Two compressive sensing inspired approaches for the solution of non-linear inverse scattering problems are introduced and discussed. Differently from the sparsity promoting approaches proposed in most of the papers published in the literature, the two methods here tackle the problem in its full non-linearity, by adopting a contrast source inversion scheme. In the first approach, the 11-norm of the unknown is added as a weighted penalty term to the contrast source cost functional. The second, and (to the best of our knowledge) completely original, approach enforces sparsity by constraining the solution of the non-linear problem into a convex set defined by the 11 -norm of the unknown. A numerical assessment against a widely used benchmark example (the “Austria” profile) is given to assess the capabilities of the proposed approaches. Notably, the two approaches can be applied to any kind of basis functions and they can successfully tackle both reduced number of data (with respect to Nyquist sampling) and/or overcomplete dictionaries.

Non linear inverse scattering via sparsity regularized Contrast Source Inversion

M. Bevacqua;Isernia T
2017

Abstract

Two compressive sensing inspired approaches for the solution of non-linear inverse scattering problems are introduced and discussed. Differently from the sparsity promoting approaches proposed in most of the papers published in the literature, the two methods here tackle the problem in its full non-linearity, by adopting a contrast source inversion scheme. In the first approach, the 11-norm of the unknown is added as a weighted penalty term to the contrast source cost functional. The second, and (to the best of our knowledge) completely original, approach enforces sparsity by constraining the solution of the non-linear problem into a convex set defined by the 11 -norm of the unknown. A numerical assessment against a widely used benchmark example (the “Austria” profile) is given to assess the capabilities of the proposed approaches. Notably, the two approaches can be applied to any kind of basis functions and they can successfully tackle both reduced number of data (with respect to Nyquist sampling) and/or overcomplete dictionaries.
File in questo prodotto:
File Dimensione Formato  
Bevacqua_2017_TCI_Nonlinear_Post.pdf

accesso aperto

Tipologia: Documento in Post-print
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 608.71 kB
Formato Adobe PDF
608.71 kB Adobe PDF Visualizza/Apri
Bevacqua_2017_TCI_Nonlinear_Editorial.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 630.23 kB
Formato Adobe PDF
630.23 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS 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: http://hdl.handle.net/20.500.12318/544
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 28
social impact