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 procedure 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.

Inexact Bregman iteration for deconvolution of superimposed extended and point sources

RUGGIERO, Valeria
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 procedure 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.
2015
Benfenati, Alessandro; Ruggiero, Valeria
File in questo prodotto:
File Dimensione Formato  
1-s2.0-S1007570414003086-main.pdf

solo gestori archivio

Tipologia: Full text (versione editoriale)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 866.64 kB
Formato Adobe PDF
866.64 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2028212
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 9
  • ???jsp.display-item.citation.isi??? 10
social impact