Microwave imaging: Reconstructions from experimental data using conjugate gradient and enhancement by edge-preserving regularization

Lobel, P.; Pichot, Christian; Blanc‐Féraud, Laure; Barlaud, Michel

doi:10.1002/(sici)1098-1098(1997)8:4<337::aid-ima1>3.0.co;2-b

Cited by 17 publications

(11 citation statements)

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“…Here, • stands for the regularization parameter, and 4( ) is a function of the gradient of the reconstructed image and is called the edge-preserving regularization function. Many researchers have proposed a variety of functions to be f( ) [Herbert and Leahy, 1989;Lange, 1990] and derived satisfying results for inverse problems [Bouman and Sauer, 1993;Delaney and Breslet, 1998], including the inverse scattering problem itself [Lobel et al, 1997].…”

Section: Edge-preserving Regularized Formulationmentioning

confidence: 99%

A neural network approach to the microwave inverse scattering problem with edge‐preserving regularization

Gong¹,

Wang²

2001

Radio Science

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Abstract. A neural network approach to the inverse scattering problem for microwave tomographic reconstruction is presented. Although the technique of microwave tomography has been developed for more than two decades, it is still in its infancy in that it is necessary to solve the inverse scattering problem, which is well known as an ill-posed and nonlinear problem and therefore difficult to deal with. To improve the inherent ill-posedness of the problem, good regularization procedures are required. In this paper, an edge-preserving regularization is proposed with a set of line processes to preserve the edge of the reconstructed image. Since the unknown dielectric permittivities are continuous complex variables and the line processes are binary variables, an augmented Hopfield network is applied to the mixed-variable optimization problem. With this method, a priori knowledge can be conveniently incorporated into the optimization process, and inversions of large matrices are avoided. A numerical example of a simple model illuminated by the transverse magnetic incident waves is reported, and the advantages and limitations of the method are discussed. IntroductionAccording the internal characteristics of objects or media and their responses to the incidence of electromagnetic wave to get the properties of the scattering field is called a direct scattering problem. Here, the word "scattering" is a generalized concept, which includes transmission, reflection, refraction, diffraction, and scattering. On the contrary, when the characteristics of objects are unknown, the problem to obtain them in terms of the scattering properties detected by certain devices outside of the objects is called the inverse scattering problem.There are various kinds of electromagnetic waves according to their different frequencies. When the incident radiation comes from microwave, the inverse scattering problem is the so-called microwave tomography, which reconstructs the internal complex permittivity tompographic image of the object from the scattered near-field measurements. The real part of complex permittivity is proportional to the dielectric . Thus it will be competitive with these sophisticated diagnostic methods or be applied as a complementary method. However, microwave tomography is quite difficult to develop to its full potential because the inverse scattering problem is nonlinear and ill-posed. In the sense of Hadamard, ill-posedness means that the solutions of problems cannot satisfy existence, uniqueness, and stability simultaneously.As we all know, if the frequency of the incident wave is high, the relation between the measured data and the internal characteristics of the object is linear. For example, X rays travel along straight lines without diffracting in the object, and then it is relatively easy to

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Section: Edge-preserving Regularized Formulationmentioning

confidence: 99%

A neural network approach to the microwave inverse scattering problem with edge‐preserving regularization

Gong¹,

Wang²

2001

Radio Science

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“…Different approaches exist for solving this ill-posed nonlinear inverse problem [1][2][3][4][5][6]. In [1], edge preserving regularization was imposed on the real and imaginary part of the complex permittivity separately. Multiplicative smoothing (MS) [4] applies Tikhonov regularization in a multiplicative fashion.…”

Section: Introductionmentioning

confidence: 99%

Quantitative microwave tomography from sparse measurements using a robust huber regularizer

Bai

Pižurica

Loocke

et al. 2012

2012 19th IEEE International Conference on Image Processing

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In statistical theory, the Huber function yields robust estimations reducing the effect of outliers. In this paper, we employ the Huber function as regularization in a challenging inverse problem: quantitative microwave imaging. Quantitative microwave tomography aims at estimating the permittivity profile of a scattering object based on measured scattered fields, which is a nonlinear, ill-posed inverse problem. The results on 3D data sets are encouraging: the reconstruction error is reduced and the permittivity profile can be estimated from fewer measurements compared to state-of-the art inversion procedures.

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“…Conjugate gradients is often used in this type of restoration problem [9], [10]. However, conjugate gradients does not exploit the fact that the edges are sparse and the problem is mostly shift-invariant.…”

Section: Introductionmentioning

confidence: 99%

Efficient Huber-Markov Edge-Preserving Image Restoration

Pan

Reeves

2006

IEEE Trans. on Image Process.

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The regularization of the least-squares criterion is an effective approach in image restoration to reduce noise amplification. To avoid the smoothing of edges, edge-preserving regularization using a Gaussian Markov random field (GMRF) model is often used to allow realistic edge modeling and provide stable maximum a posteriori (MAP) solutions. However, this approach is computationally demanding because the introduction of a non-Gaussian image prior makes the restoration problem shift-variant. In this case, a direct solution using fast Fourier transforms (FFTs) is not possible, even when the blurring is shift-invariant. We consider a class of edge-preserving GMRF functions that are convex and have nonquadratic regions that impose less smoothing on edges. We propose a decomposition-enabled edge-preserving image restoration algorithm for maximizing the likelihood function. By decomposing the problem into two subproblems, with one shift-invariant and the other shift-variant, our algorithm exploits the sparsity of edges to define an FFT-based iteration that requires few iterations and is guaranteed to converge to the MAP estimate.

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Microwave imaging: Reconstructions from experimental data using conjugate gradient and enhancement by edge-preserving regularization

Cited by 17 publications

References 0 publications

A neural network approach to the microwave inverse scattering problem with edge‐preserving regularization

A neural network approach to the microwave inverse scattering problem with edge‐preserving regularization

Quantitative microwave tomography from sparse measurements using a robust huber regularizer

Efficient Huber-Markov Edge-Preserving Image Restoration

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