Algebraic reconstruction and postprocessing in one-step diffuse optical tomography

Konovalov, A. B.; Vlasov, Vitaly V.; Mogilenskikh, Dmitry V.; Kravtsenyuk, Olga V.; Lyubimov, V. V.

doi:10.1070/qe2008v038n06abeh013834

Cited by 12 publications

(9 citation statements)

References 6 publications

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“…An algorithm that finds the maximum entropy solution of a consistent system of equations with nonnegativity constraints is the multiplicative algebraic reconstruction technique (MART), as was proved in Lent (1977). MART is actively used in various applications (see, e.g., Konovalov et al, 2008; Worth and Nickels, 2008). For images q that satisfy for , with at least one value strictly greater than 0, the negative‐entropy of q is where Q is a constant provided to us by estimating the sum of the q g , h from the measured data (see the end of Section 6.4 of Herman, 1980) for a discussion as to why we may assume in image reconstruction from projections that this estimate is extremely accurate).…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Perturbation‐resilient block‐iterative projection methods with application to image reconstruction from projections

Davidi¹,

Herman²,

Censor

2009

Int Trans Operational Res

109

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A block-iterative projection algorithm for solving the consistent convex feasibility problem in a finite-dimensional Euclidean space that is resilient to bounded and summable perturbations (in the sense that convergence to a feasible point is retained even if such perturbations are introduced in each iterative step of the algorithm) is proposed. This resilience can be used to steer the iterative process towards a feasible point that is superior in the sense of some functional on the points in the Euclidean space having a small value. The potential usefulness of this is illustrated in image reconstruction from projections, using both total variation and negative entropy as the functional.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Perturbation‐resilient block‐iterative projection methods with application to image reconstruction from projections

Davidi¹,

Herman²,

Censor

2009

Int Trans Operational Res

109

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“…In our further consideration we will follow in part an approach presented many years ago by Dr. Vladimir Lyubimov 63 . Lyubimov dealt with the photon average trajectory method ‐ an approximate method of DOT and FMT, which solves the inverse problem in real time 63‐66 . It reduces the problem to the inversion of the integral equation with integration over the photon average trajectory.…”

Section: Mathematical Model Of the Ep‐fmt Forward Problemmentioning

confidence: 99%

“…We studied feasibility of their reconstruction for sizes 0.5, 0.2, and 0.1 mm. Distances between inclusions were taken to be equal to their diameter in order to create the periodical spatial structures and be able to evaluate the modulation transfer coefficient and therefore the spatial resolution 52,64‐66 . Probing depths were 3, 6, and 9 mm.…”

Section: Numerical Experiments On Fluorescent Image Reconstructionmentioning

confidence: 99%

Early‐photon reflectance fluorescence molecular tomography for small animal imaging: Mathematical model and numerical experiment

Konovalov

Vlasov

Uglov

2020

Numer Methods Biomed Eng

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The paper presents an original approach to time‐domain reflectance fluorescence molecular tomography (FMT) of small animals. It is based on the use of early arriving photons and state‐of‐the‐art compressed‐sensing‐like reconstruction algorithms and aims to improve the spatial resolution of fluorescent images. We deduce the fundamental equation that models the imaging operator and derive analytical representations for the sensitivity functions which are responsible for the reconstruction of the fluorophore absorption coefficient. The idea of fluorescence lifetime tomography with our approach is also discussed. We conduct a numerical experiment on 3D reconstruction of box phantoms with spherical fluorescent inclusions of small diameters. For modeling measurement data and constructing the sensitivity matrix we assume a virtual fluorescence tomograph with a scanning fiber probe that illuminates and collects light in reflectance geometry. It provides for large source‐receiver separations which correspond to the macroscopic regime. Two compressed‐sensing‐like reconstruction algorithms are used to solve the inverse problem. These are the algebraic reconstruction technique with total variation regularization and our modification of the fast iterative shrinkage‐thresholding algorithm. Results of our numerical experiment show that our approach is capable of achieving as good spatial resolution as 0.2 mm and even better at depths to 9 mm inclusive.

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“…Davis et al compared the Tikhonov approach with a modified Levenberg-Marquardt formulation [60]. Schweiger et al attempted Gauss-Newton method [61], and Konovalov et al used algebraic reconstruction with post-processing [62]. Generally, these approaches can be categorized into linear reconstruction and non-linear reconstruction [63].…”

Section: Introductionmentioning

confidence: 99%

In Vivo Diffuse Optical Tomography and Fluorescence Molecular Tomography

Zhang

Bai

2010

Journal of Healthcare Engineering

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Diffuse optical tomography (DOT) and fluorescence molecular tomography (FMT) are two attractive imaging techniques for in vivo physiological and psychological research. They have distinct advantages such as non-invasiveness, non-ionizing radiation, high sensitivity and longitudinal monitoring. This paper reviews the key components of DOT and FMT. Light propagation model, mathematical reconstruction algorithm, imaging instrumentation and medical applications are included. Future challenges and perspective on optical tomography are discussed.

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Algebraic reconstruction and postprocessing in one-step diffuse optical tomography

Cited by 12 publications

References 6 publications

Perturbation‐resilient block‐iterative projection methods with application to image reconstruction from projections

Perturbation‐resilient block‐iterative projection methods with application to image reconstruction from projections

Early‐photon reflectance fluorescence molecular tomography for small animal imaging: Mathematical model and numerical experiment

In Vivo Diffuse Optical Tomography and Fluorescence Molecular Tomography

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