyze this problem when the detected image is corrupted by Poisson noise and Tikhonov-like regularization is used, giving conditions for the existence and the uniqueness of the solution. Furthermore, since only an overestimation of the regularization parameter is available, we propose to solve the variational problem by inexact Bregman iteration combined with a Scaled Gradient Projection method (SGP). Numerical simulations show that the images obtained with this approach enable us to reconstruct the original intensity distribution around the point source with satisfactory accuracy.
High contrast imaging; Inexact Bregman iteration; Poisson noise; Scaled Gradient Projection method
Settore MAT/08 - Analisi Numerica
19-ott-2014
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/660099
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