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Accelerated gradient based diffuse optical tomographic image reconstruction
Author(s) -
Biswas Samir Kumar,
Rajan K.,
Vasu R. M.
Publication year - 2011
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.3531572
Subject(s) - jacobian matrix and determinant , conjugate gradient method , inverse problem , iterative reconstruction , computation , imaging phantom , diffuse optical imaging , algorithm , nonlinear system , mathematics , tomographic reconstruction , nonlinear conjugate gradient method , inverse , gradient descent , computer science , mathematical analysis , computer vision , artificial intelligence , geometry , physics , artificial neural network , quantum mechanics , optics
Purpose: Fast reconstruction of interior optical parameter distribution using a new approach called Broyden‐based model iterative image reconstruction (BMOBIIR) and adjoint Broyden‐based MOBIIR (ABMOBIIR) of a tissue and a tissue mimicking phantom from boundary measurement data in diffuse optical tomography (DOT). Methods: DOT is a nonlinear and ill‐posed inverse problem. Newton‐based MOBIIR algorithm, which is generally used, requires repeated evaluation of the Jacobian which consumes bulk of the computation time for reconstruction. In this study, we propose a Broyden approach‐based accelerated scheme for Jacobian computation and it is combined with conjugate gradient scheme (CGS) for fast reconstruction. The method makes explicit use of secant and adjoint information that can be obtained from forward solution of the diffusion equation. This approach reduces the computational time many fold by approximating the system Jacobian successively through low‐rank updates. Results: Simulation studies have been carried out with single as well as multiple inhomogeneities. Algorithms are validated using an experimental study carried out on a pork tissue with fat acting as an inhomogeneity. The results obtained through the proposed BMOBIIR and ABMOBIIR approaches are compared with those of Newton‐based MOBIIR algorithm. The mean squared error and execution time are used as metrics for comparing the results of reconstruction. Conclusions: We have shown through experimental and simulation studies that Broyden‐based MOBIIR and adjoint Broyden‐based methods are capable of reconstructing single as well as multiple inhomogeneities in tissue and a tissue‐mimicking phantom. Broyden MOBIIR and adjoint Broyden MOBIIR methods are computationally simple and they result in much faster implementations because they avoid direct evaluation of Jacobian. The image reconstructions have been carried out with different initial values using Newton, Broyden, and adjoint Broyden approaches. These algorithms work well when the initial guess is close to the true solution. However, when initial guess is far away from true solution, Newton‐based MOBIIR gives better reconstructed images. The proposed methods are found to be stable with noisy measurement data.