Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography

Biswas, Samir Kumar; Rajan, K.; Vasu, Ram Mohan; Roy, Debasish

doi:10.1364/josaa.28.001784

Cited by 3 publications

(4 citation statements)

References 30 publications

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“…We use 12 source locations around the circular cylindrical phantom and for each source location, 7 detectors opposite to source are used for gathering transmitted photon from sample boundary. 5,16 Only transmitted data is captured by moving detector placed diametrically opposite side of source. For each source location we have 13 detector and for 24 source location around the phantom we take 12x7=84 data as computed experimental measurements.…”

Section: Resultsmentioning

confidence: 99%

“…The data gathering and geometrical configurations are discussed in. 5,16 The vector update Equantion 1 is solved with and without regularization and Equation 8 is solved by CGS method for recovering the optical properties distribution. The reconstructed results using Equation 1 with and without regularization are shown in Fig.1(a) and Fig.1(c) respectively.…”

Section: Resultsmentioning

confidence: 99%

“…The inverse problem or the image reconstruction problem seeks to find the solution (x) such that the difference between the model predicted F (x) and the experimental measurement on the tissue boundary (M expt ) is minimum. 1,16 To minimize the mismatch between the theoretically predicted data and experimental measurements, the cost functional is minimized. 2, 15 DOT based imaging technique where optical parameter recovery is used for reconstruction of the internal parameter map has been studied well.…”

Section: Introductionmentioning

confidence: 99%

“…10, 12 Some potential reconstruction algorithms to invert data (J T J) with and without regularization from single laser source can be found in Ref. 5,16 as well as dual-source systems in Ref. 7 Pogue et al 11 have modeled regularization parameter in terms of exponential function of the amplitude of the image.…”

Section: Introductionmentioning

confidence: 99%

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Linearization and reconstruction of nonlinear diffuse optical tomographic image

2012

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Diffuse optical tomography (DOT) is one of the ways to probe highly scattering media such as tissue using low-energy near infra-red light (NIR) to reconstruct a map of the optical property distribution. The interaction of the photons in biological tissue is a non-linear process and the phton transport through the tissue is modelled using diffusion theory. The inversion problem is often solved through iterative methods based on nonlinear optimization for the minimization of a data-model misfit function. The solution of the non-linear problem can be improved by modeling and optimizing the cost functional. The cost functional is f (x) = x T Ax − b T x + c and after minimization, the cost functional reduces to Ax = b. The spatial distribution of optical parameter can be obtained by solving the above equation iteratively for x. As the problem is non-linear, ill-posed and illconditioned, there will be an error or correction term for x at each iteration. A linearization strategy is proposed for the solution of the nonlinear ill-posed inverse problem by linear combination of system matrix and error in solution. By propagating the error (e) information (obtained from previous iteration) to the minimization function f(x), we can rewrite the minimization function as f (The self guided spatial weighted prior (e T Ae) error (e, error in estimating x) information along the principal nodes facilitates a well resolved dominant solution over the region of interest. The local minimization reduces the spreading of inclusion and removes the side lobes, thereby improving the contrast, localization and resolution of reconstructed image which has not been possible with conventional linear and regularization algorithm.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Linearization and reconstruction of nonlinear diffuse optical tomographic image

2012

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Data Structure Assisted Accelerated Reconstruction Strategy for Handheld Photoacoustic Imaging

Biswas¹,

Burman²

2020

LED-Based Photoacoustic Imaging

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Practical fully three-dimensional reconstruction algorithms for diffuse optical tomography

et al. 2012

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We have developed an efficient fully three-dimensional (3D) reconstruction algorithm for diffuse optical tomography (DOT). The 3D DOT, a severely ill-posed problem, is tackled through a pseudodynamic (PD) approach wherein an ordinary differential equation representing the evolution of the solution on pseudotime is integrated that bypasses an explicit inversion of the associated, ill-conditioned system matrix. One of the most computationally expensive parts of the iterative DOT algorithm, the reevaluation of the Jacobian in each of the iterations, is avoided by using the adjoint-Broyden update formula to provide low rank updates to the Jacobian. In addition, wherever feasible, we have also made the algorithm efficient by integrating along the quadratic path provided by the perturbation equation containing the Hessian. These algorithms are then proven by reconstruction, using simulated and experimental data and verifying the PD results with those from the popular Gauss-Newton scheme. The major findings of this work are as follows: (i) the PD reconstructions are comparatively artifact free, providing superior absorption coefficient maps in terms of quantitative accuracy and contrast recovery; (ii) the scaling of computation time with the dimension of the measurement set is much less steep with the Jacobian update formula in place than without it; and (iii) an increase in the data dimension, even though it renders the reconstruction problem less ill conditioned and thus provides relatively artifact-free reconstructions, does not necessarily provide better contrast property recovery. For the latter, one should also take care to uniformly distribute the measurement points, avoiding regions close to the source so that the relative strength of the derivatives for measurements away from the source does not become insignificant.

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Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography

Cited by 3 publications

References 30 publications

Linearization and reconstruction of nonlinear diffuse optical tomographic image

Linearization and reconstruction of nonlinear diffuse optical tomographic image

Data Structure Assisted Accelerated Reconstruction Strategy for Handheld Photoacoustic Imaging

Practical fully three-dimensional reconstruction algorithms for diffuse optical tomography

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