B M Graham

University of Ottawa, Ottawa, Ontario, Canada

Are you B M Graham?

Claim your profile

Publications (6)2.99 Total impact

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We show that electrical impedance tomography (EIT) image reconstruction algorithms with regularization based on the total variation (TV) functional are suitable for in vivo imaging of physiological data. This reconstruction approach helps to preserve discontinuities in reconstructed profiles, such as step changes in electrical properties at interorgan boundaries, which are typically smoothed by traditional reconstruction algorithms. The use of the TV functional for regularization leads to the minimization of a nondifferentiable objective function in the inverse formulation. This cannot be efficiently solved with traditional optimization techniques such as the Newton method. We explore two implementations methods for regularization with the TV functional: the lagged diffusivity method and the primal dual-interior point method (PD-IPM). First we clarify the implementation details of these algorithms for EIT reconstruction. Next, we analyze the performance of these algorithms on noisy simulated data. Finally, we show reconstructed EIT images of in vivo data for ventilation and gastric emptying studies. In comparison to traditional quadratic regularization, TV regularization shows improved ability to reconstruct sharp contrasts.
    IEEE transactions on medical imaging. 01/2010; 29(1):44-54.
  • Source
    B M Graham, A Adler
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper investigates several configurations for placing electrodes on a 3D cylindrical medium to reconstruct 3D images using 16 electrode EIT equipment intended for use with a 2D adjacent drive protocol. Seven different electrode placement configurations are compared in terms of the following figures of merit: resolution, radial and vertical position error, image magnitude, immunity to noise, immunity to electrode placement errors, and qualitative evaluation of image artefacts. Results show that for ideal conditions, none of the configurations considered performed significantly better than the others. However, when noise and electrode placement errors were considered the planar electrode placement configuration (two rings of vertically aligned electrodes with electrodes placed sequentially in each ring) had the overall best performance. Based on these results, we recommend planar electrode placement configuration for 3D EIT lung imaging of the thorax.
    Physiological Measurement 08/2007; 28(7):S29-44. · 1.50 Impact Factor
  • Source
    Brad Graham, A. Adler
    [Show abstract] [Hide abstract]
    ABSTRACT: We test strategies for placing EIT electrodes on a 3D medium for the purpose of calculating 3D reconstructions using clinical equipment intended for use with a 2D adjacent drive protocol. The goal of this work was to compare seven such strategies in order to determine if any were clearly superior to the others for clinical applications. For the limited set of strategies investigated, none were significantly better than the others in terms of performance under ideal conditions. However, when noise and electrode placement errors were considered the Planar Electrode Placement Strategy emerged as a recommended strategy for clinical use.
    12/2006: pages 3866-3869;
  • B M Graham, A Adler
    [Show abstract] [Hide abstract]
    ABSTRACT: An algorithm for objectively calculating the hyperparameter for linearized one-step electrical impedance tomography (EIT) image reconstruction algorithms is proposed and compared to existing strategies. EIT is an ill-conditioned problem in which regularization is used to calculate a stable and accurate solution by incorporating some form of prior knowledge into the solution. A hyperparameter is used to control the trade-off between conformance to data and conformance to the prior. A remaining challenge is to develop and validate methods of objectively selecting the hyperparameter. In this paper, we evaluate and compare five different strategies for hyperparameter selection. We propose a calibration-based method of objective hyperparameter selection, called BestRes, that leads to repeatable and stable image reconstructions that are indistinguishable from heuristic selections. Results indicate: (1) heuristic selections of hyperparameter are inconsistent among experts, (2) generalized cross-validation approaches produce under-regularized solutions, (3) L-curve approaches are unreliable for EIT and (4) BestRes produces good solutions comparable to expert selections. Additionally, we show that it is possible to reliably detect an inverse crime based on analysis of these parameters.
    Physiological Measurement 06/2006; 27(5):S65-79. · 1.50 Impact Factor
  • Source
    B. M. GRAHAM, A. ADLER
    [Show abstract] [Hide abstract]
    ABSTRACT: Electrical impedance tomography (EIT) uses surface electrodes to make measurements from which an image of the conductivity distribution within some medium is calculated. Calculation of conductivity solutions re- quires inverting large linear systems that have to date restricted reconstructions to 2D or coarse 3D domains. This paper presents a Nodal Jacobian Inverse Solver that scales with the number of nodes in a finite element mesh rather than with the number of elements. For the example used in this paper the size of the linear system is reduced by a factor of 26. We validate the algorithm by comparing its performance to traditional 2D Elemental Jacobian algorithms. We then analyze its performance with a 21504 element 3D mesh that is too large to be solved with linear algebra systems based on 32 bit pointers (such as is available in current versions of Matlab). Finally, we demonstrate the applicability of the algorithm for clinical use by reconstructing experimentally measured human lung data. Electrical Impedance Tomography (EIT) uses body surface electrodes to make measurements from which an image of the conductivity distribution within some medium is calculated. Calculation of conductivity solutions using one of the New- ton type methods requires inverting large linear systems derived from finite element models of the medium under analysis. The Hessian matrix in these linear systems scale with the square of number of elements in the model and the square of the number of measurements used in the reconstruction. Almost all EIT algorithms use a piecewise constant conductivity model, in which the conductivity is consid- ered to be constant over an element. The large number of elements required and large number of measurements available for 3D reconstructions have to date re- stricted 3D reconstructions to coarse, low resolution models. Complex, accurate geometries, a priori structures, the increased number of measurements possible with newer machines and the desire for improved resolution in the third dimension leads to a requirement to solve large 3D models. Such reconstructions are beyond the capability of contemporary computers such as the AMD Athlon 64 3000+, 2GB RAM computers used in our lab. Thus the development of algorithms that can ef- ficiently calculate full 3D solutions over dense finite element models with many measurements is required. In this paper we present and evaluate a Nodal Jacobian Inverse Solver algorithm that reduces the execution time and memory required to calculate reconstructions. In addition to gains in reconstruction efficiency, the extraction and display of data
    International Journal of Information & Systems Sciences. 01/2006; 2(4).
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper presents an evaluation of the use of Primal Dual Methods for efficiently regularizing the electric impedance tomography (EIT) problem with the Total Variation (TV) functional. The Total Variation functional is assuming an important role in the regularization of inverse problems thanks to its ability to preserve dis- continuities in reconstructed profiles. This property is desirable in many fields of application of EIT imaging, such as the medical and the industrial, where inter-organ boundaries, in the first case, and inter-phase boundaries, in the latter case, present step changes in electrical properties which are difficult to be reconstructed with traditional regularization methods, as they tend to smooth the reconstructed image. Though desirable, the TV functional leads to the formulation of the inverse problem as a minimization of a non-differentiable function whichcannot be efficiently solved with traditional optimization techniques such as the Newton Method. In this paper we demonstrate the use of Primal Dual - Interior Point Methods (PD-IPM) as a framework for TV regularized inversion.