Direct Sampling Method for Diffusive Optical Tomography

Chow, Yat Tin; Liu, Keji; Zou, Jun

doi:10.1137/14097519x

Cited by 49 publications

(46 citation statements)

References 34 publications

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“…This new DSM is essentially different from the existing DSMs that have been developed, e.g., in [11,12,19,20,21,23], for recovering the stationary inclusions; it has several novel features and brings the family of DSMs to a new stage of development. First of all, our new family of probing functions in this work involves high-order derivatives of the fundamental solutions inside the domain \Omega , which is completely different from those generated by monopoles/dipoles/multipoles in our previous works and therefore much easier to compute.…”

mentioning

confidence: 95%

“…This index function has been shown to be a very effective tool for reconstructing extended scatterers in two-and three-dimensional scattering media with a limited number of incident plane waves. It was later extended to various other coefficient determination inverse problems, such as electrical impedance tomography (EIT) [12], diffusive optical tomography (DOT) [11], and the electromagnetic inverse scattering problem [19]. In each of the aforementioned tomographies, a family of probing functions is introduced and an index function is defined as a dual product between the observed data and the probing function under an appropriate choice of Sobolev scale.…”

mentioning

confidence: 99%

“…The evaluation of the index function is very efficient computationally, and the images obtained from the index functions are proven to be effective in locating inhomogeneous inclusions. For more details about the existing DSMs for locating stationary inhomogeneous inclusions, we refer the reader to [2,11,12,19,20,21,23].…”

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confidence: 99%

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A Time-Dependent Direct Sampling Method for Recovering Moving Potentials in a Heat Equation

Chow¹,

Zou²

2018

SIAM J. Sci. Comput.

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We are concerned with a numerical reconstruction of the moving potential/absorption coefficient in a heat conduction process when only a single set of boundary measurements of the thermal reflection is available. We propose an efficient direct sampling method (DSM) to locate moving extended objects, represented by time-dependent potentials in a heat equation, and track the trajectories of the moving objects. This appears to be the first DSM for recovering and tracking moving inhomogeneous inclusions in a time-dependent PDE system. Our new method is essentially different from the existing DSMs for solving various stationary or time-harmonic inverse problems but still preserves several important features: it is robust against the noise in the data, easy to implement, and inexpensive computationally. Mathematical justifications are provided to verify the validity of this new method, and insightful mathematical analysis is performed to understand the behavior of the key probing functions proposed. Numerical experiments are presented to demonstrate the effectiveness and efficiency of the method. The DSM provides a new promising numerical strategy for the ill-posed inverse problem of recovering time-dependent moving inhomogeneous media.

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confidence: 95%

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confidence: 99%

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A Time-Dependent Direct Sampling Method for Recovering Moving Potentials in a Heat Equation

Chow¹,

Zou²

2018

SIAM J. Sci. Comput.

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“…Recently, various non-iterative techniques have been investigated, including MUltiple SIgnal classification (MUSIC) [27,28,29], direct-sampling method [30,31,32], linear-sampling method [33,34,35], and topological derivatives [36,37,38]. Subspace and Kirchhoff migrations are also known as non-iterative techniques in inverse scattering problem.…”

Section: Introductionmentioning

confidence: 99%

Real-time microwave imaging of unknown anomalies via scattering matrix

Park

2019

Mechanical Systems and Signal Processing

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We consider an inverse scattering problem to identify the locations or shapes of unknown anomalies from scattering parameter data collected by a small number of dipole antennas. Most of researches does not considered the influence of dipole antennas but in the experimental simulation, they are significantly affect to the identification of anomalies. Moreover, opposite to the theoretical results, it is impossible to handle scattering parameter data when the locations of the transducer and receiver are the same in real-world application. Motivated by this, we design an imaging function with and without diagonal elements of the so-called scattering matrix. This concept is based on the Born approximation and the physical interpretation of the measurement data when the locations of the transducer and receiver are the same and different. We carefully explore the mathematical structures of traditional and proposed imaging functions by finding relationships with the infinite series of Bessel functions of integer order. The explored structures reveal certain properties of imaging functions and show why the proposed method is better than the traditional approach. We present the experimental results for small and extended anomalies using synthetic and real data at several angular frequencies to demonstrate the effectiveness of our technique.

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“…Furthermore, it requires only a few (one or two) incident fields and does not requires additional operations (e.g., singular value decomposition, solving adjoint problems or ill-posed integral equations, etc.). Due to this reason, it applied to many inverse scattering problems [6,5,1,2,3].…”

Section: Introductionmentioning

confidence: 99%

Direct sampling method for retrieving small perfectly conducting cracks

Park

2018

Journal of Computational Physics

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We consider direct sampling method for finding location of a set of linear perfectly conducting cracks with small length from collected far-field data corresponding to the single incident field. To show the feasibility of direct sampling method, we first prove that the indicator function of direct sampling method can be represented by the Bessel function of order zero and the length of cracks. Results of numerical simulations are shown to support the fact that the imaging performance is highly depending on the length of cracks. To explain the fact that imaging performance is highly depending on the rotation of crack, we perform further analysis of direct sampling method by establishing a representation by the Bessel functions of order zero and one.

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Direct Sampling Method for Diffusive Optical Tomography

Cited by 49 publications

References 34 publications

A Time-Dependent Direct Sampling Method for Recovering Moving Potentials in a Heat Equation

A Time-Dependent Direct Sampling Method for Recovering Moving Potentials in a Heat Equation

Real-time microwave imaging of unknown anomalies via scattering matrix

Direct sampling method for retrieving small perfectly conducting cracks

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