Abstract
This paper considers the microwave imaging reconstruction problem, based on additive penalization and gradient-based optimization. Each evaluation of the cost function and of its gradient requires the resolution of as many high-dimensional linear systems as the number of incident fields, which represents a large amount of computations. Since all such systems involve the same matrix, we propose a block inversion strategy, based on the block-biconjugate gradient stabilized (BiCGStab) algorithm, with efficient implementations specific to the microwave imaging context. Numerical experiments performed on synthetic data and on real measurements show that savings in computing time can reach a factor of two compared to the standard, sequential, BiCGStab implementation. Improvements brought by the block approach are even more important for the most difficult reconstruction problems, that is, with high-frequency illuminations and/or highly contrasted objects. The proposed reconstruction strategy is shown to achieve satisfactory estimates for objects of the Fresnel database, even on the most contrasted ones.
Highlights
Microwave imaging aims at estimating the dielectric properties of objects illuminated by incident electromagnetic fields [1]
The solution to the 3D forward problem corresponding to the experimental setup presented in Section 4.1 was computed with both BiCGStab and block-BiCGStab algorithms
The results reported in Sections 4.3.1 and 4.3.2 suggest that block-BiCGStab is best suited for the resolution of difficult problems, i.e., involving large and/or highly contrasted objects
Summary
Microwave imaging aims at estimating the dielectric properties (permittivity and conductivity) of objects illuminated by incident electromagnetic fields [1]. Previous works based on multiplicative [33] or additive [13], edge-preserving or sparsity-enhancing [41], regularization fall within this category All these methods rely on repeated computations of forward scattering problems. We propose a reconstruction procedure based on additive penalization, where the evaluation of both the cost function and its gradient are performed with a dedicated block-BiCGStab implementation. Specific tunings of the block-BiCGStab algorithm are discussed, and the overall efficiency of the inversion method is evaluated as a function of the problem difficulty (illuminating frequency and contrast).
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