# Soft Shrinkage Thresholding Algorithm for Nonlinear Microwave Imaging

Abstract : In this paper, we analyze a sparse nonlinear inverse scattering problem arising in microwave imaging and numerically solved it for retrieving dielectric contrast from measured fields. In sparsity reconstruction, contrast profiles are a priori assumed to be sparse with respect to a certain base. We proposed an approach which is motivated by a Tikhonov functional incorporating a sparsity promoting $l_{1}$-penalty term. The proposed iterative algorithm of soft shrinkage type enforces the sparsity constraint at each nonlinear iteration. The scheme produces sharp and good reconstruction of dielectric profiles in sparse domains by adapting Barzilai and Borwein (BB) step size selection criteria and positivity by maintaining its convergence during the reconstruction.
Document type :
Conference papers

https://hal-centralesupelec.archives-ouvertes.fr/hal-01341979
Contributor : Marc Lambert <>
Submitted on : Tuesday, July 5, 2016 - 11:20:16 AM
Last modification on : Wednesday, January 13, 2021 - 1:52:02 PM

### Identifiers

• HAL Id : hal-01341979, version 1

### Citation

Hidayet Zaimaga, Marc Lambert. Soft Shrinkage Thresholding Algorithm for Nonlinear Microwave Imaging. International Workshop on New Computational Methods for Inverse Problems (NCMIP 2016), May 2016, Cachan, France. 4 p. ⟨hal-01341979⟩

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