Article

Implementation of a computationally efficient least-squares algorithm for highly under-determined three-dimensional diffuse optical tomography problems

Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755, USA.
Medical Physics (Impact Factor: 3.01). 06/2008; 35(5):1682-97. DOI: 10.1118/1.2889778
Source: PubMed

ABSTRACT Three-dimensional (3D) diffuse optical tomography is known to be a nonlinear, ill-posed and sometimes under-determined problem, where regularization is added to the minimization to allow convergence to a unique solution. In this work, a generalized least-squares (GLS) minimization method was implemented, which employs weight matrices for both data-model misfit and optical properties to include their variances and covariances, using a computationally efficient scheme. This allows inversion of a matrix that is of a dimension dictated by the number of measurements, instead of by the number of imaging parameters. This increases the computation speed up to four times per iteration in most of the under-determined 3D imaging problems. An analytic derivation, using the Sherman-Morrison-Woodbury identity, is shown for this efficient alternative form and it is proven to be equivalent, not only analytically, but also numerically. Equivalent alternative forms for other minimization methods, like Levenberg-Marquardt (LM) and Tikhonov, are also derived. Three-dimensional reconstruction results indicate that the poor recovery of quantitatively accurate values in 3D optical images can also be a characteristic of the reconstruction algorithm, along with the target size. Interestingly, usage of GLS reconstruction methods reduces error in the periphery of the image, as expected, and improves by 20% the ability to quantify local interior regions in terms of the recovered optical contrast, as compared to LM methods. Characterization of detector photo-multiplier tubes noise has enabled the use of the GLS method for reconstructing experimental data and showed a promise for better quantification of target in 3D optical imaging. Use of these new alternative forms becomes effective when the ratio of the number of imaging property parameters exceeds the number of measurements by a factor greater than 2.

Download full-text

Full-text

Available from: Daniel R. Lynch, Mar 17, 2015
0 Followers
 · 
71 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The diffusion equation based modeling of near infrared light propagation in tissue is achieved by using finite element mesh for imaging real-tissue types, such as breast and brain. The finite element mesh size (number of nodes) dictates the parameter space in the optical tomographic imaging. Most commonly used finite element meshing algorithms does not provide the flexibility of distinct nodal spacing in different regions of imaging domain to take the sensitivity of the problem into con-sideration. This work aims to present a computationally efficient mesh simplification method that can be used as a preprocessing step to iterative image reconstruction, where the finite element mesh is simplified by using an edge collapsing algorithm to reduce the parameter space at regions where the sensitivity of the problem is relatively low. It is shown, using simulations and experimental phantom data for simple meshes/domains, that a significant reduction in parameter space could be achieved without compromising on the reconstructed image quality. The maximum errors observed by using the simplified meshes were less than 0.27% in the forward problem and 5% for inverse problem.
    IEEE Journal of Selected Topics in Quantum Electronics 07/2012; DOI:10.1109/JSTQE.2012.2187276 · 3.47 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Image-guided near infrared spectroscopy (IG-NIRS) can provide high-resolution vascular, metabolic and molecular characterization of localized tissue volumes in-vivo. The approach for IG-NIRS uses hybrid systems where the spatial anatomical structure of tissue obtained from standard imaging modalities (such as MRI) is combined with tissue information from diffuse optical imaging spectroscopy. There is need to optimize these hybrid systems for large-scale clinical trials anticipated in the near future in order to evaluate the feasibility of this technology across a larger population. However, existing computational methods such as the finite element method mesh arbitrary image volumes, which inhibit automation, especially with large numbers of datasets. Circumventing this issue, a boundary element method (BEM) for IG-NIRS systems in 3-D is presented here using only surface rendering and discretization. The process of surface creation and meshing is faster, more reliable, and is easily generated automatically as compared to full volume meshing. The proposed method has been implemented here for multi-spectral non-invasive characterization of tissue. In phantom experiments, 3-D spectral BEM-based spectroscopy recovered the oxygen dissociation curve with mean error of 6.6% and tracked variation in total hemoglobin linearly.
    Proceedings - Society of Photo-Optical Instrumentation Engineers 02/2009; 7171:717103. DOI:10.1117/12.808938
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Diffuse Optical Tomography (DOT) has been growing significantly in the past two decades as a promising tool for in-vivo and non-invasive imaging of tissues using near-infrared light. It can improve our ability to probe complex biologic interactions dynamically and to study disease and treatment responses over time in near real time. Recent advances on the transfer of techniques from laboratory to clinics have led to the development of various diagnostic applications such as imaging of the female breast and infant brain. The potential value of the promising tool, however, can be limited by the reconstruction time for tomographically imaging tissue optical properties. The current solution procedure in DOT consumes a considerable amount of time due to discretization of the problem domain and nonlinear nature of tissue optical properties. It is becoming ever more important to develop faster imaging tools as measurement data sets increase in size as a result of the application of newer generation instruments. Here we provide a fast solution strategy that significantly reduces imaging effort for DOT. The fast imaging strategy adopts advanced model-order reduction (MOR) techniques for reducing system complexity, while preserving (to the greatest possible extent) system input-output behavior for the forward problem. Our results demonstrate that the MOR-based imaging method can be an order of magnitude faster than the conventional approach while maintaining a relatively small error tolerance. The goal is to develop inexpensive, noninvasive imaging system that can run at patient's bedside in real time and produce data continuously over a long period of time.
    Optics Express 04/2009; 17(7):5285-97. DOI:10.1364/OE.17.005285 · 3.53 Impact Factor