Sparsity Regularized Nonlinear Inversion for Microwave Imaging

Taskin, Ulas; Ozdemir, Özgür

doi:10.1109/lgrs.2017.2757087

Cited by 8 publications

(7 citation statements)

References 23 publications

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“…The same arguments of (18) and (19) apply to the inexact Newton approach too, leading to a new version of the inner iterations (13) in Banach spaces, involving the duality maps J Y r and J X * r * . Specifically, Step III of Algorithm 1 now reads: (III) INNER STEP: Find a (regularized) solution of the linear Equation (11) by means of an iterative minimization, with respect to h, of the n-th residual 1 2…”

Section: Extension To Banach Spacesmentioning

confidence: 99%

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Microwave Imaging by Means of Lebesgue-Space Inversion: An Overview

et al. 2019

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An overview of the recent advancements in the development of microwave imaging procedures based on the exploitation of the regularization theory in Lebesgue spaces is reported in this paper. Such inversion schemes have been found to provide accurate results in several microwave imaging scenarios, thanks to the different geometrical properties that Lebesgue spaces can exhibit with respect to the more classical Hilbert ones. Moreover, the recent extension to the more general case of variable-exponent Lebesgue spaces is also addressed. Experimental results involving reference data are shown for supporting the theoretical description of the approaches.

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Section: Extension To Banach Spacesmentioning

confidence: 99%

“…Consequently, proper inversion procedures need to be devised, to consider both these theoretical problems. To this end, several approaches have been proposed in the last years [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. They have been investigated in the context of Hilbert spaces, in most cases.…”

Section: Introductionmentioning

confidence: 99%

Microwave Imaging by Means of Lebesgue-Space Inversion: An Overview

et al. 2019

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“…In equation ( 16), two hyperparameters λ 1 and λ 2 have to be determined. Following [23], they are chosen adaptively according to the magnitudes of wavelet coefficients, and updated at each iteration. Let us denote P i% ( ) the i-th percentile of an vector, λ 1 is set to P q% (β) and λ 2 is associated with λ 1 where the ratio of λ 2 to λ 1 is set to P q% ( z g 2,1 ).…”

Section: Contrast Source Inversionmentioning

confidence: 99%

“…Sparsity has been widely investigated and incorporated within classical computational methods in order to solve ISPs [22]. In [23], the fast iterative shrinkage-thresholding algorithm (FISTA) [24] is combined with a modified gradient method (MGM) to enforce the sparsity in both non-sparse and sparse domain, where the discrete wavelet transform (DWT) [25] is employed to reach a sparse representation of the unknown. In [23], an iterative algorithm incorporating a Tikhonov functional with a sparsity promoting 1 term is proposed, which allows a sharp reconstruction in the sparse domain.…”

Section: Introductionmentioning

confidence: 99%

“…In [23], the fast iterative shrinkage-thresholding algorithm (FISTA) [24] is combined with a modified gradient method (MGM) to enforce the sparsity in both non-sparse and sparse domain, where the discrete wavelet transform (DWT) [25] is employed to reach a sparse representation of the unknown. In [23], an iterative algorithm incorporating a Tikhonov functional with a sparsity promoting 1 term is proposed, which allows a sharp reconstruction in the sparse domain. Iterative shrinkage thresholding algorithm (ISTA) [24] is implemented within the framework of a boundary integral method in [26] to solve the optimization problem with zeroth/first-norm penalty term.…”

Section: Introductionmentioning

confidence: 99%

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Group Sparsity Penalized Contrast Source Solution Method for 2-D Non-Linear Inverse Scattering

Zhang

Lambert

Fraysse

et al. 2022

IEEE Open J. Antennas Propag.

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A group sparsity penalized CSI in the wavelet domain is proposed to alleviate ill-posedness within the framework of a contrast-source inversion (CSI) method. It is then applied to the retrieval of a large inhomogeneous dielectric scatterer from time-harmonic single-frequency data. As dependency exists between wavelet coefficients at different scales, referred to as the parent-child relationship, it enables to yield the wavelet quad tree structure. Therefore, wavelet coefficients can be regarded not only as pixel-wise sparse, but also group-wise sparse. Focus is put on using the dual-tree complex wavelet transform (CWT) to properly achieve the sought-after group-wise sparse representation of the spatial distribution of the contrast. It provides a 2,1 norm which is added to the standard cost functional to enforce group sparsity onto the wavelet coefficients of the spatially-varying contrast. The replication strategy is combined with the proximal method in order to solve the overlapping group penalized problem. Simulations from synthetic data in different configurations with in particular different signal-to-noise ratios illustrate pros and cons of the proposed method. The approach is shown to overcome the standard CSI method in demanding situations. Comparisons with the discrete wavelet transform (DWT) as usually performed and the 1 norm confirm the advantage of the proposed methodology.

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Complex Permittivity Retrieval Approach With Radar Enhanced Contrast Source Inversion for Microwave Nondestructive Road Evaluation

Suzuki,

Nakamura,

Kidera

2024

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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An experimental investigation of microwave quantitative imaging of nondestructive testing applications for concrete road structures is presented. A radar prior-based contrast source inversion (CSI) scheme is introduced to achieve an accurate reconstruction for target shape and dielectric property by applying the promising radar approach-range points migration (RPM). Moreover, to address the local optimum problem, we introduce an appropriate initial estimate for complex permittivity that focuses on the cost function of the CSI. A numerical and real data from an actual concrete road model, where a thin-layer water-filled cavity is buried into the boundary area between the asphalt and the concrete floorboard, show that our proposed approach improves reconstruction accuracy for permittivity and conductivity in a real nondestructive testing model.

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Sparsity Regularized Nonlinear Inversion for Microwave Imaging

Cited by 8 publications

References 23 publications

Microwave Imaging by Means of Lebesgue-Space Inversion: An Overview

Microwave Imaging by Means of Lebesgue-Space Inversion: An Overview

Group Sparsity Penalized Contrast Source Solution Method for 2-D Non-Linear Inverse Scattering

Complex Permittivity Retrieval Approach With Radar Enhanced Contrast Source Inversion for Microwave Nondestructive Road Evaluation

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