Frequency Domain Optical Tomography Based on the Equation of Radiative Transfer

Ren, Kui; Bal, Guillaume; Hielscher, Andreas H.

doi:10.1137/040619193

Cited by 139 publications

(118 citation statements)

References 59 publications

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“…The regularization term R(σ) is selected as the Tikhonov regularization functional, the L 2 norm of ∇σ. We solve the above least-square problem with a quasi-Newton type of iterative scheme implemented in [20].…”

Section: Numerical Experimentsmentioning

confidence: 99%

Quantitative thermo-acoustics and related problems

et al. 2011

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Abstract. Thermo-acoustic tomography is a hybrid medical imaging modality that aims to combine the good optical contrast observed in tissues with the good resolution properties of ultrasounds. Thermo-acoustic imaging may be decomposed into two steps. The first step aims at reconstructing an amount of electromagnetic radiation absorbed by tissues from boundary measurements of ultrasounds generated by the heating caused by these radiations. We assume this first step done. Quantitative thermo-acoustics then consists of reconstructing the conductivity coefficient in the equation modeling radiation from the now known absorbed radiation. This second step is the problem of interested in this paper.Mathematically, quantitative thermo-acoustics consists of reconstructing the conductivity in Maxwell's equations from available internal data that are linear in the conductivity and quadratic in the electric field. We consider several inverse problems of this type with applications in thermo-acoustics as well as in acousto-optics. In this framework, we obtain uniqueness and stability results under a smallness constraint on the conductivity. This smallness constraint is removed in the specific of a scalar model for electromagnetic wave propagation for appropriate illuminations constructed by the method of complex geometric optics (CGO) solutions.

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Section: Numerical Experimentsmentioning

confidence: 99%

Quantitative thermo-acoustics and related problems

et al. 2011

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“…Details on how to obtain the derivative with respect to optical properties can be found in Ref. 8. The overall flowchart for an image reconstruction algorithm that makes use of the parametric-DCT method is presented in Fig.…”

Section: Ot With Parametric-dct Methodsmentioning

confidence: 99%

Parametric image reconstruction using the discrete cosine transform for optical tomography

Ren

Masciotti

et al. 2009

J. Biomed. Opt.

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Abstract.It is well known that the inverse problem in optical tomography is highly ill-posed. The image reconstruction process is often unstable and nonunique, because the number of the boundary measurements data is far fewer than the number of the unknown parameters to be reconstructed. To overcome this problem, one can either increase the number of measurement data ͑e.g., multispectral or multifrequency methods͒, or reduce the number of unknowns ͑e.g., using prior structural information from other imaging modalities͒. We introduce a novel approach for reducing the unknown parameters in the reconstruction process. The discrete cosine transform ͑DCT͒, which has long been used in image compression, is here employed to parameterize the reconstructed image. In general, only a few DCT coefficients are needed to describe the main features in an optical tomographic image. Thus, the number of unknowns in the image reconstruction process can be drastically reduced. We show numerical and experimental examples that illustrate the performance of the new algorithm as compared to a standard model-based iterative image reconstructions scheme. We especially focus on the influence of initial guesses and noise levels on the reconstruction results.

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“…The methods employed to solve this problem include the non-linear conjugate-gradient method [3], Gauss-Newton based methods [4][5][6][7], the L-BFGS method [8][9][10][11][12], shape-based reconstruction method [13,14] or, in a Bayesian framework, the approximation error method [15,16]. Regarding the first three listed methods, some problems remain to be overcome such as the stability with respect to the initial guesses and the blurring effect of the reconstructed images due to the need for relatively strong regularization tools [17,14].…”

Section: Introductionmentioning

confidence: 99%

A wavelet multi-scale method for the inverse problem of diffuse optical tomography

Dubot

Favennec

Rousseau

et al. 2015

Journal of Computational and Applied Mathematics

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a b s t r a c tThis paper deals with the estimation of optical property distributions of participating media from a set of light sources and sensors located on the boundaries of the medium. This is the so-called diffuse optical tomography problem. Such a non-linear ill-posed inverse problem is solved through the minimization of a cost function which depends on the discrepancy, in a least-square sense, between some measurements and associated predictions. In the present case, predictions are based on the diffuse approximation model in the frequency domain while the optimization problem is solved by the L-BFGS algorithm. To cope with the local convergence property of the optimizer and the presence of numerous local minima in the cost function, a wavelet multi-scale method associated with the L-BFGS method is developed, implemented, and validated. This method relies on a reformulation of the original inverse problem into a sequence of sub-inverse problems of different scales using wavelet transform, from the largest scale to the smallest one. Numerical results show that the proposed method brings more stability with respect to the ordinary L-BFGS method and enhances the reconstructed images for most of initial guesses of optical properties.

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Frequency Domain Optical Tomography Based on the Equation of Radiative Transfer

Cited by 139 publications

References 59 publications

Quantitative thermo-acoustics and related problems

Quantitative thermo-acoustics and related problems

Parametric image reconstruction using the discrete cosine transform for optical tomography

A wavelet multi-scale method for the inverse problem of diffuse optical tomography

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